2tan (problem 3.3.2)

Time bar (total: 17.7s)

analyze58.0ms (0.3%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%74.7%0%0%0%3
0%0%25.3%74.7%0%0%0%4
0%0%19%81%0%0%0%5
0%0%15.8%84.2%0%0%0%6
0%0%11.1%88.9%0%0%0%7
0%0%8.7%91.3%0%0%0%8
0%0%5.9%94.1%0%0%0%9
0%0%4.5%95.5%0%0%0%10
0%0%3.1%96.9%0%0%0%11
0%0%2.7%97.3%0%0%0%12
Compiler

Compiled 28 to 18 computations (35.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-tan: 8.0ms (25.3% of total)
...c/correct-round.rkt:119:19: 7.0ms (22.1% of total)
ival-mult: 3.0ms (9.5% of total)
ival-fabs: 3.0ms (9.5% of total)
ival-<=: 3.0ms (9.5% of total)
ival-<: 3.0ms (9.5% of total)
ival-add: 2.0ms (6.3% of total)
ival-sub: 2.0ms (6.3% of total)
ival-and: 1.0ms (3.2% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample7.8s (44%)

Results
4.3s26063×0precondition
1.2s4539×1valid
520.0ms3717×0valid
Precisions
Click to see histograms. Total time spent on operations: 4.6s
ival-mult: 833.0ms (18.3% of total)
...c/correct-round.rkt:119:19: 793.0ms (17.4% of total)
ival-tan: 661.0ms (14.5% of total)
ival-sub: 585.0ms (12.8% of total)
ival-<: 390.0ms (8.6% of total)
ival-<=: 370.0ms (8.1% of total)
ival-add: 329.0ms (7.2% of total)
ival-fabs: 314.0ms (6.9% of total)
ival-and: 135.0ms (3% of total)
backward-pass: 99.0ms (2.2% of total)
const: 49.0ms (1.1% of total)
Bogosity

preprocess65.0ms (0.4%)

Algorithm
egg-herbie
Rules
376×fnmadd-define
344×fnmsub-define
344×fmsub-define
320×sum3-define
308×fmm-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02146
14342
29442
319842
450742
591742
6128542
7154842
8168442
9171142
067
197
2147
3217
4317
5637
61227
72107
82957
94017
104797
114857
04857
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- (tan (+ x eps)) (tan x))
Outputs
(- (tan (+ x eps)) (tan x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Call 2
Inputs
(- (tan (+ x eps)) (tan x))
(- (tan (+ (neg x) eps)) (tan (neg x)))
(- (tan (+ x (neg eps))) (tan x))
(neg (- (tan (+ (neg x) eps)) (tan (neg x))))
(neg (- (tan (+ x (neg eps))) (tan x)))
(- (tan (+ eps x)) (tan eps))
Outputs
(- (tan (+ x eps)) (tan x))
(- (tan (+ (neg x) eps)) (tan (neg x)))
(+ (tan x) (tan (- eps x)))
(- (tan (+ x (neg eps))) (tan x))
(- (tan (- x eps)) (tan x))
(neg (- (tan (+ (neg x) eps)) (tan (neg x))))
(- (tan (- x eps)) (tan x))
(neg (- (tan (+ x (neg eps))) (tan x)))
(+ (tan x) (tan (- eps x)))
(- (tan (+ eps x)) (tan eps))
(- (tan (+ x eps)) (tan eps))

explain100.0ms (0.6%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2283(-4.28718533615325e-244 2.596565261760719e-246)4(-3.078977089395929e-248 4.894015027365364e-250)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
40-0-(tan.f64 (+.f64 x eps))
00-0-x
00-0-(+.f64 x eps)
00-0-(tan.f64 x)
00-0-eps
Results
47.0ms276×1valid
20.0ms234×0valid
1.0ms3valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 35.0ms
ival-tan: 15.0ms (43.5% of total)
backward-pass: 10.0ms (29% of total)
ival-add: 5.0ms (14.5% of total)
ival-sub: 4.0ms (11.6% of total)
const: 1.0ms (2.9% of total)

eval0.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify17.0ms (0.1%)

Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(tan.f64 x)
cost-diff0
(+.f64 x eps)
cost-diff0
(tan.f64 (+.f64 x eps))
cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Rules
124×fnmadd-define
122×sum3-define
80×fma-lowering-fma.f32
80×fnmsub-define
80×fmsub-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
1918
21418
32118
43118
56318
612218
721018
829518
940118
1047918
1148518
048518
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(- (tan (+ x eps)) (tan x))
(tan (+ x eps))
(+ x eps)
x
eps
(tan x)
Outputs
(- (tan (+ x eps)) (tan x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan (+ x eps))
(tan.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(tan x)
(tan.f64 x)

localize41.0ms (0.2%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x eps)
accuracy100.0%
(tan.f64 x)
accuracy99.7%
(tan.f64 (+.f64 x eps))
accuracy62.2%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
22.0ms138×1valid
11.0ms117×0valid
1.0ms3valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-tan: 7.0ms (49.7% of total)
ival-add: 3.0ms (21.3% of total)
backward-pass: 2.0ms (14.2% of total)
ival-sub: 2.0ms (14.2% of total)
const: 0.0ms (0% of total)

series14.0ms (0.1%)

Counts
4 → 84
Calls
Call 1
Inputs
#<alt (- (tan (+ x eps)) (tan x))>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (tan x)>
Outputs
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin x) (cos x))>
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
Calls

21 calls:

TimeVariablePointExpression
4.0ms
x
@0
(- (tan (+ x eps)) (tan x))
2.0ms
eps
@0
(- (tan (+ x eps)) (tan x))
2.0ms
eps
@inf
(- (tan (+ x eps)) (tan x))
1.0ms
x
@inf
(- (tan (+ x eps)) (tan x))
1.0ms
x
@-inf
(- (tan (+ x eps)) (tan x))

rewrite321.0ms (1.8%)

Algorithm
batch-egg-rewrite
Rules
3856×*-lowering-*.f32
3856×*-lowering-*.f64
3276×/-lowering-/.f32
3276×/-lowering-/.f64
1940×fma-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
14616
241916
3655516
0850716
Stop Event
iter limit
node limit
Counts
4 → 239
Calls
Call 1
Inputs
(- (tan (+ x eps)) (tan x))
(tan (+ x eps))
(+ x eps)
(tan x)
Outputs
(+.f64 (tan.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x) (tan.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (/.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))))
(-.f64 (+.f64 (tan.f64 (+.f64 x eps)) #s(literal 0 binary64)) (tan.f64 x))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))))
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
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(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))))
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x x) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (*.f64 x x) (*.f64 eps eps)))
(*.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x x) (*.f64 eps eps))) (+.f64 x eps))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x)))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)))))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x eps))))
(tan.f64 x)
(neg.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

simplify324.0ms (1.8%)

Algorithm
egg-herbie
Rules
3412×*-lowering-*.f32
3412×*-lowering-*.f64
2990×fma-lowering-fma.f32
2990×fma-lowering-fma.f64
2652×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01571381
14941286
218911261
377211261
085671261
Stop Event
iter limit
node limit
Counts
84 → 84
Calls
Call 1
Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 x (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 x (-.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (*.f64 x (-.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal 1/6 binary64) (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64)))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))))))))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

eval52.0ms (0.3%)

Compiler

Compiled 8812 to 983 computations (88.8% saved)

prune61.0ms (0.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New30716323
Fresh000
Picked011
Done000
Total30717324
Accuracy
100.0%
Counts
324 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
62.3%
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
62.3%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
61.9%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
60.9%
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
97.2%
(/.f64 (sin.f64 eps) (cos.f64 eps))
62.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
61.9%
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
61.4%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
60.8%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64)))))))))
60.7%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
60.5%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
60.4%
(-.f64 (tan.f64 (+.f64 x eps)) x)
100.0%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
99.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
100.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Compiler

Compiled 1051 to 456 computations (56.6% saved)

simplify288.0ms (1.6%)

Algorithm
egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(tan.f64 x)
cost-diff0
(+.f64 (tan.f64 x) (tan.f64 eps))
cost-diff0
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))))
cost-diff6400
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
cost-diff0
(+.f64 x eps)
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff6528
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
cost-diff0
(cos.f64 eps)
cost-diff0
(sin.f64 eps)
cost-diff0
(/.f64 (sin.f64 eps) (cos.f64 eps))
cost-diff0
(+.f64 x eps)
cost-diff0
(tan.f64 (+.f64 x eps))
cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) x)
cost-diff143744
(*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))))))))
cost-diff156416
(+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff163008
(+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff163008
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Rules
3172×--lowering--.f32
3172×--lowering--.f64
2988×*-lowering-*.f32
2988×*-lowering-*.f64
2300×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0611754
11821468
26961162
333251049
084581049
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
eps
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
1
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (sin x) (cos x))
(sin x)
x
(cos x)
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
2
(pow (cos x) 2)
(* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))
(- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
-1/6
(+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
-1/2
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(* -1/2 (pow (sin x) 2))
(- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))
(* 1/6 (pow (sin x) 2))
1/6
(* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))
(+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))
(/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x))
(* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)
-1/3
(- (tan (+ x eps)) x)
(tan (+ x eps))
(+ x eps)
x
eps
(/ (sin eps) (cos eps))
(sin eps)
eps
(cos eps)
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))
(/ 1 (cos (+ x eps)))
1
(cos (+ x eps))
(+ x eps)
x
eps
(sin (+ x eps))
(- 0 (tan x))
0
(tan x)
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x)))
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))
(+ (tan x) (tan eps))
(tan x)
x
(tan eps)
eps
(- 1 (pow (* (tan x) (tan eps)) 2))
1
(pow (* (tan x) (tan eps)) 2)
(* (tan x) (tan eps))
2
(+ 1 (* (tan x) (tan eps)))
(- 0 (tan x))
0
Outputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))) (*.f64 (+.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
eps
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (*.f64 eps (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))) (*.f64 (+.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 (*.f64 eps (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))) (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))))
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))
(+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))))))
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(sin x)
(sin.f64 x)
x
(cos x)
(cos.f64 x)
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))
(- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))
(-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))))
(- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))
-1/6
#s(literal -1/6 binary64)
(+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))))
-1/2
#s(literal -1/2 binary64)
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/2 (pow (sin x) 2))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -5/6 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))
(/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))
(* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))
(*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))
(+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))
(+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))
(/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))))
(* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))))
(+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)
(*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- (tan (+ x eps)) x)
(-.f64 (tan.f64 (+.f64 eps x)) x)
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin eps)
(sin.f64 eps)
eps
(cos eps)
(cos.f64 eps)
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/ 1 (cos (+ x eps)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
1
#s(literal 1 binary64)
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(- 0 (tan x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
0
#s(literal 0 binary64)
(tan x)
(tan.f64 x)
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x)))
(-.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (tan.f64 x))
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))))
(+ (tan x) (tan eps))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan x)
(tan.f64 x)
x
(tan eps)
(tan.f64 eps)
eps
(- 1 (pow (* (tan x) (tan eps)) 2))
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(pow (* (tan x) (tan eps)) 2)
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))
(* (tan x) (tan eps))
(*.f64 (tan.f64 x) (tan.f64 eps))
2
#s(literal 2 binary64)
(+ 1 (* (tan x) (tan eps)))
(+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(- 0 (tan x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
0
#s(literal 0 binary64)

localize773.0ms (4.4%)

Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 (tan.f64 x) (tan.f64 eps))
accuracy100.0%
(+.f64 (tan.f64 x) (tan.f64 eps))
accuracy99.9%
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))
accuracy92.4%
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
accuracy100.0%
(tan.f64 x)
accuracy99.9%
(cos.f64 (+.f64 x eps))
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy92.4%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
accuracy100.0%
(sin.f64 eps)
accuracy100.0%
(cos.f64 eps)
accuracy100.0%
(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy100.0%
(+.f64 x eps)
accuracy99.8%
(tan.f64 (+.f64 x eps))
accuracy92.8%
(-.f64 (tan.f64 (+.f64 x eps)) x)
accuracy99.7%
(*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
accuracy99.7%
(*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))
accuracy99.3%
(-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))
accuracy99.3%
(+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))
Results
440.0ms138×5exit
93.0ms107×0valid
19.0ms3valid
11.0ms1valid
Compiler

Compiled 1811 to 60 computations (96.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 337.0ms
backward-pass: 90.0ms (26.7% of total)
ival-mult: 60.0ms (17.8% of total)
compiled-spec: 39.0ms (11.6% of total)
ival-sin: 28.0ms (8.3% of total)
ival-add: 24.0ms (7.1% of total)
ival-div: 21.0ms (6.2% of total)
ival-tan: 18.0ms (5.3% of total)
...c/correct-round.rkt:119:19: 17.0ms (5% of total)
ival-pow: 16.0ms (4.7% of total)
ival-sub: 12.0ms (3.6% of total)
ival-cos: 9.0ms (2.7% of total)
const: 1.0ms (0.3% of total)

series112.0ms (0.6%)

Counts
24 → 480
Calls
Call 1
Inputs
#<alt (* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))>
#<alt (- (tan (+ x eps)) x)>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (/ (sin eps) (cos eps))>
#<alt (sin eps)>
#<alt (cos eps)>
#<alt (+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))>
#<alt (/ 1 (cos (+ x eps)))>
#<alt (cos (+ x eps))>
#<alt (+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x)))>
#<alt (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))>
#<alt (+ (tan x) (tan eps))>
#<alt (tan x)>
#<alt (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))>
#<alt (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))>
#<alt (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)>
#<alt (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))))>
#<alt (sin (+ x eps))>
#<alt (pow (* (tan x) (tan eps)) 2)>
#<alt (* (tan x) (tan eps))>
Outputs
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))) eps))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
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#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))>
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#<alt (sin eps)>
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#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* x (sin eps)) (cos eps))>
#<alt (* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))>
#<alt (* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))>
#<alt (* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* eps (sin x)) (cos x))>
#<alt (* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))>
#<alt (* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))>
#<alt (* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
Calls

120 calls:

TimeVariablePointExpression
30.0ms
x
@-inf
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x)))
13.0ms
x
@-inf
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
8.0ms
x
@inf
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
7.0ms
eps
@0
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
3.0ms
x
@inf
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x)))

rewrite339.0ms (1.9%)

Algorithm
batch-egg-rewrite
Rules
3442×*-lowering-*.f32
3442×*-lowering-*.f64
2488×/-lowering-/.f32
2488×/-lowering-/.f64
1938×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
061850
1477452
25906442
08182442
Stop Event
iter limit
node limit
Counts
24 → 444
Calls
Call 1
Inputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))
(- (tan (+ x eps)) x)
(tan (+ x eps))
(+ x eps)
(/ (sin eps) (cos eps))
(sin eps)
(cos eps)
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))
(/ 1 (cos (+ x eps)))
(cos (+ x eps))
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x)))
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))
(+ (tan x) (tan eps))
(tan x)
(+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)
(* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(sin (+ x eps))
(pow (* (tan x) (tan eps)) 2)
(* (tan x) (tan eps))
Outputs
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) eps) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))
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(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 eps))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (tan.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 eps)))
(/.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (cos.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 eps))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 eps))))
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 eps)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps))))
(/.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (cos.f64 eps))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (cos.f64 eps)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps))))
(/.f64 (*.f64 (sin.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (cos.f64 eps) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (sin.f64 x)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
(/.f64 (*.f64 (tan.f64 eps) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))
(/.f64 (*.f64 (tan.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (tan.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (sin.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 eps)))
(*.f64 (sin.f64 eps) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (tan.f64 x)))
(*.f64 (tan.f64 x) (tan.f64 eps))
(*.f64 (tan.f64 eps) (tan.f64 x))
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (tan.f64 eps) #s(literal 1 binary64)))
(*.f64 (pow.f64 (tan.f64 eps) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))
(*.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))

simplify426.0ms (2.4%)

Algorithm
egg-herbie
Rules
5526×+-lowering-+.f64
5526×+-lowering-+.f32
4372×*-lowering-*.f32
4372×*-lowering-*.f64
1872×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
079515992
1280115392
0831415392
Stop Event
iter limit
node limit
Counts
480 → 480
Calls
Call 1
Inputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))) eps))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
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(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(/ (sin eps) (cos eps))
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-1/3
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1/3 x)
(* x (- (* -4/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))
(* -1/3 x)
(* x (- (* -23/18 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -601/360 (pow x 2)) 23/18)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -23183/15120 (pow x 2)) 601/360)) 23/18)) 1/3))
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* x (sin eps)) (cos eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
Outputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))))) (/.f64 (*.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(*.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/3 binary64))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps))))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
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(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
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(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
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(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(+.f64 (sin.f64 x) (*.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))
(/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 x x)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 x x)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 17/45 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 x x)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 x x)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 62/315 binary64)) (/.f64 (*.f64 #s(literal 17/45 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
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(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 62/315 binary64) (*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal 17/45 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* x (sin eps)) (cos eps))
(/.f64 (*.f64 x (sin.f64 eps)) (cos.f64 eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (sin.f64 eps) (*.f64 x x)) (cos.f64 eps)))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 2/15 binary64) (/.f64 (*.f64 (sin.f64 eps) (*.f64 x x)) (cos.f64 eps))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps))))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 17/315 binary64) (/.f64 (*.f64 (sin.f64 eps) (*.f64 x x)) (cos.f64 eps))) (/.f64 (*.f64 #s(literal 2/15 binary64) (sin.f64 eps)) (cos.f64 eps))))))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
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(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* eps (sin x)) (cos x))
(/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 17/315 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 #s(literal 2/15 binary64) (sin.f64 x)) (cos.f64 x))))))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))

eval192.0ms (1.1%)

Compiler

Compiled 65270 to 3890 computations (94% saved)

prune145.0ms (0.8%)

Pruning

25 alts after pruning (23 fresh and 2 done)

PrunedKeptTotal
New1190171207
Fresh5611
Picked415
Done011
Total1199251224
Accuracy
100.0%
Counts
1224 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
62.3%
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
62.3%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
60.5%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))))
61.5%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
60.9%
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
97.2%
(/.f64 eps (cos.f64 eps))
62.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
61.9%
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
61.4%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
100.0%
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) eps) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))
100.0%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
97.3%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
97.4%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
99.7%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
97.3%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
97.4%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
99.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)))))
98.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.2%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
97.4%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))))
97.2%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
97.2%
eps
Compiler

Compiled 1378 to 739 computations (46.4% saved)

simplify202.0ms (1.1%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff256
(+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))
cost-diff256
(+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff256
(+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff256
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff128
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))
cost-diff6528
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))))
cost-diff0
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
cost-diff384
(+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))
cost-diff384
(*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
cost-diff512
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
cost-diff32640
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))
cost-diff38976
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))
cost-diff38976
(*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))
cost-diff38976
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
Rules
3232×*-lowering-*.f32
3232×*-lowering-*.f64
2524×+-lowering-+.f64
2524×+-lowering-+.f32
1662×fma-lowering-fma.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0761168
12691059
211221008
34923998
08132998
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(pow (tan x) 2)
(tan x)
x
2
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+ (tan x) (pow (tan x) 3))
(pow (tan x) 3)
3
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(- 1/3 (* (pow (tan x) 2) -1/3))
1/3
(* (pow (tan x) 2) -1/3)
-1/3
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+ 1 (pow (tan x) 2))
1
(* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))
(+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3)
(- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
eps
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))
(* eps (+ 1 (* 1/3 (* eps eps))))
eps
(+ 1 (* 1/3 (* eps eps)))
1
(* 1/3 (* eps eps))
1/3
(* eps eps)
(* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))
x
(+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))
(* eps (* x (+ 1 (* (* eps eps) 4/3))))
(* x (+ 1 (* (* eps eps) 4/3)))
(+ 1 (* (* eps eps) 4/3))
(* (* eps eps) 4/3)
4/3
(* (* eps eps) (+ 1 (* (* eps eps) 2/3)))
(+ 1 (* (* eps eps) 2/3))
(* (* eps eps) 2/3)
2/3
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (* x (+ 1 (* 1/3 (* x x))))))
(/ 1 (cos (+ x eps)))
1
(cos (+ x eps))
(+ x eps)
x
eps
(sin (+ x eps))
(- 0 (* x (+ 1 (* 1/3 (* x x)))))
0
(* x (+ 1 (* 1/3 (* x x))))
(+ 1 (* 1/3 (* x x)))
(* 1/3 (* x x))
1/3
(* x x)
(* eps (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
eps
(+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
1
(+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))))
(* 1/3 (* eps eps))
1/3
(* eps eps)
(* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))
x
(+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))
(* eps (+ 1 (* (* eps eps) 2/3)))
(+ 1 (* (* eps eps) 2/3))
(* (* eps eps) 2/3)
2/3
(* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))
(+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))
(* (* eps eps) 4/3)
4/3
(* eps (* x (+ 4/3 (* (* eps eps) 17/9))))
(* x (+ 4/3 (* (* eps eps) 17/9)))
(+ 4/3 (* (* eps eps) 17/9))
(* (* eps eps) 17/9)
17/9
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(sin x)
2
(pow (cos x) 2)
(cos x)
Outputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))))))))))
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))))))))
(pow (tan x) 2)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan x)
(tan.f64 x)
x
2
#s(literal 2 binary64)
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))))))
(+ (tan x) (pow (tan x) 3))
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(pow (tan x) 3)
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))))
(- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))))
(+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(- 1/3 (* (pow (tan x) 2) -1/3))
(+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* (pow (tan x) 2) -1/3)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(+ 1 (pow (tan x) 2))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))
(*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3)
(+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
eps
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (*.f64 x (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 eps #s(literal 2/3 binary64)) (*.f64 x #s(literal 4/3 binary64)))))))))
(* eps (+ 1 (* 1/3 (* eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))
eps
(+ 1 (* 1/3 (* eps eps)))
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))
1
#s(literal 1 binary64)
(* 1/3 (* eps eps))
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* eps eps)
(*.f64 eps eps)
(* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))
(*.f64 eps (*.f64 x (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 eps #s(literal 2/3 binary64)) (*.f64 x #s(literal 4/3 binary64))))))))
x
(+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))
(*.f64 eps (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 eps #s(literal 2/3 binary64)) (*.f64 x #s(literal 4/3 binary64)))))))
(* eps (* x (+ 1 (* (* eps eps) 4/3))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps x))
(* x (+ 1 (* (* eps eps) 4/3)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(+ 1 (* (* eps eps) 4/3))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))
(* (* eps eps) 4/3)
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
4/3
#s(literal 4/3 binary64)
(* (* eps eps) (+ 1 (* (* eps eps) 2/3)))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))
(+ 1 (* (* eps eps) 2/3))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))
(* (* eps eps) 2/3)
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
2/3
#s(literal 2/3 binary64)
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (* x (+ 1 (* 1/3 (* x x))))))
(+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (*.f64 x (-.f64 (*.f64 x (*.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64))))
(/ 1 (cos (+ x eps)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
1
#s(literal 1 binary64)
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(- 0 (* x (+ 1 (* 1/3 (* x x)))))
(*.f64 x (-.f64 (*.f64 x (*.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64)))
0
#s(literal 0 binary64)
(* x (+ 1 (* 1/3 (* x x))))
(*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/3 binary64)))))
(+ 1 (* 1/3 (* x x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))
(* 1/3 (* x x))
(*.f64 x (*.f64 x #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* x x)
(*.f64 x x)
(* eps (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
eps
(+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(* 1/3 (* eps eps))
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* eps eps)
(*.f64 eps eps)
(* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))
(*.f64 x (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 x (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64))))))))
x
(+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 x (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))))))
(* eps (+ 1 (* (* eps eps) 2/3)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))
(+ 1 (* (* eps eps) 2/3))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))
(* (* eps eps) 2/3)
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
2/3
#s(literal 2/3 binary64)
(* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))
(*.f64 (*.f64 eps x) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))))
(+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))
(*.f64 eps (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))))
(* (* eps eps) 4/3)
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
4/3
#s(literal 4/3 binary64)
(* eps (* x (+ 4/3 (* (* eps eps) 17/9))))
(*.f64 (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) (*.f64 eps x))
(* x (+ 4/3 (* (* eps eps) 17/9)))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(+ 4/3 (* (* eps eps) 17/9))
(+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))
(* (* eps eps) 17/9)
(*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))
17/9
#s(literal 17/9 binary64)
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin x)
(sin.f64 x)
2
#s(literal 2 binary64)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos x)
(cos.f64 x)

localize782.0ms (4.4%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy99.9%
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
accuracy99.9%
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
accuracy99.9%
(+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy99.7%
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
accuracy99.9%
(cos.f64 (+.f64 x eps))
accuracy99.8%
(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy93.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))))
accuracy99.9%
(+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))
accuracy99.9%
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
accuracy99.9%
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
accuracy99.9%
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
accuracy99.9%
(*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))
accuracy99.8%
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
accuracy99.7%
(*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x))
accuracy99.7%
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
Results
481.0ms137×5exit
91.0ms112×0valid
11.0ms2valid
7.0ms1valid
Compiler

Compiled 1312 to 76 computations (94.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 328.0ms
backward-pass: 108.0ms (33% of total)
ival-mult: 72.0ms (22% of total)
ival-pow: 40.0ms (12.2% of total)
ival-add: 39.0ms (11.9% of total)
...c/correct-round.rkt:119:19: 29.0ms (8.9% of total)
ival-sub: 8.0ms (2.4% of total)
compiled-spec: 7.0ms (2.1% of total)
ival-cos: 7.0ms (2.1% of total)
ival-div: 6.0ms (1.8% of total)
ival-sin: 6.0ms (1.8% of total)
ival-tan: 4.0ms (1.2% of total)
const: 1.0ms (0.3% of total)

series88.0ms (0.5%)

Counts
26 → 516
Calls
Call 1
Inputs
#<alt (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)>
#<alt (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))>
#<alt (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))>
#<alt (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))>
#<alt (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))>
#<alt (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))>
#<alt (* eps (+ 1 (* 1/3 (* eps eps))))>
#<alt (+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (* x (+ 1 (* 1/3 (* x x))))))>
#<alt (- 0 (* x (+ 1 (* 1/3 (* x x)))))>
#<alt (/ 1 (cos (+ x eps)))>
#<alt (cos (+ x eps))>
#<alt (* eps (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))))>
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)>
#<alt (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))>
#<alt (* (pow (tan x) 2) -1/3)>
#<alt (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))>
#<alt (* 1/3 (* eps eps))>
#<alt (* (* eps eps) 2/3)>
#<alt (* (* eps eps) 4/3)>
#<alt (sin (+ x eps))>
#<alt (* 1/3 (* x x))>
#<alt (* x (+ 4/3 (* (* eps eps) 17/9)))>
Outputs
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))>
#<alt (+ eps (* 1/3 (pow eps 3)))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
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#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))>
#<alt (* 4/3 x)>
#<alt (+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))>
#<alt (+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))>
#<alt (+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))>
#<alt (* 17/9 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))>
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))>
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))>
#<alt (* 17/9 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))>
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))>
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))>
Calls

129 calls:

TimeVariablePointExpression
16.0ms
eps
@0
(+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))))
9.0ms
x
@inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
5.0ms
x
@-inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
4.0ms
eps
@inf
(sin (+ x eps))
3.0ms
eps
@0
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))

rewrite348.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
3804×*-lowering-*.f32
3804×*-lowering-*.f64
2166×+-lowering-+.f64
2166×+-lowering-+.f32
1968×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
076656
1613569
27098566
08233566
Stop Event
iter limit
node limit
Counts
26 → 396
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))
(* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))
(+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))
(* eps (+ 1 (* 1/3 (* eps eps))))
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (* x (+ 1 (* 1/3 (* x x))))))
(- 0 (* x (+ 1 (* 1/3 (* x x)))))
(/ 1 (cos (+ x eps)))
(cos (+ x eps))
(* eps (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))
(* (pow (tan x) 2) -1/3)
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(* 1/3 (* eps eps))
(* (* eps eps) 2/3)
(* (* eps eps) 4/3)
(sin (+ x eps))
(* 1/3 (* x x))
(* x (+ 4/3 (* (* eps eps) 17/9)))
Outputs
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) eps)
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps))
(+.f64 (+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))
(-.f64 (/.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) #s(literal 2 binary64)) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) eps)))
(fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps eps)
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(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
(*.f64 (sin.f64 (+.f64 eps x)) #s(literal 1 binary64))
(*.f64 x (*.f64 x #s(literal 1/3 binary64)))
(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))
(*.f64 (*.f64 x x) #s(literal 1/3 binary64))
(*.f64 (*.f64 x (*.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))
(*.f64 (*.f64 x #s(literal 1/3 binary64)) x)
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64))) x)
(+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(+.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) (*.f64 x #s(literal 4/3 binary64)))
(fma.f64 x #s(literal 4/3 binary64) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(fma.f64 #s(literal 4/3 binary64) x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 4/3 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 x #s(literal 4/3 binary64))) (-.f64 (*.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) (*.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))
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(/.f64 (*.f64 x (+.f64 #s(literal 64/27 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 289/81 binary64))))) (+.f64 #s(literal 16/9 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) #s(literal 4/3 binary64)))))
(/.f64 (*.f64 x (-.f64 #s(literal 16/9 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 289/81 binary64)))) (-.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 64/27 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 289/81 binary64)))) x) (+.f64 #s(literal 16/9 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) #s(literal 4/3 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 16/9 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 289/81 binary64))) x) (-.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(*.f64 (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) x)

simplify426.0ms (2.4%)

Algorithm
egg-herbie
Rules
5576×*-lowering-*.f32
5576×*-lowering-*.f64
5254×+-lowering-+.f64
5254×+-lowering-+.f32
1730×distribute-lft-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
093917262
1343016961
0874816961
Stop Event
iter limit
node limit
Counts
516 → 516
Calls
Call 1
Inputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
(* 1/3 (pow eps 3))
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (+ (* eps x) (pow x 2))))
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))))
(* 2/3 (* (pow eps 4) x))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))
(* 2/3 (* (pow eps 4) x))
(* (pow eps 4) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1/3) eps)) (* 2/3 x)))
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3) eps)) (* 2/3 x)))
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3) eps)) (* 2/3 x)))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))
(* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* eps (pow x 2))
(* eps (+ (* eps x) (pow x 2)))
(* eps (+ (* eps (+ x (* 4/3 (* eps (pow x 2))))) (pow x 2)))
(* eps (+ (* eps (+ x (* eps (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2)))))) (pow x 2)))
(* 2/3 (* (pow eps 4) x))
(* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ x (pow eps 2)))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))
(* 2/3 (* (pow eps 4) x))
(* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) eps)) (* 2/3 x)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x)))
(* eps x)
(* eps (+ eps x))
(* eps (+ x (* eps (+ 1 (* 4/3 (* eps x))))))
(* eps (+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x)))))))
(* 2/3 (pow eps 4))
(* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps))))
(* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2)))))
(* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3))))))
(* 2/3 (pow eps 4))
(* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps))))
(* (pow eps 4) (+ 2/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps))))
(* (pow eps 4) (+ 2/3 (* -1 (/ (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps))) eps))))
(* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))
(* eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(* -1/3 (pow x 3))
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (- (/ (sin (+ eps x)) (* (pow x 3) (cos (+ eps x)))) (+ 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (- (/ (sin (+ eps x)) (* (pow x 3) (cos (+ eps x)))) (+ 1/3 (/ 1 (pow x 2)))))
(* -1/3 (pow x 3))
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (+ 1/3 (+ (* -1 (/ (sin (- eps (* -1 x))) (* (pow x 3) (cos (- eps (* -1 x)))))) (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/3 (+ (* -1 (/ (sin (- eps (* -1 x))) (* (pow x 3) (cos (- eps (* -1 x)))))) (/ 1 (pow x 2))))))
(- (/ (sin x) (cos x)) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2)))))
(* -1 x)
(* x (- (* -1/3 (pow x 2)) 1))
(* x (- (* -1/3 (pow x 2)) 1))
(* x (- (* -1/3 (pow x 2)) 1))
(* -1/3 (pow x 3))
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))
(* -1/3 (pow x 3))
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos x))
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 4) (* x (+ 2/3 (* 17/9 (pow x 2)))))
(* (pow eps 4) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (* 1/3 (/ 1 eps)))))
(* (pow eps 4) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2))))))
(* (pow eps 4) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))))
(* -1 (* (pow eps 4) (* x (- (* -17/9 (pow x 2)) 2/3))))
(* (pow eps 4) (+ (* -1 (* x (- (* -17/9 (pow x 2)) 2/3))) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
(* (pow eps 4) (+ (* -1 (* x (- (* -17/9 (pow x 2)) 2/3))) (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) eps))))
(* (pow eps 4) (+ (* -1 (* x (- (* -17/9 (pow x 2)) 2/3))) (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ (* -1 (* x (- (* -4/3 (pow x 2)) 1))) (+ (/ 1 eps) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))) eps))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* (pow eps 2) (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2)))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 3) x)) (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2))))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 3) x)) (+ (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 3) x)) (+ (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2)))) (+ (/ (* eps (+ 1 (+ (* 1/3 (pow eps 2)) (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow x 3)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) (pow x 2))))))
(* (pow eps 2) (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -4/3 (/ (pow eps 3) x)) (* -1 (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2))))))))
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* 4/3 (pow eps 3)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (+ (* 1/3 (pow eps 2)) (/ (pow (sin x) 2) (pow (cos x) 2))))) x))) x)) (* 4/3 (pow eps 3))) x)))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 3) (* x (+ 2/3 (* 17/9 (pow x 2)))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (* 1/3 (/ 1 eps)))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2))))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))))
(* -1 (* (pow eps 3) (* x (- (* -17/9 (pow x 2)) 2/3))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* x (- (* -4/3 (pow x 2)) 1))) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2)))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (* eps (+ 4/3 (* 17/9 (pow eps 2))))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)))))
(* (pow x 3) (+ (* 1/3 (/ (pow eps 2) (pow x 3))) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (+ (/ 1 (pow x 3)) (+ (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)) (/ (pow (sin x) 2) (* (pow x 3) (pow (cos x) 2)))))))))
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -4/3 (/ (pow eps 2) x)) (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ 1 (+ (* 1/3 (pow eps 2)) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))) x)) (* 4/3 (pow eps 2))) x)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 3) (* x (+ 2/3 (* 17/9 (pow x 2)))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (* 1/3 (/ 1 eps)))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2))))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))
(* -1 (* (pow eps 3) (* x (- (* -17/9 (pow x 2)) 2/3))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* x (- (* -4/3 (pow x 2)) 1))) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2)))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (* eps (+ 4/3 (* 17/9 (pow eps 2))))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)))))
(* (pow x 3) (+ (* 1/3 (/ (pow eps 2) (pow x 3))) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)) (/ (pow (sin x) 2) (* (pow x 3) (pow (cos x) 2))))))))
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -4/3 (/ (pow eps 2) x)) (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ (* 1/3 (pow eps 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) x))) x)) (* 4/3 (pow eps 2))) x)))))
(* eps (* x (+ 1 (* 4/3 (pow x 2)))))
(* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2))))))
(* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2))))))
(* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2))))))
(* (pow eps 3) (* x (+ 2/3 (* 17/9 (pow x 2)))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (* 1/3 (/ 1 eps)))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2))))))
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2))))))
(* -1 (* (pow eps 3) (* x (- (* -17/9 (pow x 2)) 2/3))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2)))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (* eps (+ 4/3 (* 17/9 (pow eps 2))))))
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)))))
(* (pow x 3) (+ (* 1/3 (/ (pow eps 2) (pow x 3))) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2))))))
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -4/3 (/ (pow eps 2) x)) (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))) x)))))
(* -1/3 x)
(* x (- (* -4/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 x)
(* x (- (* -13/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(* -1/3 (pow x 2))
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(* 4/3 x)
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))
(* 17/9 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(* 17/9 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
Outputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(*.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x))) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))))) (+.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))))
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(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
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(* 1/3 (pow eps 3))
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(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* 1/3 (pow eps 2))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ 1 (pow x 2)))
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(* eps (+ 1 (+ (* eps x) (pow x 2))))
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(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))
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(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))))
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(* 2/3 (* (pow eps 4) x))
(*.f64 #s(literal 2/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
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(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))
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(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))
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(* 2/3 (* (pow eps 4) x))
(*.f64 #s(literal 2/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1/3) eps)) (* 2/3 x)))
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(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3) eps)) (* 2/3 x)))
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(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3) eps)) (* 2/3 x)))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
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(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
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(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
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eps
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps eps) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* 1/3 eps)
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(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
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(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
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(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
(* 1/3 (pow x 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 x x))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* x (+ 4/3 (* 17/9 (pow eps 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))
(* 17/9 (* (pow eps 2) x))
(*.f64 #s(literal 17/9 binary64) (*.f64 x (*.f64 eps eps)))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64))))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64))))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64))))
(* 17/9 (* (pow eps 2) x))
(*.f64 #s(literal 17/9 binary64) (*.f64 x (*.f64 eps eps)))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64))))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64))))
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64))))

eval144.0ms (0.8%)

Compiler

Compiled 62740 to 3426 computations (94.5% saved)

prune137.0ms (0.8%)

Pruning

28 alts after pruning (25 fresh and 3 done)

PrunedKeptTotal
New96419983
Fresh12618
Picked415
Done022
Total980281008
Accuracy
100.0%
Counts
1008 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
62.3%
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
61.5%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
49.7%
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))))
62.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
61.4%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
97.4%
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
97.4%
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x)))
100.0%
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps))
98.7%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
99.4%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps)
100.0%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
99.8%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
98.9%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
97.4%
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
97.2%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
97.4%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x))))
98.2%
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
97.4%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x)))
97.4%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x)))
97.4%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
97.2%
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
97.4%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
97.2%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
97.2%
eps
Compiler

Compiled 1635 to 897 computations (45.1% saved)

simplify199.0ms (1.1%)

Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff256
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
cost-diff256
(sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))))
cost-diff6784
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
cost-diff0
(+.f64 x eps)
cost-diff0
(tan.f64 (+.f64 x eps))
cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
cost-diff256
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
cost-diff256
(*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
cost-diff256
(+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
cost-diff256
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
cost-diff256
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
cost-diff0
(*.f64 x x)
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 x x))
cost-diff0
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
cost-diff19456
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))
cost-diff25792
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))
cost-diff25792
(*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))
cost-diff25792
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
Rules
2926×*-lowering-*.f32
2926×*-lowering-*.f64
2872×+-lowering-+.f64
2872×+-lowering-+.f32
1470×associate-+r+
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
060697
1200635
2749588
33177574
47788574
08273574
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(pow (tan x) 2)
(tan x)
x
2
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+ (tan x) (pow (tan x) 3))
(pow (tan x) 3)
3
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(- 1/3 (* (pow (tan x) 2) -1/3))
1/3
(* (pow (tan x) 2) -1/3)
-1/3
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+ 1 (pow (tan x) 2))
1
(* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(* x -1/3)
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* eps (+ 1 (* x x)))
eps
(+ 1 (* x x))
1
(* x x)
x
(+ (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) eps)
(* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))
eps
(+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))
(* 1/3 (* eps eps))
1/3
(* eps eps)
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))
x
(+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))
(* x (+ 1 (* (* eps eps) 4/3)))
(+ 1 (* (* eps eps) 4/3))
1
(* (* eps eps) 4/3)
4/3
(* eps (+ 1 (* (* eps eps) 2/3)))
(+ 1 (* (* eps eps) 2/3))
(* (* eps eps) 2/3)
2/3
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))
(tan (+ x eps))
(+ x eps)
x
eps
(/ 1 (/ 1 (tan x)))
1
(/ 1 (tan x))
(tan x)
(+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x)))
(/ 1 (cos (+ x eps)))
1
(cos (+ x eps))
(+ x eps)
x
eps
(sin (* eps (+ 1 (/ x eps))))
(* eps (+ 1 (/ x eps)))
(+ 1 (/ x eps))
(/ x eps)
(- 0 (tan x))
0
(tan x)
Outputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps))) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64))))))))))))
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))))) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))))) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)))
(pow (tan x) 2)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan x)
(tan.f64 x)
x
2
#s(literal 2 binary64)
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64))))))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))))
(+ (tan x) (pow (tan x) 3))
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(pow (tan x) 3)
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64))))))))
(- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))
(+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(- 1/3 (* (pow (tan x) 2) -1/3))
(-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* (pow (tan x) 2) -1/3)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(+ 1 (pow (tan x) 2))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 x (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 x (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(* x -1/3)
(*.f64 x #s(literal -1/3 binary64))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
(* eps (+ 1 (* x x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
eps
(+ 1 (* x x))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(* x x)
(*.f64 x x)
x
(+ (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) eps)
(*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x))))))
(* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x)))))
eps
(+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x))))
(* 1/3 (* eps eps))
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* eps eps)
(*.f64 eps eps)
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))
(*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x)))
x
(+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x))
(* x (+ 1 (* (* eps eps) 4/3)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(+ 1 (* (* eps eps) 4/3))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))
1
#s(literal 1 binary64)
(* (* eps eps) 4/3)
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
4/3
#s(literal 4/3 binary64)
(* eps (+ 1 (* (* eps eps) 2/3)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))))
(+ 1 (* (* eps eps) 2/3))
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))))
(* (* eps eps) 2/3)
(*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))
2/3
#s(literal 2/3 binary64)
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(/ 1 (/ 1 (tan x)))
(tan.f64 x)
1
#s(literal 1 binary64)
(/ 1 (tan x))
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan x)
(tan.f64 x)
(+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/ 1 (cos (+ x eps)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
1
#s(literal 1 binary64)
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(sin (* eps (+ 1 (/ x eps))))
(sin.f64 (+.f64 eps x))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(+ 1 (/ x eps))
(+.f64 #s(literal 1 binary64) (/.f64 x eps))
(/ x eps)
(/.f64 x eps)
(- 0 (tan x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
0
#s(literal 0 binary64)
(tan x)
(tan.f64 x)

localize619.0ms (3.5%)

Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy99.9%
(cos.f64 (+.f64 x eps))
accuracy99.8%
(sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))))
accuracy99.8%
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
accuracy93.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
accuracy100.0%
(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy99.9%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
accuracy99.8%
(tan.f64 (+.f64 x eps))
accuracy93.1%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
accuracy99.9%
(*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
accuracy99.9%
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
accuracy99.9%
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
accuracy99.9%
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
accuracy100.0%
(+.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
accuracy99.9%
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
accuracy99.9%
(*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))
accuracy99.7%
(*.f64 x #s(literal -1/3 binary64))
accuracy99.7%
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
Results
418.0ms147×5exit
71.0ms104×0valid
7.0ms1valid
Compiler

Compiled 750 to 60 computations (92% saved)

Precisions
Click to see histograms. Total time spent on operations: 276.0ms
backward-pass: 97.0ms (35.1% of total)
ival-mult: 56.0ms (20.3% of total)
ival-add: 31.0ms (11.2% of total)
...c/correct-round.rkt:119:19: 24.0ms (8.7% of total)
ival-pow: 17.0ms (6.2% of total)
ival-tan: 12.0ms (4.3% of total)
ival-div: 12.0ms (4.3% of total)
ival-sub: 8.0ms (2.9% of total)
compiled-spec: 8.0ms (2.9% of total)
ival-sin: 7.0ms (2.5% of total)
ival-cos: 4.0ms (1.4% of total)
const: 1.0ms (0.4% of total)

series46.0ms (0.3%)

Counts
28 → 552
Calls
Call 1
Inputs
#<alt (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)>
#<alt (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))>
#<alt (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))>
#<alt (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))>
#<alt (* eps (+ 1 (* x x)))>
#<alt (+ 1 (* x x))>
#<alt (* x x)>
#<alt (+ (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) eps)>
#<alt (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))>
#<alt (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))>
#<alt (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))>
#<alt (- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))>
#<alt (/ 1 (/ 1 (tan x)))>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x)))>
#<alt (sin (* eps (+ 1 (/ x eps))))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (/ 1 (cos (+ x eps)))>
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)>
#<alt (* x -1/3)>
#<alt (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))>
#<alt (* (pow (tan x) 2) -1/3)>
#<alt (* 1/3 (* eps eps))>
#<alt (* (* eps eps) 2/3)>
#<alt (* (* eps eps) 4/3)>
#<alt (/ 1 (tan x))>
#<alt (cos (+ x eps))>
Outputs
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
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#<alt (* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/9 (* (pow eps 2) x)) (* 4/3 eps))))))>
#<alt (* 1/3 (* (pow eps 2) x))>
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))>
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))>
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))>
#<alt (* 1/3 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))>
#<alt (* -1/3 (pow x 2))>
#<alt (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/3 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
Calls

138 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
2.0ms
x
@-inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
1.0ms
eps
@-inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
1.0ms
eps
@0
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
1.0ms
eps
@-inf
(+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x)))

rewrite321.0ms (1.8%)

Algorithm
batch-egg-rewrite
Rules
2666×*-lowering-*.f32
2666×*-lowering-*.f64
2170×fma-lowering-fma.f32
2170×fma-lowering-fma.f64
1920×fmm-def
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
060444
1478401
25292391
08020391
Stop Event
iter limit
node limit
Counts
28 → 356
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(* eps (+ 1 (* x x)))
(+ 1 (* x x))
(* x x)
(+ (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) eps)
(* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))
(+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))
(/ 1 (/ 1 (tan x)))
(tan (+ x eps))
(+ x eps)
(+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x)))
(sin (* eps (+ 1 (/ x eps))))
(* eps (+ 1 (/ x eps)))
(/ 1 (cos (+ x eps)))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* x -1/3)
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(* (pow (tan x) 2) -1/3)
(* 1/3 (* eps eps))
(* (* eps eps) 2/3)
(* (* eps eps) 4/3)
(/ 1 (tan x))
(cos (+ x eps))
Outputs
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))) eps)
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) (*.f64 eps eps)) eps))
(+.f64 (+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) (*.f64 eps eps)))
(-.f64 (/.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))) #s(literal 2 binary64)) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))) eps)))
(fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))) eps)
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))) eps eps)
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(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64))) #s(literal -1/3 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) #s(literal -1/3 binary64)) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(*.f64 x #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) x)
(+.f64 (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))
(+.f64 (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) (*.f64 eps (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))
(+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) eps) (*.f64 (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) eps))
(+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) eps) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) eps))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 2 binary64)))) (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 3 binary64))) eps) (+.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 2 binary64))) eps) (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))
(*.f64 (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) eps)
(*.f64 (tan.f64 x) (*.f64 (tan.f64 x) #s(literal -1/3 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (tan.f64 x))
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))
(*.f64 (*.f64 eps #s(literal 1/3 binary64)) eps)
(*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps #s(literal 2/3 binary64)) eps)
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 2/3 binary64))
(*.f64 eps (*.f64 eps #s(literal 4/3 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps #s(literal 4/3 binary64)) eps)
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 4/3 binary64))
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(pow.f64 (tan.f64 x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x))
(+.f64 (cos.f64 (+.f64 eps x)) (fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(cos.f64 (+.f64 eps x))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (/.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 1 binary64)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))))
(/.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) (+.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))) (+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))

simplify408.0ms (2.3%)

Algorithm
egg-herbie
Rules
6400×+-lowering-+.f64
6400×+-lowering-+.f32
4756×*-lowering-*.f32
4756×*-lowering-*.f64
1418×distribute-lft-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
081312442
1288411993
0834611993
Stop Event
iter limit
node limit
Counts
552 → 552
Calls
Call 1
Inputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(* 1/3 (* (pow eps 4) x))
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))
(* 1/3 (* (pow eps 4) x))
(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4)))))
(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4)))))
(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4)))))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
(* 1/3 (pow eps 3))
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* 1/3 (* (pow eps 4) x))
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))
(* 1/3 (* (pow eps 4) x))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4)))))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4)))))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 4/9 (pow eps 2)))))))))))
(* 1/3 (* (pow eps 3) x))
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))
(* 1/3 (* (pow eps 3) x))
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3)))))
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3)))))
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 4/9 (pow eps 2))))))))))
(* 1/3 (* (pow eps 3) x))
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)))
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)))
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)))
(* 1/3 (* (pow eps 3) x))
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(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (+ 1 (/ x eps))))
(sin (* eps (- 1 (* -1 (/ x eps)))))
(sin (* eps (- 1 (* -1 (/ x eps)))))
(sin (* eps (- 1 (* -1 (/ x eps)))))
(sin (* eps (- 1 (* -1 (/ x eps)))))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos x))
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(* -1/3 x)
(* x (- (* -4/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/9 (* (pow eps 2) x)) (* 4/3 eps))))))
(* 1/3 (* (pow eps 2) x))
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
(* 1/3 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
Outputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
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(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
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(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
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(+ eps (* 1/3 (pow eps 3)))
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(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
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(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
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(* 1/3 (* (pow eps 4) x))
(*.f64 #s(literal 1/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64))))
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(* 1/3 (* (pow eps 4) x))
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(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
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(* 1/3 (pow eps 3))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps)))
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
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(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
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(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
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(* 1/3 (* (pow eps 4) x))
(*.f64 #s(literal 1/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64))))
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))
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(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
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(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(*.f64 (-.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x)))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(*.f64 (-.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) eps)) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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(*.f64 x #s(literal -1/3 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* -1/3 x)
(*.f64 x #s(literal -1/3 binary64))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/9 (* (pow eps 2) x)) (* 4/3 eps))))))
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(* 1/3 (* (pow eps 2) x))
(*.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 eps eps)))
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
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(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
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(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
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(* 1/3 (* (pow eps 2) x))
(*.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 eps eps)))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
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(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
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(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
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(* -1/3 (pow x 2))
(*.f64 #s(literal -1/3 binary64) (*.f64 x x))
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/9 binary64)) #s(literal -1/3 binary64)))
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))
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(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))
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(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps)) (sin.f64 eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 (cos.f64 eps) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps))))) (sin.f64 eps))))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x)) (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))

eval160.0ms (0.9%)

Compiler

Compiled 36811 to 2548 computations (93.1% saved)

prune127.0ms (0.7%)

Pruning

31 alts after pruning (25 fresh and 6 done)

PrunedKeptTotal
New93312945
Fresh71320
Picked235
Done033
Total94231973
Accuracy
100.0%
Counts
973 → 31
Alt Table
Click to see full alt table
StatusAccuracyProgram
62.3%
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
61.5%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
49.7%
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))))
62.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
61.5%
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x))
61.4%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
61.4%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x))))
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
97.4%
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
97.4%
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x)))
100.0%
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) (*.f64 eps eps)) eps))
98.7%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
99.4%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps)
100.0%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
99.8%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
98.9%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
97.4%
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
97.4%
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
97.2%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
97.2%
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps)
97.4%
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
97.4%
(+.f64 (*.f64 eps (*.f64 x x)) eps)
98.2%
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
97.4%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
97.4%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
97.2%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
6.5%
(*.f64 eps (*.f64 x x))
97.2%
eps
Compiler

Compiled 2841 to 866 computations (69.5% saved)

regimes85.0ms (0.5%)

Counts
65 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
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(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
Calls

3 calls:

37.0ms
x
19.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
16.0ms
eps
Results
AccuracySegmentsBranch
100.0%1x
100.0%1eps
100.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes53.0ms (0.3%)

Counts
57 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))))
(/.f64 eps (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64)))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)))))
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
Calls

3 calls:

15.0ms
eps
14.0ms
x
14.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes57.0ms (0.3%)

Counts
49 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))))
(/.f64 eps (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64)))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Calls

3 calls:

26.0ms
x
13.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms
eps
Results
AccuracySegmentsBranch
98.9%1x
98.9%1eps
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes46.0ms (0.3%)

Counts
46 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))))
(/.f64 eps (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64)))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
Calls

3 calls:

15.0ms
eps
12.0ms
x
12.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
98.9%1x
98.9%1eps
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes57.0ms (0.3%)

Counts
33 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))))
(/.f64 eps (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64)))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
Outputs
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
Calls

3 calls:

37.0ms
x
9.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms
eps
Results
AccuracySegmentsBranch
97.4%1x
97.4%1eps
97.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0%)

Counts
11 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x)))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x)))
Outputs
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
Calls

2 calls:

4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
97.4%1x
97.4%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts
7 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x)))
Outputs
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
Calls

2 calls:

3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
97.4%1x
97.4%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
5 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
Calls

2 calls:

2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
97.4%1x
97.4%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Accuracy

Total -58.1b remaining (-3296.6%)

Threshold costs -58.1b (-3296.6%)

Counts
2 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
Outputs
eps
Calls

2 calls:

4.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
97.2%1eps
97.2%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify81.0ms (0.5%)

Algorithm
egg-herbie
Rules
700×distribute-lft-neg-in_binary64
440×cancel-sign-sub_binary64
420×neg-mul-1_binary64
398×unsub-neg_binary64
328×neg-sub0_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
074180
1141179
2183179
3218179
4279179
5343179
6497179
7793179
81229179
91648179
101947179
112095179
122173179
132214179
142220179
152220179
162220179
Stop Event
saturated
Calls
Call 1
Inputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
eps
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal 1/3 binary64))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal 4/3 binary64))) eps)))) #s(literal 1 binary64)))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal 4/3 binary64))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps)
(+.f64 eps (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))))
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps)
(+.f64 eps (*.f64 eps (*.f64 x (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 eps (+.f64 (*.f64 x x) #s(literal 1 binary64)))
eps

soundness2.1s (11.9%)

Rules
6400×+-lowering-+.f64
6400×+-lowering-+.f32
5576×*-lowering-*.f32
5576×*-lowering-*.f64
5526×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
061850
1477452
25906442
08182442
093917262
1343016961
0874816961
01571381
14941286
218911261
377211261
085671261
079515992
1280115392
0831415392
081312442
1288411993
0834611993
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 508 to 257 computations (49.4% saved)

preprocess61.0ms (0.3%)

Compiler

Compiled 404 to 172 computations (57.4% saved)

end0.0ms (0%)

Profiling

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