2cos (problem 3.3.5)

Time bar (total: 16.6s)

analyze60.0ms (0.4%)

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: 36.0ms
ival-cos: 9.0ms (25.2% of total)
...c/correct-round.rkt:119:19: 7.0ms (19.6% of total)
ival-add: 4.0ms (11.2% of total)
ival-<: 4.0ms (11.2% of total)
ival-mult: 3.0ms (8.4% of total)
ival-fabs: 3.0ms (8.4% of total)
ival-<=: 3.0ms (8.4% of total)
ival-sub: 2.0ms (5.6% of total)
ival-and: 1.0ms (2.8% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample9.0s (54.1%)

Results
3.5s26295×0precondition
3.2s5718×2valid
681.0ms2458×1valid
16.0ms80×0valid
Precisions
Click to see histograms. Total time spent on operations: 5.7s
ival-cos: 2.2s (39% of total)
...c/correct-round.rkt:119:19: 869.0ms (15.2% of total)
ival-<: 438.0ms (7.7% of total)
ival-mult: 384.0ms (6.7% of total)
ival-<=: 362.0ms (6.3% of total)
ival-add: 336.0ms (5.9% of total)
ival-sub: 323.0ms (5.7% of total)
ival-fabs: 309.0ms (5.4% of total)
backward-pass: 264.0ms (4.6% of total)
ival-and: 148.0ms (2.6% of total)
const: 50.0ms (0.9% of total)
Bogosity

preprocess53.0ms (0.3%)

Algorithm
egg-herbie
Rules
414×fnmadd-define
382×sum3-define
370×fmsub-define
356×fnmsub-define
316×fmm-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02148
14344
28942
317842
443842
586342
6127942
7161142
8174942
9183242
10185042
067
197
2147
3217
4317
5637
61227
72107
82957
94017
104797
114857
04857
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- (cos (+ x eps)) (cos x))
Outputs
(- (cos (+ x eps)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Call 2
Inputs
(- (cos (+ x eps)) (cos x))
(- (cos (+ (neg x) eps)) (cos (neg x)))
(- (cos (+ x (neg eps))) (cos x))
(neg (- (cos (+ (neg x) eps)) (cos (neg x))))
(neg (- (cos (+ x (neg eps))) (cos x)))
(- (cos (+ eps x)) (cos eps))
Outputs
(- (cos (+ x eps)) (cos x))
(- (cos (+ (neg x) eps)) (cos (neg x)))
(- (cos (- eps x)) (cos x))
(- (cos (+ x (neg eps))) (cos x))
(- (cos (- eps x)) (cos x))
(neg (- (cos (+ (neg x) eps)) (cos (neg x))))
(- (cos x) (cos (- eps x)))
(neg (- (cos (+ x (neg eps))) (cos x)))
(- (cos x) (cos (- eps x)))
(- (cos (+ eps x)) (cos eps))
(- (cos (+ x eps)) (cos eps))

explain238.0ms (1.4%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1250-0-(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
30-2(4.009635370991742 0.6432748087946674)(cos.f64 (+.f64 x eps))
00-0-x
00-0-(+.f64 x eps)
00-0-(cos.f64 x)
00-0-eps
Results
175.0ms368×2valid
21.0ms132×1valid
7.0ms12×0valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 151.0ms
ival-cos: 102.0ms (67.7% of total)
ival-sub: 20.0ms (13.3% of total)
backward-pass: 15.0ms (10% of total)
ival-add: 13.0ms (8.6% of total)
const: 1.0ms (0.7% 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
56.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify15.0ms (0.1%)

Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 x)
cost-diff0
(+.f64 x eps)
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(-.f64 (cos.f64 (+.f64 x eps)) (cos.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
(- (cos (+ x eps)) (cos x))
(cos (+ x eps))
(+ x eps)
x
eps
(cos x)
Outputs
(- (cos (+ x eps)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos (+ x eps))
(cos.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(cos x)
(cos.f64 x)

localize100.0ms (0.6%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x eps)
accuracy100.0%
(cos.f64 x)
accuracy99.8%
(cos.f64 (+.f64 x eps))
accuracy56.5%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
78.0ms184×2valid
11.0ms66×1valid
1.0ms0valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 66.0ms
ival-cos: 51.0ms (77.6% of total)
backward-pass: 7.0ms (10.6% of total)
ival-add: 4.0ms (6.1% of total)
ival-sub: 4.0ms (6.1% of total)
const: 0.0ms (0% of total)

series4.0ms (0%)

Counts
4 → 84
Calls
Call 1
Inputs
#<alt (- (cos (+ x eps)) (cos x))>
#<alt (cos (+ x eps))>
#<alt (+ x eps)>
#<alt (cos x)>
Outputs
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos 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)))>
#<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 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
Calls

21 calls:

TimeVariablePointExpression
1.0ms
eps
@inf
(- (cos (+ x eps)) (cos x))
0.0ms
x
@0
(- (cos (+ x eps)) (cos x))
0.0ms
eps
@0
(- (cos (+ x eps)) (cos x))
0.0ms
x
@-inf
(- (cos (+ x eps)) (cos x))
0.0ms
x
@inf
(+ x eps)

rewrite249.0ms (1.5%)

Algorithm
batch-egg-rewrite
Rules
2774×*-lowering-*.f32
2774×*-lowering-*.f64
2148×/-lowering-/.f32
2148×/-lowering-/.f64
1850×sum5-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
15016
241216
3524716
0806116
Stop Event
iter limit
node limit
Counts
4 → 173
Calls
Call 1
Inputs
(- (cos (+ x eps)) (cos x))
(cos (+ x eps))
(+ x eps)
(cos x)
Outputs
(+.f64 (cos.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(+.f64 (cos.f64 (+.f64 x eps)) (+.f64 (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(+.f64 (cos.f64 (+.f64 x eps)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(+.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (cos.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (+.f64 (cos.f64 (+.f64 x eps)) #s(literal 0 binary64)) (cos.f64 x))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(fma.f64 #s(literal -1 binary64) (cos.f64 x) (cos.f64 (+.f64 x eps)))
(neg.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))))
(neg.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (cos.f64 (+.f64 x eps))))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (neg.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (cos.f64 (+.f64 x eps)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (-.f64 #s(literal 0 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
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(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(neg.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(neg.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 eps eps))) (-.f64 x eps)))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 eps eps))) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))
(/.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 (+.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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (-.f64 (*.f64 eps eps) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))))
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (-.f64 x eps) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (*.f64 (-.f64 x eps) (+.f64 (*.f64 x x) (*.f64 eps eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.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))))) #s(literal 1 binary64)) (*.f64 (+.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 x x) (*.f64 eps (-.f64 eps x)))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))) (-.f64 x eps)))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps)))
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 eps eps)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (*.f64 x x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (+.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.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 eps (*.f64 eps eps))) (-.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 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x 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 (+.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 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(*.f64 #s(literal 1 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 (*.f64 x 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 (*.f64 x 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))))
(cos.f64 x)

simplify174.0ms (1%)

Algorithm
egg-herbie
Rules
3196×*-lowering-*.f32
3196×*-lowering-*.f64
1368×fnmadd-define
1248×neg-lowering-neg.f64
1248×neg-lowering-neg.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0105481
1304458
2777457
32938457
08476457
Stop Event
iter limit
node limit
Counts
84 → 84
Calls
Call 1
Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos 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)))
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)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
Outputs
(- (cos eps) 1)
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (+.f64 (*.f64 x (sin.f64 eps)) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(+.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64)))) (sin.f64 eps))))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(+.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 eps) (+.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.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 (cos.f64 eps) (*.f64 x #s(literal -1/2 binary64))) (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 (cos.f64 eps) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (sin.f64 eps) (+.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(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 eps (*.f64 #s(literal -1/2 binary64) (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 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(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))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.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 x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

eval28.0ms (0.2%)

Compiler

Compiled 6681 to 740 computations (88.9% saved)

prune30.0ms (0.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2507257
Fresh000
Picked011
Done000
Total2508258
Accuracy
99.8%
Counts
258 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
56.5%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
56.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
80.9%
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
54.1%
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
99.6%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.5%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
99.2%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
99.5%
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
Compiler

Compiled 229 to 158 computations (31% saved)

simplify118.0ms (0.7%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
cost-diff0
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
cost-diff0
(+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
cost-diff0
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
cost-diff0
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
cost-diff0
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
cost-diff0
(-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
cost-diff0
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
cost-diff0
(sin.f64 x)
cost-diff0
(*.f64 eps (sin.f64 x))
cost-diff0
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
cost-diff0
(cos.f64 eps)
cost-diff0
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
cost-diff128
(/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))
cost-diff128
(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
cost-diff128
(*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
cost-diff128
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
Rules
1858×fmsub-define
1832×sum3-define
1732×fma-define
1708×sum5-define
1600×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033195
179185
2251185
31098185
42608185
53478185
66225185
08013185
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(+ eps 0)
eps
0
2
(sin (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
-2
(+ (cos eps) -1)
(cos eps)
eps
-1
(- 0 (* eps (sin x)))
0
(* eps (sin x))
eps
(sin x)
x
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
eps
(- (* eps (* -1/2 (cos x))) (sin x))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
-1/2
(cos x)
x
(sin x)
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
eps
(+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
-1/2
(cos x)
x
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(sin x)
(+ (* eps (* eps 1/6)) -1)
(* eps (* eps 1/6))
(* eps 1/6)
1/6
-1
Outputs
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -2 binary64)))
(* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(sin (/ (+ eps 0) 2))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/ (+ eps 0) 2)
(/.f64 eps #s(literal 2 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
2
#s(literal 2 binary64)
(sin (/ (+ eps (* x 2)) 2))
(sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x 2)
(*.f64 #s(literal 2 binary64) x)
x
-2
#s(literal -2 binary64)
(+ (cos eps) -1)
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(cos eps)
(cos.f64 eps)
eps
-1
#s(literal -1 binary64)
(- 0 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
0
#s(literal 0 binary64)
(* eps (sin x))
(*.f64 eps (sin.f64 x))
eps
(sin x)
(sin.f64 x)
x
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
eps
(- (* eps (* -1/2 (cos x))) (sin x))
(-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))
(* eps (* -1/2 (cos x)))
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
x
(sin x)
(sin.f64 x)
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
eps
(+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))
(* eps (* -1/2 (cos x)))
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
x
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))
(sin x)
(sin.f64 x)
(+ (* eps (* eps 1/6)) -1)
(+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))
(* eps (* eps 1/6))
(*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)

localize300.0ms (1.8%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy99.9%
(+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64))))
accuracy99.9%
(*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))
accuracy99.8%
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
accuracy99.5%
(*.f64 eps #s(literal 1/6 binary64))
accuracy100.0%
(cos.f64 x)
accuracy100.0%
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
accuracy100.0%
(-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
accuracy99.8%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
accuracy100.0%
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
accuracy100.0%
(sin.f64 x)
accuracy100.0%
(*.f64 eps (sin.f64 x))
accuracy100.0%
(cos.f64 eps)
accuracy55.8%
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy100.0%
(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
accuracy100.0%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
accuracy99.8%
(sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
accuracy99.8%
(*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
Results
225.0ms251×1valid
9.0ms3valid
1.0ms2valid
0.0ms0valid
Compiler

Compiled 217 to 34 computations (84.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 132.0ms
ival-mult: 38.0ms (28.9% of total)
backward-pass: 21.0ms (16% of total)
ival-sin: 16.0ms (12.2% of total)
ival-cos: 13.0ms (9.9% of total)
ival-add: 13.0ms (9.9% of total)
ival-div: 11.0ms (8.4% of total)
ival-sub: 10.0ms (7.6% of total)
...c/correct-round.rkt:119:19: 8.0ms (6.1% of total)
const: 2.0ms (1.5% of total)

series32.0ms (0.2%)

Counts
19 → 348
Calls
Call 1
Inputs
#<alt (* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)>
#<alt (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))>
#<alt (sin (/ (+ eps 0) 2))>
#<alt (/ (+ eps 0) 2)>
#<alt (+ (cos eps) -1)>
#<alt (cos eps)>
#<alt (- 0 (* eps (sin x)))>
#<alt (* eps (sin x))>
#<alt (sin x)>
#<alt (* eps (- (* eps (* -1/2 (cos x))) (sin x)))>
#<alt (- (* eps (* -1/2 (cos x))) (sin x))>
#<alt (* eps (* -1/2 (cos x)))>
#<alt (* -1/2 (cos x))>
#<alt (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))>
#<alt (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))>
#<alt (sin (/ (+ eps (* x 2)) 2))>
#<alt (cos x)>
#<alt (* eps 1/6)>
#<alt (* eps (* eps 1/6))>
Outputs
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps x))>
#<alt (* x (- (* 1/6 (* eps (pow x 2))) eps))>
#<alt (* x (- (* (pow x 2) (- (* -1/120 (* eps (pow x 2))) (* -1/6 eps))) eps))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* 1/5040 (* eps (pow x 2))) (* 1/120 eps))) (* -1/6 eps))) eps))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps x)>
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
Calls

87 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
1.0ms
x
@-inf
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
1.0ms
x
@inf
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
1.0ms
eps
@0
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
1.0ms
x
@inf
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))

rewrite377.0ms (2.3%)

Algorithm
batch-egg-rewrite
Rules
4020×*-lowering-*.f32
4020×*-lowering-*.f64
2552×+-lowering-+.f64
2552×+-lowering-+.f32
2374×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033130
1178124
21852124
08466124
Stop Event
iter limit
node limit
Counts
19 → 411
Calls
Call 1
Inputs
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(+ (cos eps) -1)
(cos eps)
(- 0 (* eps (sin x)))
(* eps (sin x))
(sin x)
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
(- (* eps (* -1/2 (cos x))) (sin x))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
(+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(sin (/ (+ eps (* x 2)) 2))
(cos x)
(* eps 1/6)
(* eps (* eps 1/6))
Outputs
(/.f64 (*.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal 2 binary64))
(/.f64 (*.f64 (-.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal -2 binary64)) #s(literal 2 binary64))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal -2 binary64)))
(*.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -2 binary64)) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (cos.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))) #s(literal 2 binary64)))
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(*.f64 (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))))))
(sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(neg.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64))))
(cos.f64 x)
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64)))
(+.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/6 binary64) eps #s(literal 0 binary64))
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) eps)
(/.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps))
(*.f64 eps #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) eps)
(+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) (*.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64)))
(+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64))))
(+.f64 (*.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64))) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) (*.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64))))
(fma.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64))))
(fma.f64 (*.f64 eps #s(literal 1/6 binary64)) eps (*.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps #s(literal 1/6 binary64)) eps (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64))))
(fma.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64))))
(/.f64 (*.f64 (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps eps)) eps)
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps #s(literal 1/6 binary64))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/6 binary64))) eps)
(*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))
(*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps #s(literal 1/6 binary64)) eps)
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))

simplify308.0ms (1.9%)

Algorithm
egg-herbie
Rules
5490×*-lowering-*.f32
5490×*-lowering-*.f64
4126×+-lowering-+.f64
4126×+-lowering-+.f32
1382×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03803250
113102852
242372792
082872792
Stop Event
iter limit
node limit
Counts
348 → 348
Calls
Call 1
Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps x))
(* x (- (* 1/6 (* eps (pow x 2))) eps))
(* x (- (* (pow x 2) (- (* -1/120 (* eps (pow x 2))) (* -1/6 eps))) eps))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* 1/5040 (* eps (pow x 2))) (* 1/120 eps))) (* -1/6 eps))) eps))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
Outputs
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(*.f64 eps (+.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))))) (sin.f64 x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+.f64 (*.f64 (*.f64 (*.f64 x #s(literal -2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (+.f64 (*.f64 x x) #s(literal -2 binary64))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(+.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 x (+.f64 (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (sin x)))
(*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal 1/4 binary64)))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/12 binary64))) (*.f64 (cos.f64 x) #s(literal 1/4 binary64))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/4 binary64)) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal -1/12 binary64)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/48 binary64))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x (+.f64 (*.f64 x (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1/2 (pow eps 2))
(*.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/24 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/40320 binary64)))))))))))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
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(* -1 (sin x))
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1
#s(literal 1 binary64)
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(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 1/6 eps)
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(* 1/6 eps)
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eval93.0ms (0.6%)

Compiler

Compiled 20070 to 1817 computations (90.9% saved)

prune232.0ms (1.4%)

Pruning

38 alts after pruning (35 fresh and 3 done)

PrunedKeptTotal
New82934863
Fresh112
Picked325
Done011
Total83338871
Accuracy
100.0%
Counts
871 → 38
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.7%
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)))
19.1%
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps (*.f64 eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))) (*.f64 eps (*.f64 eps eps)))
24.2%
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps eps)) eps) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))) (*.f64 eps eps))
84.2%
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)) (*.f64 eps eps)) eps)
56.5%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
56.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
72.0%
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps))
79.6%
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
79.2%
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
54.1%
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
96.7%
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
99.2%
(+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x))))
99.5%
(+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
54.1%
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
99.5%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.5%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.4%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.2%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.6%
(*.f64 (*.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.6%
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
31.7%
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
79.6%
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
79.3%
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
79.5%
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
32.9%
(*.f64 eps (/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) eps) #s(literal 1/36 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 eps eps)) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 eps eps))))
8.0%
(*.f64 eps (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) #s(literal 3 binary64))) (+.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))) (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))))))
99.5%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))))) (sin.f64 x)))
97.8%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
99.2%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
98.2%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
96.1%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
99.5%
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
96.7%
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
96.1%
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
96.1%
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
99.1%
(*.f64 eps (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
55.2%
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
80.9%
(neg.f64 (*.f64 eps (sin.f64 x)))
Compiler

Compiled 1557 to 978 computations (37.2% saved)

simplify171.0ms (1%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))
cost-diff0
(-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))
cost-diff0
(*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)) (*.f64 eps eps))
cost-diff256
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)) (*.f64 eps eps)) eps)
cost-diff0
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))
cost-diff0
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))
cost-diff0
(-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x))
cost-diff0
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
cost-diff0
(-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps)
cost-diff0
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
cost-diff128
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
cost-diff0
(+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))
cost-diff0
(sin.f64 x)
cost-diff0
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))
cost-diff6400
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)))
Rules
3322×*-lowering-*.f32
3322×*-lowering-*.f64
1834×sum3-define
1740×+-lowering-+.f64
1740×+-lowering-+.f32
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
038223
1110215
2321212
3918210
42172210
54014209
08360209
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(+ (* (* (sin x) (+ -1 (* eps (* eps 1/6)))) eps) (* (* eps -1/2) (* (cos x) eps)))
(* (sin x) (+ -1 (* eps (* eps 1/6))))
(sin x)
x
(+ -1 (* eps (* eps 1/6)))
-1
(* eps (* eps 1/6))
eps
(* eps 1/6)
1/6
(* (* eps -1/2) (* (cos x) eps))
(* eps -1/2)
-1/2
(* (cos x) eps)
(cos x)
(+ 1 -1)
1
-1
(* x (- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps))
x
(- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps)
(* (* x x) (* eps (+ (* (* x x) -1/120) 1/6)))
(* x x)
(* eps (+ (* (* x x) -1/120) 1/6))
eps
(+ (* (* x x) -1/120) 1/6)
(* (* x x) -1/120)
-1/120
1/6
(* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x)))
eps
(- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x))
(* eps (+ -1/2 (* 1/4 (* x x))))
(+ -1/2 (* 1/4 (* x x)))
-1/2
(* 1/4 (* x x))
1/4
(* x x)
x
(sin x)
(/ (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps)) eps)
(* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps))
(- (* -1/2 (* (cos x) eps)) (sin x))
(* -1/2 (* (cos x) eps))
-1/2
(* (cos x) eps)
(cos x)
x
eps
(sin x)
(* eps eps)
Outputs
(+ (* (* (sin x) (+ -1 (* eps (* eps 1/6)))) eps) (* (* eps -1/2) (* (cos x) eps)))
(*.f64 eps (-.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 x))))
(* (sin x) (+ -1 (* eps (* eps 1/6))))
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))
(sin x)
(sin.f64 x)
x
(+ -1 (* eps (* eps 1/6)))
(+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))
-1
#s(literal -1 binary64)
(* eps (* eps 1/6))
(*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))
eps
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* (* eps -1/2) (* (cos x) eps))
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps (cos.f64 x)))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* (cos x) eps)
(*.f64 eps (cos.f64 x))
(cos x)
(cos.f64 x)
(+ 1 -1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
-1
#s(literal -1 binary64)
(* x (- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps))
(*.f64 eps (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))))))))
x
(- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps)
(*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(* (* x x) (* eps (+ (* (* x x) -1/120) 1/6)))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x x)))
(* x x)
(*.f64 x x)
(* eps (+ (* (* x x) -1/120) 1/6))
(*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))))
eps
(+ (* (* x x) -1/120) 1/6)
(+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))
(* (* x x) -1/120)
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
-1/120
#s(literal -1/120 binary64)
1/6
#s(literal 1/6 binary64)
(* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (sin.f64 x)))
eps
(- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x))
(-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (sin.f64 x))
(* eps (+ -1/2 (* 1/4 (* x x))))
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(+ -1/2 (* 1/4 (* x x)))
(+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
-1/2
#s(literal -1/2 binary64)
(* 1/4 (* x x))
(*.f64 x (*.f64 x #s(literal 1/4 binary64)))
1/4
#s(literal 1/4 binary64)
(* x x)
(*.f64 x x)
x
(sin x)
(sin.f64 x)
(/ (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (sin.f64 x)))
(* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps))
(*.f64 (-.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (sin.f64 x)) (*.f64 eps eps))
(- (* -1/2 (* (cos x) eps)) (sin x))
(-.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (sin.f64 x))
(* -1/2 (* (cos x) eps))
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(* (cos x) eps)
(*.f64 eps (cos.f64 x))
(cos x)
(cos.f64 x)
x
eps
(sin x)
(sin.f64 x)
(* eps eps)
(*.f64 eps eps)

localize192.0ms (1.2%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 (cos.f64 x) eps)
accuracy100.0%
(-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))
accuracy99.8%
(*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)) (*.f64 eps eps))
accuracy84.9%
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)) (*.f64 eps eps)) eps)
accuracy100.0%
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))
accuracy100.0%
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))
accuracy99.9%
(-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x))
accuracy99.8%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
accuracy100.0%
(+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
accuracy99.9%
(*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
accuracy99.5%
(*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
accuracy100.0%
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
accuracy100.0%
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)))
accuracy100.0%
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))
accuracy99.9%
(*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))
accuracy99.5%
(*.f64 eps #s(literal 1/6 binary64))
Results
102.0ms251×0valid
6.0ms3valid
1.0ms2valid
1.0ms1valid
Compiler

Compiled 263 to 37 computations (85.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 64.0ms
ival-mult: 32.0ms (50.1% of total)
...c/correct-round.rkt:119:19: 8.0ms (12.5% of total)
ival-add: 6.0ms (9.4% of total)
ival-sub: 4.0ms (6.3% of total)
ival-sin: 4.0ms (6.3% of total)
compiled-spec: 4.0ms (6.3% of total)
ival-cos: 3.0ms (4.7% of total)
ival-div: 2.0ms (3.1% of total)
const: 1.0ms (1.6% of total)
backward-pass: 1.0ms (1.6% of total)

series30.0ms (0.2%)

Counts
23 → 432
Calls
Call 1
Inputs
#<alt (+ (* (* (sin x) (+ -1 (* eps (* eps 1/6)))) eps) (* (* eps -1/2) (* (cos x) eps)))>
#<alt (* (sin x) (+ -1 (* eps (* eps 1/6))))>
#<alt (sin x)>
#<alt (+ -1 (* eps (* eps 1/6)))>
#<alt (+ 1 -1)>
#<alt (* x (- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps))>
#<alt (- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps)>
#<alt (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6)))>
#<alt (* x x)>
#<alt (* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x)))>
#<alt (- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x))>
#<alt (* eps (+ -1/2 (* 1/4 (* x x))))>
#<alt (+ -1/2 (* 1/4 (* x x)))>
#<alt (/ (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps)) eps)>
#<alt (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps))>
#<alt (- (* -1/2 (* (cos x) eps)) (sin x))>
#<alt (* -1/2 (* (cos x) eps))>
#<alt (* eps 1/6)>
#<alt (* eps (* eps 1/6))>
#<alt (* eps (+ (* (* x x) -1/120) 1/6))>
#<alt (* (* x x) -1/120)>
#<alt (+ (* (* x x) -1/120) 1/6)>
#<alt (* (cos x) eps)>
Outputs
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* x (- (* 1/6 (pow eps 2)) 1))>
#<alt (* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))>
#<alt (* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt -1>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))>
#<alt (* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))>
#<alt (* -1 eps)>
#<alt (- (* 1/6 (* eps (pow x 2))) eps)>
#<alt (- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)>
#<alt (- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)>
#<alt (* -1/120 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* -1/120 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))>
#<alt (* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))>
#<alt (* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))>
#<alt (* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))>
#<alt (* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* -1/120 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* -1/120 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))>
#<alt (* -1 (sin x))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 3))>
#<alt (+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))>
#<alt (+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* 1/4 (* (pow eps 3) x)))))>
#<alt (+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* x (+ (* 1/6 (* (pow eps 2) x)) (* 1/4 (pow eps 3)))))))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* eps (+ 1/6 (* -1/120 (pow x 2))))>
#<alt (* 1/6 eps)>
#<alt (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))>
#<alt (* -1/120 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* -1/120 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt (* -1/120 (pow x 2))>
#<alt 1/6>
#<alt (+ 1/6 (* -1/120 (pow x 2)))>
#<alt (+ 1/6 (* -1/120 (pow x 2)))>
#<alt (+ 1/6 (* -1/120 (pow x 2)))>
#<alt (* -1/120 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* -1/120 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
Calls

108 calls:

TimeVariablePointExpression
5.0ms
eps
@0
(* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x)))
1.0ms
eps
@0
(* x (- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps))
1.0ms
x
@inf
(+ (* (* (sin x) (+ -1 (* eps (* eps 1/6)))) eps) (* (* eps -1/2) (* (cos x) eps)))
1.0ms
eps
@inf
(* x (- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps))
1.0ms
x
@-inf
(+ (* (* (sin x) (+ -1 (* eps (* eps 1/6)))) eps) (* (* eps -1/2) (* (cos x) eps)))

rewrite365.0ms (2.2%)

Algorithm
batch-egg-rewrite
Rules
4874×*-lowering-*.f32
4874×*-lowering-*.f64
3242×/-lowering-/.f32
3242×/-lowering-/.f64
1866×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038174
1204166
21733162
08620162
Stop Event
iter limit
node limit
Counts
23 → 560
Calls
Call 1
Inputs
(+ (* (* (sin x) (+ -1 (* eps (* eps 1/6)))) eps) (* (* eps -1/2) (* (cos x) eps)))
(* (sin x) (+ -1 (* eps (* eps 1/6))))
(sin x)
(+ -1 (* eps (* eps 1/6)))
(+ 1 -1)
(* x (- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps))
(- (* (* x x) (* eps (+ (* (* x x) -1/120) 1/6))) eps)
(* (* x x) (* eps (+ (* (* x x) -1/120) 1/6)))
(* x x)
(* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x)))
(- (* eps (+ -1/2 (* 1/4 (* x x)))) (sin x))
(* eps (+ -1/2 (* 1/4 (* x x))))
(+ -1/2 (* 1/4 (* x x)))
(/ (* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps)) eps)
(* (- (* -1/2 (* (cos x) eps)) (sin x)) (* eps eps))
(- (* -1/2 (* (cos x) eps)) (sin x))
(* -1/2 (* (cos x) eps))
(* eps 1/6)
(* eps (* eps 1/6))
(* eps (+ (* (* x x) -1/120) 1/6))
(* (* x x) -1/120)
(+ (* (* x x) -1/120) 1/6)
(* (cos x) eps)
Outputs
(+.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(-.f64 (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))) (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))))) (*.f64 eps (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x))))) (*.f64 eps (/.f64 (pow.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x))))))
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))) (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))) (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))))
(fma.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))) eps (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps (cos.f64 x))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps (cos.f64 x)) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (*.f64 eps (cos.f64 x)) (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) eps (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)))) (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 eps (*.f64 eps (cos.f64 x))) #s(literal -1/2 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps) (cos.f64 x) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (*.f64 (*.f64 eps (cos.f64 x)) eps) #s(literal -1/2 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)))
(fma.f64 (*.f64 eps (sin.f64 x)) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
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(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/1728000 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/1728000 binary64)))) #s(literal 1/46656 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64))) (+.f64 #s(literal 1/1296 binary64) (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) #s(literal 1/36 binary64)))) (+.f64 (*.f64 x (*.f64 x #s(literal -1/120 binary64))) #s(literal -1/6 binary64))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64))) #s(literal 1/1296 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) #s(literal 1/36 binary64)) (+.f64 (*.f64 x (*.f64 x #s(literal -1/120 binary64))) #s(literal -1/6 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/1728000 binary64))) #s(literal 1/216 binary64)))) (neg.f64 (neg.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) #s(literal -1/36 binary64)))) (neg.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/120 binary64))) #s(literal -1/6 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)))) (neg.f64 (-.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64))))))
(pow.f64 (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/1728000 binary64))) #s(literal 1/216 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/120 binary64))) #s(literal -1/6 binary64)) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) #s(literal -1/36 binary64))) #s(literal -1 binary64))
(*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/1728000 binary64))) #s(literal 1/216 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
(*.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/14400 binary64)) #s(literal -1/36 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x #s(literal -1/120 binary64))) #s(literal -1/6 binary64))))
(*.f64 eps (cos.f64 x))
(*.f64 (cos.f64 x) eps)

simplify309.0ms (1.9%)

Algorithm
egg-herbie
Rules
5110×*-lowering-*.f32
5110×*-lowering-*.f64
3464×+-lowering-+.f64
3464×+-lowering-+.f32
1200×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03054500
110743847
237483732
080213732
Stop Event
iter limit
node limit
Counts
432 → 432
Calls
Call 1
Inputs
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* -1 (sin x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
-1
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* -1/120 (* eps (pow x 5)))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* -1/120 (* eps (pow x 5)))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* eps (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))
(* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))
(* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))
(* -1 (* eps (* x (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))))))
(* -1 eps)
(- (* 1/6 (* eps (pow x 2))) eps)
(- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)
(- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)
(* -1/120 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* -1/120 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* eps (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))
(* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))
(* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))
(* -1 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2))))))))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(* -1/120 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/120 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 2))))
(* -1 (sin x))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (sin x))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ (sin x) (pow x 2))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 3))
(+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))
(+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* 1/4 (* (pow eps 3) x)))))
(+ (* -1/2 (pow eps 3)) (* x (+ (* -1 (pow eps 2)) (* x (+ (* 1/6 (* (pow eps 2) x)) (* 1/4 (pow eps 3)))))))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* (pow eps 2) (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* (pow eps 2) (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* (pow eps 3) (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* 1/6 (pow eps 2))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* eps (+ 1/6 (* -1/120 (pow x 2))))
(* 1/6 eps)
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))
(* -1/120 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/120 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
(* -1/120 (pow x 2))
1/6
(+ 1/6 (* -1/120 (pow x 2)))
(+ 1/6 (* -1/120 (pow x 2)))
(+ 1/6 (* -1/120 (pow x 2)))
(* -1/120 (pow x 2))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* -1/120 (pow x 2))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
Outputs
(* -1/2 (pow eps 2))
(*.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(+.f64 (*.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))) #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))) (*.f64 x x)) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 eps (*.f64 eps (sin.f64 x)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(*.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* 1/6 (* (pow eps 3) (sin x)))
(*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 eps (*.f64 eps (sin.f64 x)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(*.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* x (- (* 1/6 (pow eps 2)) 1))
(*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))
(*.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))
(*.f64 x (+.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))
(*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x x)) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(* -1 (sin x))
(-.f64 #s(literal 0 binary64) (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
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(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
(* -1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
(* -1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
(* -1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
(* -1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
(* -1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
(* -1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* -1/120 (pow x 2)))
(+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))
(+ 1/6 (* -1/120 (pow x 2)))
(+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))
(+ 1/6 (* -1/120 (pow x 2)))
(+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))
(* -1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(* -1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(* (pow x 2) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (*.f64 x x))))))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))

eval142.0ms (0.9%)

Compiler

Compiled 32345 to 2562 computations (92.1% saved)

prune129.0ms (0.8%)

Pruning

41 alts after pruning (38 fresh and 3 done)

PrunedKeptTotal
New1064161080
Fresh82230
Picked505
Done033
Total1077411118
Accuracy
100.0%
Counts
1118 → 41
Alt Table
Click to see full alt table
StatusAccuracyProgram
24.2%
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps eps)) eps) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))) (*.f64 eps eps))
84.2%
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 eps eps))) eps)
81.1%
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
98.8%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (sin.f64 x)))))
56.5%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
56.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
79.6%
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
79.2%
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
54.1%
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
99.5%
(+.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
96.7%
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
96.2%
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
99.5%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.5%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.4%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.2%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.6%
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
31.7%
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
79.3%
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
98.7%
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
97.3%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
54.5%
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
79.6%
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
2.9%
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
79.5%
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
32.9%
(*.f64 eps (/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) eps) #s(literal 1/36 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 eps eps)) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 eps eps))))
8.0%
(*.f64 eps (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) #s(literal 3 binary64))) (+.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))) (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))))))
99.5%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))))) (sin.f64 x)))
96.9%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
96.7%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
96.1%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
99.2%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
98.2%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
96.1%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
99.5%
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
96.7%
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
54.5%
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
55.5%
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
55.2%
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
80.9%
(neg.f64 (*.f64 eps (sin.f64 x)))
54.1%
#s(literal 0 binary64)
Compiler

Compiled 1659 to 1040 computations (37.3% saved)

simplify161.0ms (1%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
cost-diff0
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
cost-diff0
(*.f64 eps eps)
cost-diff0
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
cost-diff0
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))
cost-diff0
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))
cost-diff128
(-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))
cost-diff128
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
cost-diff0
(*.f64 #s(literal -1/2 binary64) eps)
cost-diff0
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
cost-diff0
(*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps))
cost-diff256
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
cost-diff0
(*.f64 eps #s(literal 1/2 binary64))
cost-diff0
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff0
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
Rules
2716×+-lowering-+.f64
2716×+-lowering-+.f32
2616×*-lowering-*.f32
2616×*-lowering-*.f64
1284×sum3-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
039233
1104214
2286210
3916208
43284208
08161208
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))) -2)
(* (sin (* eps 1/2)) (sin (+ x (* eps 1/2))))
(sin (* eps 1/2))
(* eps 1/2)
eps
1/2
(sin (+ x (* eps 1/2)))
(+ x (* eps 1/2))
x
-2
0
(/ (* (- (* -1/2 eps) x) (* eps eps)) eps)
(* (- (* -1/2 eps) x) (* eps eps))
(- (* -1/2 eps) x)
(* -1/2 eps)
-1/2
eps
x
(* eps eps)
(* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120))))))))
eps
(- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120)))))))
(* eps (+ -1/2 (* 1/4 (* x x))))
(+ -1/2 (* 1/4 (* x x)))
-1/2
(* 1/4 (* x x))
1/4
(* x x)
x
(* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120))))))
(+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120)))))
1
(* x (* x (+ -1/6 (* (* x x) 1/120))))
(* x (+ -1/6 (* (* x x) 1/120)))
(+ -1/6 (* (* x x) 1/120))
-1/6
(* (* x x) 1/120)
1/120
(* (* eps eps) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps eps)
eps
(- (* -1/2 (cos x)) (/ (sin x) eps))
(* -1/2 (cos x))
-1/2
(cos x)
x
(/ (sin x) eps)
(sin x)
Outputs
(* (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))) -2)
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* (sin (* eps 1/2)) (sin (+ x (* eps 1/2))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(sin (* eps 1/2))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(sin (+ x (* eps 1/2)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(+ x (* eps 1/2))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
x
-2
#s(literal -2 binary64)
0
#s(literal 0 binary64)
(/ (* (- (* -1/2 eps) x) (* eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(* (- (* -1/2 eps) x) (* eps eps))
(*.f64 eps (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(- (* -1/2 eps) x)
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
eps
x
(* eps eps)
(*.f64 eps eps)
(* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120))))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (*.f64 x (-.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))))))))
eps
(- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120)))))))
(+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal 1/4 binary64)) (*.f64 x (-.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(* eps (+ -1/2 (* 1/4 (* x x))))
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(+ -1/2 (* 1/4 (* x x)))
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))
-1/2
#s(literal -1/2 binary64)
(* 1/4 (* x x))
(*.f64 #s(literal 1/4 binary64) (*.f64 x x))
1/4
#s(literal 1/4 binary64)
(* x x)
(*.f64 x x)
x
(* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))))
(+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120)))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))
1
#s(literal 1 binary64)
(* x (* x (+ -1/6 (* (* x x) 1/120))))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(* x (+ -1/6 (* (* x x) 1/120)))
(*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(+ -1/6 (* (* x x) 1/120))
(+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))
-1/6
#s(literal -1/6 binary64)
(* (* x x) 1/120)
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
1/120
#s(literal 1/120 binary64)
(* (* eps eps) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(* eps eps)
(*.f64 eps eps)
eps
(- (* -1/2 (cos x)) (/ (sin x) eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
x
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(sin x)
(sin.f64 x)

localize196.0ms (1.2%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(cos.f64 x)
accuracy100.0%
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
accuracy100.0%
(/.f64 (sin.f64 x) eps)
accuracy99.3%
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
accuracy99.8%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
accuracy99.8%
(*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
accuracy99.5%
(*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
accuracy100.0%
(*.f64 eps eps)
accuracy100.0%
(*.f64 #s(literal -1/2 binary64) eps)
accuracy99.9%
(*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps))
accuracy84.9%
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
accuracy100.0%
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
accuracy99.8%
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
accuracy99.8%
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
Results
99.0ms251×0valid
8.0ms3valid
2.0ms2valid
1.0ms1valid
Compiler

Compiled 267 to 40 computations (85% saved)

Precisions
Click to see histograms. Total time spent on operations: 70.0ms
ival-mult: 26.0ms (37.4% of total)
ival-add: 12.0ms (17.2% of total)
ival-sin: 12.0ms (17.2% of total)
...c/correct-round.rkt:119:19: 7.0ms (10.1% of total)
ival-div: 4.0ms (5.7% of total)
ival-sub: 4.0ms (5.7% of total)
ival-cos: 2.0ms (2.9% of total)
const: 1.0ms (1.4% of total)
backward-pass: 1.0ms (1.4% of total)

series19.0ms (0.1%)

Counts
22 → 408
Calls
Call 1
Inputs
#<alt (* (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))) -2)>
#<alt (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2))))>
#<alt (sin (* eps 1/2))>
#<alt (* eps 1/2)>
#<alt (/ (* (- (* -1/2 eps) x) (* eps eps)) eps)>
#<alt (* (- (* -1/2 eps) x) (* eps eps))>
#<alt (- (* -1/2 eps) x)>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120))))))))>
#<alt (- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120)))))))>
#<alt (* eps (+ -1/2 (* 1/4 (* x x))))>
#<alt (+ -1/2 (* 1/4 (* x x)))>
#<alt (* (* eps eps) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* eps eps)>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (* -1/2 (cos x))>
#<alt (sin (+ x (* eps 1/2)))>
#<alt (* x (+ -1/6 (* (* x x) 1/120)))>
#<alt (* (* x x) 1/120)>
#<alt (* x (* x (+ -1/6 (* (* x x) 1/120))))>
#<alt (/ (sin x) eps)>
#<alt (cos x)>
Outputs
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 x) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 x) (* -1/2 eps)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ x eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ x eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* -1 (* eps x))>
#<alt (* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 x) (* -1/2 eps)))>
#<alt (* (pow eps 2) (+ (* -1 x) (* -1/2 eps)))>
#<alt (* (pow eps 2) (+ (* -1 x) (* -1/2 eps)))>
#<alt (* -1/2 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -1 (/ x eps)) 1/2))>
#<alt (* (pow eps 3) (- (* -1 (/ x eps)) 1/2))>
#<alt (* (pow eps 3) (- (* -1 (/ x eps)) 1/2))>
#<alt (* -1/2 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))>
#<alt (* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))>
#<alt (* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))>
#<alt (* -1/2 (pow eps 3))>
#<alt (+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))>
#<alt (+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))>
#<alt (+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))>
#<alt (* -1 (* (pow eps 2) x))>
#<alt (* x (+ (* -1 (pow eps 2)) (* -1/2 (/ (pow eps 3) x))))>
#<alt (* x (+ (* -1 (pow eps 2)) (* -1/2 (/ (pow eps 3) x))))>
#<alt (* x (+ (* -1 (pow eps 2)) (* -1/2 (/ (pow eps 3) x))))>
#<alt (* -1 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2))))>
#<alt (* -1 (* x (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2))))>
#<alt (* -1 (* x (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2))))>
#<alt (* -1 x)>
#<alt (- (* -1/2 eps) x)>
#<alt (- (* -1/2 eps) x)>
#<alt (- (* -1/2 eps) x)>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1 (/ x eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (/ x eps))))>
#<alt (* -1 (* eps (+ 1/2 (/ x eps))))>
#<alt (* -1 (* eps (+ 1/2 (/ x eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (* -1 x)>
#<alt (* x (- (* -1/2 (/ eps x)) 1))>
#<alt (* x (- (* -1/2 (/ eps x)) 1))>
#<alt (* x (- (* -1/2 (/ eps x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))>
#<alt (* eps (+ (* -1 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 5) (+ (* -1/120 eps) (+ (* 1/6 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 3))))))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (+ (* 1/6 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 3)))))))>
#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/4 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps)))))>
#<alt (* -1 (* (pow x 5) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) (pow x 3))) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps)))))>
#<alt (* -1 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* -1/120 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 5) (- (+ (* 1/4 (/ eps (pow x 3))) (* 1/6 (/ 1 (pow x 2)))) 1/120))>
#<alt (* (pow x 5) (- (+ (* 1/4 (/ eps (pow x 3))) (* 1/6 (/ 1 (pow x 2)))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* -1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (* -1/4 (/ eps (pow x 3)))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (* -1 (/ (- (* 1/4 eps) (/ 1 x)) (pow x 3)))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* -1 (/ x eps)) 1/2)>
#<alt (- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)>
#<alt (- (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps))) 1/2)>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (- (* -1/2 (cos x)) (/ (sin x) eps))>
#<alt (* -1 (/ (sin x) eps))>
#<alt (/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)>
#<alt (/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)>
#<alt (/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)>
#<alt (* -1/2 (cos x))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (* -1/2 (cos x))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (* -1/6 x)>
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* 1/120 (pow x 3))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (/ x eps)>
#<alt (* x (+ (* -1/6 (/ (pow x 2) eps)) (/ 1 eps)))>
#<alt (* x (+ (* (pow x 2) (- (* 1/120 (/ (pow x 2) eps)) (* 1/6 (/ 1 eps)))) (/ 1 eps)))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/5040 (/ (pow x 2) eps)) (* 1/120 (/ 1 eps)))) (* 1/6 (/ 1 eps)))) (/ 1 eps)))>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt (/ (sin x) eps)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
Calls

102 calls:

TimeVariablePointExpression
1.0ms
eps
@0
(* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120))))))))
1.0ms
x
@inf
(* (* eps eps) (- (* -1/2 (cos x)) (/ (sin x) eps)))
1.0ms
x
@-inf
(* (* eps eps) (- (* -1/2 (cos x)) (/ (sin x) eps)))
1.0ms
eps
@inf
(* (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))) -2)
1.0ms
x
@-inf
(* (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))) -2)

rewrite327.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
3114×*-lowering-*.f32
3114×*-lowering-*.f64
2666×fma-lowering-fma.f32
2666×fma-lowering-fma.f64
2116×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038170
1221157
21925152
08627152
Stop Event
iter limit
node limit
Counts
22 → 444
Calls
Call 1
Inputs
(* (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))) -2)
(* (sin (* eps 1/2)) (sin (+ x (* eps 1/2))))
(sin (* eps 1/2))
(* eps 1/2)
(/ (* (- (* -1/2 eps) x) (* eps eps)) eps)
(* (- (* -1/2 eps) x) (* eps eps))
(- (* -1/2 eps) x)
(* -1/2 eps)
(* eps (- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120))))))))
(- (* eps (+ -1/2 (* 1/4 (* x x)))) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) 1/120)))))))
(* eps (+ -1/2 (* 1/4 (* x x))))
(+ -1/2 (* 1/4 (* x x)))
(* (* eps eps) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps eps)
(- (* -1/2 (cos x)) (/ (sin x) eps))
(* -1/2 (cos x))
(sin (+ x (* eps 1/2)))
(* x (+ -1/6 (* (* x x) 1/120)))
(* (* x x) 1/120)
(* x (* x (+ -1/6 (* (* x x) 1/120))))
(/ (sin x) eps)
(cos x)
Outputs
(/.f64 (*.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal 2 binary64))
(/.f64 (*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal -2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal -2 binary64))) #s(literal -2 binary64))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) #s(literal -2 binary64)))
(*.f64 (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(*.f64 (*.f64 (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) #s(literal -2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))
(+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) #s(literal 2 binary64)))
(fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))
(fma.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal -2 binary64))
(/.f64 (-.f64 (*.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x) (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal -1 binary64))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(*.f64 (sin.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
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(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64)))))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64))))))
(*.f64 (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64)))) (*.f64 x x))
(*.f64 (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64))))) x)
(*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64))))) #s(literal 1 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64)))))) x)
(exp.f64 (*.f64 (log.f64 (/.f64 eps (sin.f64 x))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(/.f64 #s(literal 1 binary64) (/.f64 eps (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 eps (sin.f64 x)))))
(/.f64 (sin.f64 x) eps)
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 eps (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) eps)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps))))
(pow.f64 (/.f64 eps (sin.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 eps (sin.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) eps))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) eps))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (sin.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(cos.f64 x)

simplify283.0ms (1.7%)

Algorithm
egg-herbie
Rules
5838×*-lowering-*.f32
5838×*-lowering-*.f64
3080×+-lowering-+.f64
3080×+-lowering-+.f32
1328×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04043827
113843411
244533372
084333372
Stop Event
iter limit
node limit
Counts
408 → 408
Calls
Call 1
Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* -1 (* eps x))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 x) (* -1/2 eps)))
(* (pow eps 2) (+ (* -1 x) (* -1/2 eps)))
(* (pow eps 2) (+ (* -1 x) (* -1/2 eps)))
(* -1/2 (pow eps 3))
(* (pow eps 3) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 3) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 3) (- (* -1 (/ x eps)) 1/2))
(* -1/2 (pow eps 3))
(* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))
(* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))
(* -1 (* (pow eps 3) (+ 1/2 (/ x eps))))
(* -1/2 (pow eps 3))
(+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))
(+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))
(+ (* -1 (* (pow eps 2) x)) (* -1/2 (pow eps 3)))
(* -1 (* (pow eps 2) x))
(* x (+ (* -1 (pow eps 2)) (* -1/2 (/ (pow eps 3) x))))
(* x (+ (* -1 (pow eps 2)) (* -1/2 (/ (pow eps 3) x))))
(* x (+ (* -1 (pow eps 2)) (* -1/2 (/ (pow eps 3) x))))
(* -1 (* (pow eps 2) x))
(* -1 (* x (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2))))
(* -1 (* x (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2))))
(* -1 (* x (+ (* 1/2 (/ (pow eps 3) x)) (pow eps 2))))
(* -1 x)
(- (* -1/2 eps) x)
(- (* -1/2 eps) x)
(- (* -1/2 eps) x)
(* -1/2 eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
(* eps (+ (* -1 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/120 (* eps (pow x 5)))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 5) (+ (* -1/120 eps) (+ (* 1/6 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 3))))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (+ (* 1/6 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 3)))))))
(* -1/120 (* eps (pow x 5)))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 5) (+ (* -1/4 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps)))))
(* -1 (* (pow x 5) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) (pow x 3))) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps)))))
(* -1 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* -1/120 (pow x 5))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 5) (- (+ (* 1/4 (/ eps (pow x 3))) (* 1/6 (/ 1 (pow x 2)))) 1/120))
(* (pow x 5) (- (+ (* 1/4 (/ eps (pow x 3))) (* 1/6 (/ 1 (pow x 2)))) (+ 1/120 (/ 1 (pow x 4)))))
(* -1/120 (pow x 5))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (* -1/4 (/ eps (pow x 3)))) (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (* -1 (/ (- (* 1/4 eps) (/ 1 x)) (pow x 3)))) (* 1/6 (/ 1 (pow x 2))))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* (pow eps 2) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* -1 (/ x eps)) 1/2)
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2)
(- (* x (- (* x (+ 1/4 (* 1/6 (/ x eps)))) (/ 1 eps))) 1/2)
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(- (* -1/2 (cos x)) (/ (sin x) eps))
(* -1 (/ (sin x) eps))
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(/ (- (* -1/2 (* eps (cos x))) (sin x)) eps)
(* -1/2 (cos x))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(* -1/2 (cos x))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
(+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(* -1/6 x)
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* 1/120 (pow x 2)) 1/6))
(* x (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 3))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* -1/6 (pow x 2))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(/ x eps)
(* x (+ (* -1/6 (/ (pow x 2) eps)) (/ 1 eps)))
(* x (+ (* (pow x 2) (- (* 1/120 (/ (pow x 2) eps)) (* 1/6 (/ 1 eps)))) (/ 1 eps)))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/5040 (/ (pow x 2) eps)) (* 1/120 (/ 1 eps)))) (* 1/6 (/ 1 eps)))) (/ 1 eps)))
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
(/ (sin x) eps)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
Outputs
(* -1 (* eps (sin x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))))) (sin.f64 x)))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+.f64 (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x x)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(+.f64 (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))) (*.f64 x (*.f64 x (+.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 x #s(literal 1/3 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(* 1/2 (* eps (sin x)))
(*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal 1/4 binary64)))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/12 binary64))) (*.f64 (cos.f64 x) #s(literal 1/4 binary64))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/4 binary64)) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal -1/12 binary64)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/48 binary64))))))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+.f64 (*.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+.f64 (*.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 x #s(literal -1/6 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1 (* eps x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(* eps (+ (* -1 x) (* -1/2 eps)))
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#s(literal -1/2 binary64)
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(+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x #s(literal -1/48 binary64))))))
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) #s(literal 1/1440 binary64))))))))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/6 binary64))))))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+.f64 (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 eps #s(literal 1/2 binary64))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/8 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/48 binary64)) (*.f64 (sin.f64 x) #s(literal -1/8 binary64)))))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (- x (* -1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (- x (* -1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (- x (* -1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (- x (* -1/2 eps)))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* x (- (* 1/120 (pow x 2)) 1/6))
(*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(* x (- (* 1/120 (pow x 2)) 1/6))
(*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(* x (- (* 1/120 (pow x 2)) 1/6))
(*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(* 1/120 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 3) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* 1/120 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* 1/120 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/120 binary64))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))
(* 1/120 (pow x 4))
(*.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x (*.f64 x x)) x))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* 1/120 (pow x 4))
(*.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x (*.f64 x x)) x))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(/ x eps)
(/.f64 x eps)
(* x (+ (* -1/6 (/ (pow x 2) eps)) (/ 1 eps)))
(*.f64 x (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 x (*.f64 x #s(literal -1/6 binary64))) eps)))
(* x (+ (* (pow x 2) (- (* 1/120 (/ (pow x 2) eps)) (* 1/6 (/ 1 eps)))) (/ 1 eps)))
(*.f64 x (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal -1/6 binary64) eps) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) eps)))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/5040 (/ (pow x 2) eps)) (* 1/120 (/ 1 eps)))) (* 1/6 (/ 1 eps)))) (/ 1 eps)))
(*.f64 x (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (+.f64 (*.f64 (/.f64 (*.f64 x x) eps) #s(literal -1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) eps)))) (/.f64 #s(literal -1/6 binary64) eps)))))
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
(/ (sin x) eps)
(/.f64 (sin.f64 x) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

eval101.0ms (0.6%)

Compiler

Compiled 31434 to 2197 computations (93% saved)

prune104.0ms (0.6%)

Pruning

46 alts after pruning (39 fresh and 7 done)

PrunedKeptTotal
New86917886
Fresh112233
Picked145
Done033
Total88146927
Accuracy
100.0%
Counts
927 → 46
Alt Table
Click to see full alt table
StatusAccuracyProgram
70.3%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
24.2%
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps eps)) eps) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))) (*.f64 eps eps))
81.1%
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
56.5%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
56.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
79.2%
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
54.1%
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
99.5%
(+.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
96.7%
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
96.1%
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
99.5%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
99.5%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
99.4%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
99.2%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
99.6%
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
31.7%
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
79.3%
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
98.7%
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
98.7%
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) eps) (sin.f64 x))))
80.6%
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
97.7%
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)))
95.7%
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
95.6%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
54.5%
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
55.2%
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
96.1%
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
79.6%
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
2.9%
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
79.5%
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
32.9%
(*.f64 eps (/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) eps) #s(literal 1/36 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 eps eps)) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 eps eps))))
8.0%
(*.f64 eps (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) #s(literal 3 binary64))) (+.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))) (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))))))
99.5%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))))) (sin.f64 x)))
96.9%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
96.7%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
96.1%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
79.4%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
99.2%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
96.6%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
98.2%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
99.5%
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
96.7%
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
54.5%
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
96.1%
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
55.5%
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
80.9%
(neg.f64 (*.f64 eps (sin.f64 x)))
54.1%
#s(literal 0 binary64)
Compiler

Compiled 2173 to 934 computations (57% saved)

regimes64.0ms (0.4%)

Counts
75 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(*.f64 eps (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) eps) (sin.f64 x))))
(+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (sin.f64 x)))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)) (*.f64 eps eps)) eps)
(*.f64 (*.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(+.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 eps eps))) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps eps)) eps) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))) (*.f64 eps eps))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps (*.f64 eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))) (*.f64 eps (*.f64 eps eps)))
(*.f64 eps (/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) eps) #s(literal 1/36 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 eps eps)) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 eps eps))))
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
(*.f64 eps (/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) #s(literal 3 binary64))) (+.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))) (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))))))
Outputs
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)))
Calls

3 calls:

21.0ms
eps
20.0ms
x
16.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
99.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes58.0ms (0.3%)

Counts
70 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(*.f64 eps (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) eps) (sin.f64 x))))
(+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (sin.f64 x)))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)) (*.f64 eps eps)) eps)
(*.f64 (*.f64 (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(+.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (*.f64 (sin.f64 x) eps)) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x)) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 eps eps))) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps eps)) eps) (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))) (*.f64 eps eps))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) (*.f64 eps (*.f64 eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))))) (*.f64 eps (*.f64 eps eps)))
(*.f64 eps (/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) eps) #s(literal 1/36 binary64)) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 eps eps)) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) #s(literal 1 binary64)) (*.f64 eps eps))))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
Calls

3 calls:

19.0ms
x
18.0ms
eps
15.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.6%1x
99.6%1eps
99.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes54.0ms (0.3%)

Counts
55 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(*.f64 eps (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
Outputs
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
Calls

3 calls:

20.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
15.0ms
x
14.0ms
eps
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
99.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Counts
49 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
Outputs
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
Calls

2 calls:

14.0ms
eps
13.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes29.0ms (0.2%)

Counts
47 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
Outputs
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
Calls

2 calls:

13.0ms
x
12.0ms
eps
Results
AccuracySegmentsBranch
99.4%1x
99.4%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes28.0ms (0.2%)

Counts
45 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (sin.f64 x)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (/.f64 (sin.f64 x) eps))))
Outputs
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
Calls

2 calls:

13.0ms
x
12.0ms
eps
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes26.0ms (0.2%)

Counts
41 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps))
Outputs
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
Calls

2 calls:

12.0ms
eps
11.0ms
x
Results
AccuracySegmentsBranch
98.2%1x
98.2%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes24.0ms (0.1%)

Counts
37 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(neg.f64 (*.f64 eps (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
Outputs
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
Calls

2 calls:

11.0ms
x
10.0ms
eps
Results
AccuracySegmentsBranch
96.9%1x
96.9%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes20.0ms (0.1%)

Counts
33 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (*.f64 (*.f64 eps (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (*.f64 eps (+.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal -1/120 binary64))))) (*.f64 eps #s(literal 1/6 binary64)))) eps))
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
Outputs
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
Calls

2 calls:

9.0ms
x
9.0ms
eps
Results
AccuracySegmentsBranch
96.7%1eps
96.7%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

Counts
24 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) (*.f64 eps eps)) eps)
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64)))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 eps #s(literal 1/4 binary64)))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (*.f64 eps eps)) eps)
(*.f64 x (-.f64 (*.f64 (*.f64 x x) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))) eps))
(*.f64 (*.f64 eps x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
Outputs
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
Calls

2 calls:

8.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
96.1%1eps
96.1%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts
15 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) eps)
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))))
(*.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
(+.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps x))) eps)
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
Outputs
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
Calls

2 calls:

5.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
96.1%1x
96.1%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
5 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
Outputs
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
Calls

2 calls:

2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
79.2%1eps
79.2%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
4 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
Outputs
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
Calls

2 calls:

3.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
55.2%1x
55.2%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
Outputs
#s(literal 0 binary64)
Calls

2 calls:

1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
54.1%1x
54.1%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify21.0ms (0.1%)

Algorithm
egg-herbie
Rules
124×*-commutative_binary64
72×+-commutative_binary64
42×sub-neg_binary64
34×neg-mul-1_binary64
32×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089205
1165205
2188205
3203205
4221205
5240205
6256205
7268205
8283205
9295205
10301205
11304205
12305205
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
#s(literal 0 binary64)
Outputs
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps)))
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))))) eps (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps (cos.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))))))))
(*.f64 x (-.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x) eps))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(-.f64 #s(literal 0 binary64) (*.f64 x eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
#s(literal 0 binary64)

soundness2.2s (13.3%)

Rules
5838×*-lowering-*.f32
5838×*-lowering-*.f64
5490×*-lowering-*.f32
5490×*-lowering-*.f64
5110×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105481
1304458
2777457
32938457
08476457
0616
15016
241216
3524716
0806116
033130
1178124
21852124
08466124
03054500
110743847
237483732
080213732
04043827
113843411
244533372
084333372
038174
1204166
21733162
08620162
03803250
113102852
242372792
082872792
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 657 to 397 computations (39.6% saved)

preprocess92.0ms (0.6%)

Compiler

Compiled 464 to 208 computations (55.2% saved)

end0.0ms (0%)

Profiling

Loading profile data...