2cos (problem 3.3.5)

Time bar (total: 17.2s)

analyze69.0ms (0.4%)

Algorithm
1×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: 43.0ms
...c/correct-round.rkt:119:19: 11.0ms (25.8% of total)
ival-add: 8.0ms (18.8% of total)
ival-cos: 8.0ms (18.8% of total)
ival-mult: 3.0ms (7% of total)
ival-<=: 3.0ms (7% of total)
ival-fabs: 2.0ms (4.7% of total)
ival-sub: 2.0ms (4.7% of total)
ival-and: 2.0ms (4.7% of total)
ival-<: 2.0ms (4.7% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample9.4s (54.5%)

Results
3.6s25888×0precondition
3.4s5734×2valid
740.0ms2434×1valid
13.0ms88×0valid
Precisions
Click to see histograms. Total time spent on operations: 5.9s
ival-cos: 2.5s (43.1% of total)
...c/correct-round.rkt:119:19: 809.0ms (13.7% of total)
backward-pass: 461.0ms (7.8% of total)
ival-mult: 352.0ms (6% of total)
ival-<: 330.0ms (5.6% of total)
ival-add: 318.0ms (5.4% of total)
ival-fabs: 295.0ms (5% of total)
ival-sub: 294.0ms (5% of total)
ival-<=: 274.0ms (4.6% of total)
ival-and: 190.0ms (3.2% of total)
const: 42.0ms (0.7% of total)
Bogosity

preprocess50.0ms (0.3%)

Algorithm
2×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
1×iter limit
1×saturated
1×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))

explain339.0ms (2%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1540-0-(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
10-0-(cos.f64 (+.f64 x eps))
00-0-x
00-0-(+.f64 x eps)
00-0-(cos.f64 x)
00-0-eps
Results
242.0ms334×2valid
64.0ms174×1valid
1.0ms4×0valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 172.0ms
ival-cos: 108.0ms (62.7% of total)
ival-add: 37.0ms (21.5% of total)
backward-pass: 19.0ms (11% of total)
ival-sub: 8.0ms (4.6% of total)
const: 0.0ms (0% 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
▶45.9%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify14.0ms (0.1%)

Algorithm
1×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
1×iter limit
1×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)

localize153.0ms (0.9%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 x eps)
✓accuracy100.0%
(cos.f64 x)
✓accuracy99.9%
(cos.f64 (+.f64 x eps))
✓accuracy45.9%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
126.0ms167×2valid
17.0ms87×1valid
0.0ms2×0valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 104.0ms
ival-cos: 49.0ms (47% of total)
backward-pass: 47.0ms (45.1% of total)
ival-add: 5.0ms (4.8% of total)
ival-sub: 4.0ms (3.8% 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)

rewrite294.0ms (1.7%)

Algorithm
1×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
0806216
Stop Event
1×iter limit
1×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)

simplify199.0ms (1.2%)

Algorithm
1×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
1×iter limit
1×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)

eval44.0ms (0.3%)

Compiler

Compiled 6681 to 740 computations (88.9% saved)

prune32.0ms (0.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2489257
Fresh000
Picked011
Done000
Total24810258
Accuracy
99.8%
Counts
258 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶45.9%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
76.6%
(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))
45.1%
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
✓45.9%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶44.7%
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
76.2%
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
▶44.7%
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶99.8%
(*.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 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
99.6%
(*.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 255 to 180 computations (29.4% saved)

simplify136.0ms (0.8%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(cos.f64 x)
✓cost-diff0
(*.f64 (cos.f64 x) (cos.f64 eps))
✓cost-diff0
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))
✓cost-diff6400
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
✓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
(+.f64 x eps)
✓cost-diff0
(cos.f64 (+.f64 x eps))
✓cost-diff0
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
✓cost-diff0
(cos.f64 eps)
✓cost-diff0
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓cost-diff0
(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓cost-diff0
(*.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-diff0
(*.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))
✓cost-diff128
(+.f64 eps #s(literal 0 binary64))
Rules
2564×fnmadd-define
2096×sum5-define
1780×sum3-define
1512×sum4-define
1408×fma-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033166
167160
2160160
3447160
41096160
51801160
64136160
77102160
08314160
Stop Event
1×iter limit
1×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
(- (cos (+ x eps)) 1)
(cos (+ x eps))
(+ x eps)
x
eps
1
(* 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)
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
(* (cos x) (cos eps))
(cos x)
x
(cos eps)
eps
(* (sin x) (sin eps))
(sin x)
(sin eps)
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)
(- (cos (+ x eps)) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x)))
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
1
#s(literal 1 binary64)
(* eps (- (* eps (* -1/2 (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))) (sin x))
(-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(* eps (* -1/2 (cos x)))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (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)
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
(-.f64 (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))
(* (cos x) (cos eps))
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos x)
(cos.f64 x)
x
(cos eps)
(cos.f64 eps)
eps
(* (sin x) (sin eps))
(*.f64 (sin.f64 x) (sin.f64 eps))
(sin x)
(sin.f64 x)
(sin eps)
(sin.f64 eps)

localize694.0ms (4%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 (cos.f64 x) (cos.f64 eps))
✓accuracy100.0%
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))
✓accuracy100.0%
(*.f64 (sin.f64 x) (sin.f64 eps))
✓accuracy45.9%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
✓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 x eps)
✓accuracy99.9%
(cos.f64 (+.f64 x eps))
✓accuracy46.1%
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
✓accuracy100.0%
(cos.f64 eps)
✓accuracy47.4%
(+.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))
✓accuracy99.9%
(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
534.0ms166×2valid
101.0ms88×1valid
4.0ms1×3valid
1.0ms1×0valid
Compiler

Compiled 183 to 34 computations (81.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 438.0ms
ival-cos: 157.0ms (35.8% of total)
ival-sin: 124.0ms (28.3% of total)
ival-add: 60.0ms (13.7% of total)
backward-pass: 41.0ms (9.4% of total)
ival-mult: 34.0ms (7.8% of total)
ival-sub: 13.0ms (3% of total)
ival-div: 8.0ms (1.8% of total)
const: 2.0ms (0.5% of total)

series31.0ms (0.2%)

Counts
19 → 384
Calls
Call 1
Inputs
#<alt (+ eps 0)>
#<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 (+ (cos eps) -1)>
#<alt (cos eps)>
#<alt (- (cos (+ x eps)) 1)>
#<alt (cos (+ x eps))>
#<alt (+ x eps)>
#<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 (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))>
#<alt (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))>
#<alt (* (cos x) (cos eps))>
#<alt (cos x)>
#<alt (sin (/ (+ eps (* x 2)) 2))>
#<alt (* (sin x) (sin eps))>
Outputs
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<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 (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 (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (- eps (* -1 x))) 1)>
#<alt (- (cos (- eps (* -1 x))) 1)>
#<alt (- (cos (- eps (* -1 x))) 1)>
#<alt (- (cos (- eps (* -1 x))) 1)>
#<alt (- (cos x) 1)>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) 1)>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) 1)>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (- x (* -1 eps))) 1)>
#<alt (- (cos (- x (* -1 eps))) 1)>
#<alt (- (cos (- x (* -1 eps))) 1)>
#<alt (- (cos (- x (* -1 eps))) 1)>
#<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 (* 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 (- (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) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin 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) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin 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) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))>
#<alt (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))>
#<alt (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos 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 (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 (* x (sin eps))>
#<alt (* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
Calls

96 calls:

TimeVariablePointExpression
5.0ms
eps
@0
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
3.0ms
x
@inf
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos 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
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))

rewrite382.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
5646×*-lowering-*.f32
5646×*-lowering-*.f64
3130×+-lowering-+.f64
3130×+-lowering-+.f32
3000×/-lowering-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033111
1193108
21920108
010845108
Stop Event
1×iter limit
1×node limit
Counts
19 → 427
Calls
Call 1
Inputs
(+ eps 0)
(* (* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (sin (/ (+ eps 0) 2)) (sin (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(+ (cos eps) -1)
(cos eps)
(- (cos (+ x eps)) 1)
(cos (+ x eps))
(+ x eps)
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
(- (* eps (* -1/2 (cos x))) (sin x))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
(* (cos x) (cos eps))
(cos x)
(sin (/ (+ eps (* x 2)) 2))
(* (sin x) (sin eps))
Outputs
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (neg.f64 (/.f64 #s(literal 0 binary64) eps)))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) (neg.f64 (/.f64 #s(literal 0 binary64) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (neg.f64 (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))))
(/.f64 (neg.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) (neg.f64 (cos.f64 (-.f64 x eps))))
(/.f64 (+.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 (pow.f64 (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))) #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (pow.f64 (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))) #s(literal 2 binary64))) (-.f64 (cos.f64 (+.f64 eps x)) (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps)))))
(/.f64 (*.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal 1 binary64)) (cos.f64 (-.f64 x eps)))
(/.f64 (-.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))))) #s(literal -2 binary64))
(/.f64 (+.f64 #s(literal -2 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))))) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) #s(literal -2 binary64)))
(/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))))) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) #s(literal 2 binary64)))
(/.f64 (+.f64 (*.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))))) #s(literal -4 binary64))
(/.f64 (+.f64 (*.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))))) #s(literal 4 binary64))
(/.f64 (+.f64 (*.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))))) #s(literal 4 binary64))
(/.f64 (+.f64 (*.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))))) #s(literal -4 binary64))
(/.f64 (+.f64 (*.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))))) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))))))
(/.f64 (+.f64 (*.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))))) #s(literal -4 binary64))
(/.f64 (+.f64 (*.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))))) #s(literal 4 binary64))
(/.f64 (+.f64 (*.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))))))
(/.f64 (+.f64 (*.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))))) #s(literal 4 binary64))
(/.f64 (+.f64 (*.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))))) #s(literal -4 binary64))
(pow.f64 (/.f64 (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps)))) (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (cos.f64 (-.f64 x eps)) (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64))
(*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(*.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))))
(*.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))))
(/.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps)))) #s(literal -1 binary64))
(*.f64 (cos.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(*.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64))
(cos.f64 x)
(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))))
(-.f64 (/.f64 (cos.f64 (-.f64 x eps)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))))
(/.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (sin.f64 eps))
(*.f64 (sin.f64 eps) (sin.f64 x))
(*.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64))

simplify258.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
5588×*-lowering-*.f32
5588×*-lowering-*.f64
2740×+-lowering-+.f64
2740×+-lowering-+.f32
1500×neg-lowering-neg.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04033429
113743052
244283027
080303027
Stop Event
1×iter limit
1×node limit
Counts
384 → 384
Calls
Call 1
Inputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -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 (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)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (- eps (* -1 x))) 1)
(- (cos (- eps (* -1 x))) 1)
(- (cos (- eps (* -1 x))) 1)
(- (cos (- eps (* -1 x))) 1)
(- (cos x) 1)
(- (+ (cos x) (* -1 (* eps (sin x)))) 1)
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) 1)
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (- x (* -1 eps))) 1)
(- (cos (- x (* -1 eps))) 1)
(- (cos (- x (* -1 eps))) 1)
(- (cos (- x (* -1 eps))) 1)
(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 (* 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))
(- (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) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin 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) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(cos 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) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(- (* (cos eps) (cos x)) (* (sin eps) (sin x)))
(cos eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(cos x)
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos 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)
(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))))
(* x (sin eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* eps (sin x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
Outputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -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 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 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))) (sin.f64 x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 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 (* 2 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 (* 2 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 (* 2 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 (- (* 2 x) (* -1 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 (- (* 2 x) (* -1 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 (- (* 2 x) (* -1 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 (- (* 2 x) (* -1 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 (*.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) (*.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 (+.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))))) (*.f64 x x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 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 (* 2 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 (* 2 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 (* 2 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 (* -2 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 (* -2 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 (* -2 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 (* -2 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 (cos.f64 x) (*.f64 eps #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))
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(+ (* 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))
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(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+.f64 (sin.f64 x) (*.f64 eps (*.f64 (cos.f64 x) #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 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/8 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 (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(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 (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* x (sin eps))
(*.f64 x (sin.f64 eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(*.f64 x (*.f64 (+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64)) (sin.f64 eps)))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(*.f64 x (+.f64 (sin.f64 eps) (*.f64 (*.f64 x (*.f64 x (sin.f64 eps))) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(*.f64 x (+.f64 (*.f64 (+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (sin.f64 eps))) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(*.f64 eps (*.f64 (+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) (sin.f64 x)))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(*.f64 eps (+.f64 (sin.f64 x) (*.f64 (*.f64 eps (*.f64 eps (sin.f64 x))) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))

eval98.0ms (0.6%)

Compiler

Compiled 16563 to 1605 computations (90.3% saved)

prune74.0ms (0.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New84216858
Fresh224
Picked505
Done101
Total85018868
Accuracy
100.0%
Counts
868 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
45.9%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (*.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))))))) #s(literal 1 binary64))) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
76.6%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))
76.2%
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
99.5%
(+.f64 (*.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
98.4%
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))) (*.f64 x x)))
▶97.6%
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))
▶44.7%
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
▶99.8%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps 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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.8%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 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))
99.7%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (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 #s(literal 1/2 binary64)) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
▶97.7%
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
▶99.1%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
97.6%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
99.6%
(*.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)))))
98.4%
(*.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))))))))
97.6%
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
46.3%
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
Compiler

Compiled 642 to 442 computations (31.2% saved)

simplify153.0ms (0.9%)

Algorithm
1×egg-herbie
Localize:

Found 17 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-diff128
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
✓cost-diff0
(sin.f64 x)
✓cost-diff0
(*.f64 eps #s(literal -1/2 binary64))
✓cost-diff0
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))
✓cost-diff0
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
✓cost-diff0
(*.f64 x (-.f64 (*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps))
✓cost-diff0
(*.f64 eps #s(literal -1/2 binary64))
✓cost-diff0
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
✓cost-diff256
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))
✓cost-diff128
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps 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)))))))
✓cost-diff0
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps 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))))))))
✓cost-diff0
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps 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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓cost-diff0
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps 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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
Rules
3486×*-lowering-*.f32
3486×*-lowering-*.f64
2528×+-lowering-+.f64
2528×+-lowering-+.f32
1866×distribute-lft-in
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
044280
1114256
2351256
31036256
43060255
56683252
08165252
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
eps
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
1/2
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(* eps eps)
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))
-1/48
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(+ 1/3840 (* (* eps eps) -1/645120))
1/3840
(* (* eps eps) -1/645120)
-1/645120
(sin (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
-2
(+ 1 -1)
1
-1
(+ (* eps (* eps -1/2)) (* x (- (* x (* eps (* eps 1/4))) eps)))
(* eps (* eps -1/2))
eps
(* eps -1/2)
-1/2
(* x (- (* x (* eps (* eps 1/4))) eps))
x
(- (* x (* eps (* eps 1/4))) eps)
(* x (* eps (* eps 1/4)))
(* eps (* eps 1/4))
(* eps 1/4)
1/4
(* eps (- (* eps -1/2) (sin x)))
eps
(- (* eps -1/2) (sin x))
(* eps -1/2)
-1/2
(sin x)
x
(* (* 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
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2))) -2)
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 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))))))))) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal -2 binary64))))
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 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))))))))) (*.f64 eps (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 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))))))))))
eps
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 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)))))))))
1/2
#s(literal 1/2 binary64)
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(*.f64 eps (*.f64 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))))))))
(* eps eps)
(*.f64 eps eps)
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))
(+.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))))))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))
(+ 1/3840 (* (* eps eps) -1/645120))
(+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))
1/3840
#s(literal 1/3840 binary64)
(* (* eps eps) -1/645120)
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
-1/645120
#s(literal -1/645120 binary64)
(sin (/ (+ eps (* x 2)) 2))
(sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
-2
#s(literal -2 binary64)
(+ 1 -1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
-1
#s(literal -1 binary64)
(+ (* eps (* eps -1/2)) (* x (- (* x (* eps (* eps 1/4))) eps)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
(* eps (* eps -1/2))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
eps
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* x (- (* x (* eps (* eps 1/4))) eps))
(*.f64 eps (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 x #s(literal 1/4 binary64))))))
x
(- (* x (* eps (* eps 1/4))) eps)
(*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(* x (* eps (* eps 1/4)))
(*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64))))
(* eps (* eps 1/4))
(*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))
(* eps 1/4)
(*.f64 eps #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(* eps (- (* eps -1/2) (sin x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
eps
(- (* eps -1/2) (sin x))
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(sin x)
(sin.f64 x)
x
(* (* eps eps) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (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)

localize188.0ms (1.1%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(cos.f64 x)
✓accuracy100.0%
(/.f64 (sin.f64 x) eps)
✓accuracy100.0%
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps))
✓accuracy98.1%
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)))
✓accuracy100.0%
(*.f64 eps #s(literal -1/2 binary64))
✓accuracy100.0%
(sin.f64 x)
✓accuracy100.0%
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))
✓accuracy99.8%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
✓accuracy100.0%
(*.f64 eps #s(literal 1/4 binary64))
✓accuracy100.0%
(*.f64 eps #s(literal -1/2 binary64))
✓accuracy99.9%
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))
✓accuracy99.8%
(*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64))))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓accuracy99.8%
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps 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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓accuracy99.8%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
✓accuracy99.8%
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
✓accuracy99.7%
(*.f64 (*.f64 eps 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))))))
Results
132.0ms254×0valid
3.0ms1×3valid
1.0ms1×1valid
Compiler

Compiled 323 to 44 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.0ms
ival-mult: 25.0ms (44.5% of total)
...c/correct-round.rkt:119:19: 9.0ms (16% of total)
ival-add: 6.0ms (10.7% of total)
ival-sin: 5.0ms (8.9% of total)
ival-div: 4.0ms (7.1% of total)
ival-sub: 3.0ms (5.3% of total)
ival-cos: 2.0ms (3.6% of total)
const: 1.0ms (1.8% of total)
backward-pass: 1.0ms (1.8% of total)

series31.0ms (0.2%)

Counts
23 → 384
Calls
Call 1
Inputs
#<alt (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2))) -2)>
#<alt (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2)))>
#<alt (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))>
#<alt (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))>
#<alt (+ 1 -1)>
#<alt (+ (* eps (* eps -1/2)) (* x (- (* x (* eps (* eps 1/4))) eps)))>
#<alt (* eps (* eps -1/2))>
#<alt (* eps -1/2)>
#<alt (* x (- (* x (* eps (* eps 1/4))) eps))>
#<alt (* eps (- (* eps -1/2) (sin x)))>
#<alt (- (* eps -1/2) (sin x))>
#<alt (sin 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 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))>
#<alt (* (* eps eps) -1/645120)>
#<alt (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))>
#<alt (* x (* eps (* eps 1/4)))>
#<alt (* eps 1/4)>
#<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 (* 1/322560 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/322560 (sin (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))>
#<alt (* (pow eps 7) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 6))) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))))>
#<alt (* 1/322560 (* (pow eps 7) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6)))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<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 (* -1/645120 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 7) (+ (* -1/645120 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
#<alt (* (pow eps 7) (+ (* -1/48 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))>
#<alt (* (pow eps 7) (+ (* -1/48 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (sin (* 1/2 (+ eps (* 2 x))))) (+ (* 1/3840 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/2 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))))>
#<alt (* -1/645120 (* (pow eps 7) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/645120 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/2 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/3840 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))>
#<alt (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))>
#<alt (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<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 (* -1/645120 (pow eps 7))>
#<alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 7))>
#<alt (* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 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 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ 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 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ 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) (* 1/4 (* (pow eps 2) x)))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<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 (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))>
#<alt (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))>
#<alt (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* 1/4 (* eps (pow x 2)))))>
#<alt (* eps (+ (* -1 x) (* 1/4 (* eps (pow x 2)))))>
#<alt (* eps (+ (* -1 x) (* 1/4 (* eps (pow x 2)))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 eps)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (sin x) eps)) 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) (* 1/6 (* eps (pow x 2))))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* eps (- (* -1/2 eps) (sin x)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* eps (- (* -1 (/ (sin x) eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ 1/2 (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 eps) (sin x))>
#<alt (- (* -1/2 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 (* (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 (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<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

96 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(* x (- (* x (* eps (* eps 1/4))) eps))
2.0ms
x
@inf
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2))) -2)
1.0ms
x
@0
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2))) -2)
1.0ms
eps
@inf
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2))) -2)
1.0ms
x
@-inf
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2))) -2)

rewrite276.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
2948×*-lowering-*.f32
2948×*-lowering-*.f64
2930×fma-lowering-fma.f32
2930×fma-lowering-fma.f64
2098×/-lowering-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
044202
1226184
22007184
08329184
Stop Event
1×iter limit
1×node limit
Counts
23 → 340
Calls
Call 1
Inputs
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2))) -2)
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (sin (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(+ 1 -1)
(+ (* eps (* eps -1/2)) (* x (- (* x (* eps (* eps 1/4))) eps)))
(* eps (* eps -1/2))
(* eps -1/2)
(* x (- (* x (* eps (* eps 1/4))) eps))
(* eps (- (* eps -1/2) (sin x)))
(- (* eps -1/2) (sin x))
(sin x)
(* (* eps eps) (- (* -1/2 (cos x)) (/ (sin x) eps)))
(* eps eps)
(- (* -1/2 (cos x)) (/ (sin x) eps))
(* -1/2 (cos x))
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(* (* eps eps) -1/645120)
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(* x (* eps (* eps 1/4)))
(* eps 1/4)
(/ (sin x) eps)
(cos x)
Outputs
(*.f64 eps (*.f64 (+.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 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
(*.f64 eps (*.f64 (*.f64 (+.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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(*.f64 (+.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 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
(*.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))))))))) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.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))))))))) #s(literal -2 binary64)))
(*.f64 (*.f64 (+.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 eps (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (+.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 eps (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -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))))))))))
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(cos.f64 x)

simplify268.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
5404×*-lowering-*.f32
5404×*-lowering-*.f64
2054×+-lowering-+.f64
2054×+-lowering-+.f32
1314×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04064425
114133621
248433531
081943531
Stop Event
1×iter limit
1×node limit
Counts
384 → 384
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)))))))))
(* 1/322560 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/322560 (sin (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(* (pow eps 7) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 6))) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))))
(* 1/322560 (* (pow eps 7) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 7) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6)))))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 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))))))))))
(* -1/645120 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 7) (+ (* -1/645120 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 7) (+ (* -1/48 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))
(* (pow eps 7) (+ (* -1/48 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (sin (* 1/2 (+ eps (* 2 x))))) (+ (* 1/3840 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/2 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))))
(* -1/645120 (* (pow eps 7) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 7) (+ (* -1/3840 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/645120 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 7) (+ (* -1/3840 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))
(* -1 (* (pow eps 7) (+ (* -1/2 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/3840 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))
(* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))
(* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
(* 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))))
(* -1/645120 (pow eps 7))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 7))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
1/2
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ 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) (* 1/4 (* (pow eps 2) x)))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))
(* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -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))
(* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))
(* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))
(* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* 1/4 (* eps (pow x 2)))))
(* eps (+ (* -1 x) (* 1/4 (* eps (pow x 2)))))
(* eps (+ (* -1 x) (* 1/4 (* eps (pow x 2)))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* (pow eps 2) (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 eps)))
(* eps (+ (* -1 (sin x)) (* -1/2 eps)))
(* eps (+ (* -1 (sin x)) (* -1/2 eps)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* eps (- (* -1/2 eps) (sin x)))
(* -1 (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(- (* -1/2 eps) (sin x))
(* -1/2 eps)
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* eps (- (* -1 (/ (sin x) eps)) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1 (* eps (+ 1/2 (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* -1/2 eps) (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)))
(- (* -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) (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)))))))
(* (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))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 (* (pow eps 2) x))
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(/ 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 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (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 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 (cos.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (sin.f64 x)))
(* 1/322560 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/322560 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/322560 (sin (* 1/2 (+ eps (* 2 x)))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/1920 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (*.f64 #s(literal 1/322560 binary64) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))))
(* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/1920 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (+.f64 (*.f64 #s(literal 1/322560 binary64) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/24 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))))
(* (pow eps 7) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 6))) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (+.f64 (*.f64 #s(literal 1/322560 binary64) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/24 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) (-.f64 (*.f64 #s(literal -1/1920 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64))))))
(* 1/322560 (* (pow eps 7) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/322560 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* -1 (* (pow eps 7) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/1920 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (*.f64 #s(literal 1/322560 binary64) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))))
(* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(*.f64 (+.f64 (*.f64 (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal 1/1920 binary64)) (+.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -1/322560 binary64)) (*.f64 (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal -1/24 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6)))))))
(*.f64 (+.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -1/322560 binary64)) (+.f64 (+.f64 (*.f64 (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal 1/1920 binary64)) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64)))) (*.f64 (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal -1/24 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 #s(literal -2 binary64) (*.f64 eps (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.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)))))))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))
(*.f64 #s(literal -2 binary64) (*.f64 eps (*.f64 (+.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 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))
(+.f64 (*.f64 (*.f64 (+.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 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 eps #s(literal -2 binary64))) (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.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 eps (*.f64 x x)) (*.f64 eps #s(literal -2 binary64)))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
(+.f64 (*.f64 #s(literal -2 binary64) (*.f64 eps (*.f64 (+.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 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))) (*.f64 x (*.f64 x (*.f64 (+.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 eps (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #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 (cos.f64 x) (*.f64 eps #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 (cos.f64 x) (*.f64 eps #s(literal -1/48 binary64)))))))))
(* -1/645120 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1/645120 binary64)))
(* (pow eps 7) (+ (* -1/645120 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
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(+ 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 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)

eval86.0ms (0.5%)

Compiler

Compiled 23588 to 1998 computations (91.5% saved)

prune69.0ms (0.4%)

Pruning

27 alts after pruning (26 fresh and 1 done)

PrunedKeptTotal
New79219811
Fresh6713
Picked415
Done000
Total80227829
Accuracy
100.0%
Counts
829 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶97.7%
(fma.f64 (-.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
45.9%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (*.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))))))) #s(literal 1 binary64))) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
76.6%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))
76.2%
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
75.1%
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
▶98.7%
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
97.6%
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 eps x)))
99.2%
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
98.4%
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
▶99.8%
(*.f64 (+.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 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
99.8%
(*.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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
99.7%
(*.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))
99.5%
(*.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))
99.8%
(*.f64 (*.f64 eps (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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)))))))))) #s(literal -2 binary64))
95.8%
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
95.7%
(*.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)))))
45.1%
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
▶97.6%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
98.8%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))))
98.7%
(*.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)))))))))
98.3%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
✓99.1%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
97.6%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
99.6%
(*.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)))))
98.4%
(*.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))))))))
99.0%
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
▶44.7%
#s(literal 0 binary64)
Compiler

Compiled 958 to 651 computations (32% saved)

simplify149.0ms (0.9%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))
✓cost-diff0
(*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))
✓cost-diff0
(-.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) eps)
✓cost-diff6528
(fma.f64 (-.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
✓cost-diff0
(*.f64 eps #s(literal -1/2 binary64))
✓cost-diff0
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
✓cost-diff0
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
✓cost-diff128
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
✓cost-diff0
(+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
✓cost-diff0
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))))
✓cost-diff0
(-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
✓cost-diff0
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
✓cost-diff0
(*.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))))))
✓cost-diff0
(*.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)))))))
✓cost-diff0
(+.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))))))))
✓cost-diff0
(*.f64 (+.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 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
Rules
3126×*-lowering-*.f32
3126×*-lowering-*.f64
2560×+-lowering-+.f64
2560×+-lowering-+.f32
1642×distribute-lft-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050324
1141294
2435291
31244290
43398290
57718290
08024290
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps (* (sin (/ (+ eps (* x 2)) 2)) -2)))
(+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
1/2
(* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
eps
(* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))
-1/48
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(* eps eps)
(+ 1/3840 (* (* eps eps) -1/645120))
1/3840
(* (* eps eps) -1/645120)
-1/645120
(* eps (* (sin (/ (+ eps (* x 2)) 2)) -2))
(* (sin (/ (+ eps (* x 2)) 2)) -2)
(sin (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
-2
0
(* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) x))
eps
(- (* eps (+ -1/2 (* x (* x 1/4)))) x)
(* eps (+ -1/2 (* x (* x 1/4))))
(+ -1/2 (* x (* x 1/4)))
-1/2
(* x (* x 1/4))
x
(* x 1/4)
1/4
(+ (* eps (- (* eps -1/2) x)) (* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x)))
(* eps (- (* eps -1/2) x))
eps
(- (* eps -1/2) x)
(* eps -1/2)
-1/2
x
(* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x))
(* x x)
(* (* eps (+ 1/6 (* (* x x) -1/120))) x)
(* eps (+ 1/6 (* (* x x) -1/120)))
(+ 1/6 (* (* x x) -1/120))
1/6
(* (* x x) -1/120)
-1/120
(+ (* (- (* x (* (* eps eps) 1/4)) eps) x) (* eps (* eps -1/2)))
(- (* x (* (* eps eps) 1/4)) eps)
(* x (* (* eps eps) 1/4))
x
(* (* eps eps) 1/4)
(* eps eps)
eps
1/4
(* eps (* eps -1/2))
(* eps -1/2)
-1/2
Outputs
(* (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps (* (sin (/ (+ eps (* x 2)) 2)) -2)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 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))))))))) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal -2 binary64))))
(+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 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)))))))))
1/2
#s(literal 1/2 binary64)
(* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(*.f64 eps (*.f64 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))))))))
eps
(* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(*.f64 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)))))))
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))
(+.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))))))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))
(* eps eps)
(*.f64 eps eps)
(+ 1/3840 (* (* eps eps) -1/645120))
(+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))
1/3840
#s(literal 1/3840 binary64)
(* (* eps eps) -1/645120)
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
-1/645120
#s(literal -1/645120 binary64)
(* eps (* (sin (/ (+ eps (* x 2)) 2)) -2))
(*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal -2 binary64)))
(* (sin (/ (+ eps (* x 2)) 2)) -2)
(*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))
(sin (/ (+ eps (* x 2)) 2))
(sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
-2
#s(literal -2 binary64)
0
#s(literal 0 binary64)
(* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) x))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
eps
(- (* eps (+ -1/2 (* x (* x 1/4)))) x)
(-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
(* eps (+ -1/2 (* x (* x 1/4))))
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(+ -1/2 (* x (* x 1/4)))
(+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
-1/2
#s(literal -1/2 binary64)
(* x (* x 1/4))
(*.f64 x (*.f64 x #s(literal 1/4 binary64)))
x
(* x 1/4)
(*.f64 x #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(+ (* eps (- (* eps -1/2) x)) (* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x)))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))))))
(* eps (- (* eps -1/2) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
eps
(- (* eps -1/2) x)
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
x
(* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x))
(*.f64 eps (*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))) (*.f64 x (*.f64 x x))))
(* x x)
(*.f64 x x)
(* (* eps (+ 1/6 (* (* x x) -1/120))) x)
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))) (*.f64 eps x))
(* eps (+ 1/6 (* (* x x) -1/120)))
(*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))
(+ 1/6 (* (* x x) -1/120))
(+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64))))
1/6
#s(literal 1/6 binary64)
(* (* x x) -1/120)
(*.f64 x (*.f64 x #s(literal -1/120 binary64)))
-1/120
#s(literal -1/120 binary64)
(+ (* (- (* x (* (* eps eps) 1/4)) eps) x) (* eps (* eps -1/2)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
(- (* x (* (* eps eps) 1/4)) eps)
(*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 x #s(literal 1/4 binary64)))))
(* x (* (* eps eps) 1/4))
(*.f64 eps (*.f64 eps (*.f64 x #s(literal 1/4 binary64))))
x
(* (* eps eps) 1/4)
(*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))
(* eps eps)
(*.f64 eps eps)
eps
1/4
#s(literal 1/4 binary64)
(* eps (* eps -1/2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)

localize219.0ms (1.3%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 eps eps)
✓accuracy100.0%
(*.f64 eps #s(literal -1/2 binary64))
✓accuracy100.0%
(fma.f64 (-.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
✓accuracy99.8%
(*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))
✓accuracy99.8%
(*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x))
✓accuracy99.8%
(*.f64 (*.f64 x x) #s(literal -1/120 binary64))
✓accuracy99.7%
(*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)
✓accuracy99.5%
(*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))))
✓accuracy100.0%
(*.f64 x #s(literal 1/4 binary64))
✓accuracy100.0%
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64)))))
✓accuracy100.0%
(-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x)
✓accuracy99.8%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
✓accuracy99.8%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
✓accuracy99.8%
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
✓accuracy99.7%
(*.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)))))))
✓accuracy99.5%
(*.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))))))
Results
154.0ms254×0valid
4.0ms1×3valid
1.0ms1×1valid
Compiler

Compiled 376 to 50 computations (86.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 74.0ms
ival-mult: 35.0ms (47.4% of total)
...c/correct-round.rkt:119:19: 17.0ms (23% of total)
ival-add: 9.0ms (12.2% of total)
ival-sub: 3.0ms (4.1% of total)
ival-sin: 3.0ms (4.1% of total)
compiled-spec: 3.0ms (4.1% of total)
ival-div: 2.0ms (2.7% of total)
const: 1.0ms (1.4% of total)
backward-pass: 1.0ms (1.4% of total)

series24.0ms (0.1%)

Counts
24 → 444
Calls
Call 1
Inputs
#<alt (* (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps (* (sin (/ (+ eps (* x 2)) 2)) -2)))>
#<alt (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))>
#<alt (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))>
#<alt (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))>
#<alt (* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) x))>
#<alt (- (* eps (+ -1/2 (* x (* x 1/4)))) x)>
#<alt (* eps (+ -1/2 (* x (* x 1/4))))>
#<alt (+ -1/2 (* x (* x 1/4)))>
#<alt (+ (* eps (- (* eps -1/2) x)) (* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x)))>
#<alt (* eps (- (* eps -1/2) x))>
#<alt (- (* eps -1/2) x)>
#<alt (* eps -1/2)>
#<alt (+ (* (- (* x (* (* eps eps) 1/4)) eps) x) (* eps (* eps -1/2)))>
#<alt (- (* x (* (* eps eps) 1/4)) eps)>
#<alt (* x (* (* eps eps) 1/4))>
#<alt (* (* eps eps) 1/4)>
#<alt (* (* eps eps) -1/645120)>
#<alt (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))>
#<alt (* x 1/4)>
#<alt (* eps (+ 1/6 (* (* x x) -1/120)))>
#<alt (* (* eps (+ 1/6 (* (* x x) -1/120))) x)>
#<alt (* (* x x) -1/120)>
#<alt (* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x))>
#<alt (* eps eps)>
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 (* 1/322560 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/322560 (sin (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))>
#<alt (* (pow eps 7) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 6))) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))))>
#<alt (* 1/322560 (* (pow eps 7) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6)))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/48 eps)>
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* -1/645120 (pow eps 5))>
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 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 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ 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 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ 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) (* 1/4 (* (pow eps 2) x)))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* -1 x)>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)>
#<alt (- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ 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)) (/ x eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ 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 (- (* 1/4 (* eps x)) 1)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))>
#<alt (* 1/4 (* eps (pow x 2)))>
#<alt (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))>
#<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 (* eps (+ (* -1 x) (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2))))))>
#<alt (* eps (+ (* -1 x) (+ (* -1/2 eps) (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))))>
#<alt (* eps (+ (* -1 x) (+ (* -1/2 eps) (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))))>
#<alt (* eps (+ (* -1 x) (+ (* -1/2 eps) (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (/ (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (/ (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (/ (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))) eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ x (* -1 (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ x (* -1 (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ x (* -1 (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))) eps)) 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) (* 1/6 (* eps (pow x 2))))))>
#<alt (+ (* -1/2 (pow eps 2)) (* 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))) (+ (* -1/2 (/ (pow eps 2) (pow x 5))) (+ (* -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) (+ (* 1/2 (/ (pow eps 2) (pow x 5))) (/ eps (pow x 4)))))))>
#<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 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 (* -1/2 (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) (* 1/4 (* (pow eps 2) x)))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 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 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ 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 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1 eps)>
#<alt (- (* 1/4 (* (pow eps 2) x)) eps)>
#<alt (- (* 1/4 (* (pow eps 2) x)) eps)>
#<alt (- (* 1/4 (* (pow eps 2) x)) eps)>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))>
#<alt (* -1 eps)>
#<alt (* eps (- (* 1/4 (* eps x)) 1))>
#<alt (* eps (- (* 1/4 (* eps x)) 1))>
#<alt (* eps (- (* 1/4 (* eps x)) 1))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<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 (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* x (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* 1/6 (* eps x))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* -1/120 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 3) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* -1/120 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<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 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -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) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 5) (+ (* -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))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 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 (pow eps 2)>
Calls

111 calls:

TimeVariablePointExpression
3.0ms
eps
@inf
(* eps (+ 1/6 (* (* x x) -1/120)))
1.0ms
eps
@0
(+ (* eps (- (* eps -1/2) x)) (* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x)))
1.0ms
eps
@0
(* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) x))
1.0ms
eps
@-inf
(* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) x))
1.0ms
eps
@inf
(+ (* eps (- (* eps -1/2) x)) (* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x)))

rewrite358.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
4324×*-lowering-*.f32
4324×*-lowering-*.f64
2668×/-lowering-/.f32
2668×/-lowering-/.f64
2480×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
049221
1285199
22521199
09885199
Stop Event
1×iter limit
1×node limit
Counts
24 → 483
Calls
Call 1
Inputs
(* (+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps (* (sin (/ (+ eps (* x 2)) 2)) -2)))
(+ 1/2 (* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(* eps (* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(* eps (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(* eps (- (* eps (+ -1/2 (* x (* x 1/4)))) x))
(- (* eps (+ -1/2 (* x (* x 1/4)))) x)
(* eps (+ -1/2 (* x (* x 1/4))))
(+ -1/2 (* x (* x 1/4)))
(+ (* eps (- (* eps -1/2) x)) (* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x)))
(* eps (- (* eps -1/2) x))
(- (* eps -1/2) x)
(* eps -1/2)
(+ (* (- (* x (* (* eps eps) 1/4)) eps) x) (* eps (* eps -1/2)))
(- (* x (* (* eps eps) 1/4)) eps)
(* x (* (* eps eps) 1/4))
(* (* eps eps) 1/4)
(* (* eps eps) -1/645120)
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(* x 1/4)
(* eps (+ 1/6 (* (* x x) -1/120)))
(* (* eps (+ 1/6 (* (* x x) -1/120))) x)
(* (* x x) -1/120)
(* (* x x) (* (* eps (+ 1/6 (* (* x x) -1/120))) x))
(* eps eps)
Outputs
(+.f64 (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps)) #s(literal 1/2 binary64)) (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps)) (*.f64 (*.f64 eps 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 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps)) (*.f64 (*.f64 eps 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 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps))) (*.f64 (*.f64 (*.f64 eps 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 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps))))
(+.f64 (*.f64 (*.f64 (*.f64 eps 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 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps)) (*.f64 (*.f64 (*.f64 eps 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 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps))))
(fma.f64 (*.f64 (*.f64 eps 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 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps))))
(fma.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps)) #s(literal 1/2 binary64) (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) eps)) (*.f64 (*.f64 eps 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))))))))
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(+.f64 (*.f64 (*.f64 eps #s(literal 1/6 binary64)) x) (*.f64 (*.f64 x (*.f64 (*.f64 x #s(literal -1/120 binary64)) eps)) x))
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(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(*.f64 eps eps)
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))

simplify265.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
6066×*-lowering-*.f32
6066×*-lowering-*.f64
2764×+-lowering-+.f64
2764×+-lowering-+.f32
1784×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03644879
112404095
243404016
084214016
Stop Event
1×iter limit
1×node limit
Counts
444 → 444
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)))))))))
(* 1/322560 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/322560 (sin (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(* (pow eps 7) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 6))) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))))
(* 1/322560 (* (pow eps 7) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 7) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6)))))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
1/2
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
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(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
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(* 1/4 (* (pow eps 2) (pow x 2)))
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-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
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(- (* -1/2 eps) x)
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(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
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(* -1/2 eps)
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(- (* 1/4 (* (pow eps 2) x)) eps)
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(* 1/4 (* (pow eps 2) x))
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(* 1/4 (pow eps 2))
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(* 1/4 (pow eps 2))
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(* -1/645120 (pow eps 2))
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(* -1/645120 (pow eps 4))
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(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
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(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* -1/120 (* 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))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 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)
(pow eps 2)
Outputs
(* -1 (* eps (sin x)))
(*.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(*.f64 eps (-.f64 (*.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (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 (cos.f64 x) (*.f64 eps #s(literal 1/24 binary64))))))) (sin.f64 x)))
(* 1/322560 (* (pow eps 7) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/322560 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/322560 (sin (* 1/2 (+ eps (* 2 x)))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/1920 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (*.f64 #s(literal 1/322560 binary64) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))))
(* (pow eps 7) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/1920 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (+.f64 (*.f64 #s(literal 1/322560 binary64) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/24 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))))
(* (pow eps 7) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 6))) (+ (* -1/1920 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/322560 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/24 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (+.f64 (*.f64 #s(literal -1/1920 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (*.f64 #s(literal 1/322560 binary64) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64))))))
(* 1/322560 (* (pow eps 7) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/322560 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* -1 (* (pow eps 7) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/1920 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (*.f64 #s(literal 1/322560 binary64) (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))))
(* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(*.f64 (+.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -1/322560 binary64)) (+.f64 (*.f64 (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal 1/1920 binary64)) (*.f64 #s(literal -1/24 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* -1 (* (pow eps 7) (+ (* -1/24 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/322560 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (+ (* 1/1920 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6)))))))
(*.f64 (+.f64 (+.f64 (*.f64 (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal 1/1920 binary64)) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64)))) (+.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -1/322560 binary64)) (*.f64 #s(literal -1/24 binary64) (/.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 7 binary64))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 #s(literal -2 binary64) (*.f64 eps (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.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)))))))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))
(*.f64 (*.f64 eps #s(literal -2 binary64)) (+.f64 (*.f64 x (*.f64 (+.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)))))))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.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)))))))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))
(+.f64 (*.f64 (*.f64 eps #s(literal -2 binary64)) (+.f64 (*.f64 x (*.f64 (+.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)))))))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.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 eps (*.f64 (*.f64 (+.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 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) x)))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
(+.f64 (*.f64 (*.f64 eps #s(literal -2 binary64)) (+.f64 (*.f64 x (*.f64 (+.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)))))))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (+.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 x (*.f64 x (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (+.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)))))))) eps)) (*.f64 (*.f64 x (*.f64 (+.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)))))))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 eps #s(literal 1/3 binary64)))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 eps (*.f64 (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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))))))))) #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/48 (pow eps 2)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))
(+.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)))))
(+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))
(+.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))))))))
(* -1/645120 (pow eps 6))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 6 binary64))) (+.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))))
(* -1/645120 (pow eps 6))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 6 binary64))) (+.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))))
(* -1/48 (pow eps 2))
(*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(*.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)))))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(*.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)))))))
(* -1/645120 (pow eps 6))
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(* (pow x 3) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* (pow x 3) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* (pow x 3) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* -1/120 (* eps (pow x 5)))
(*.f64 eps (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64)))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (*.f64 eps #s(literal -1/120 binary64)) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/6 binary64))))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (*.f64 eps #s(literal -1/120 binary64)) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/6 binary64))))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (*.f64 eps #s(literal -1/120 binary64)) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/6 binary64))))
(* -1/120 (* eps (pow x 5)))
(*.f64 eps (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/120 binary64)))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (*.f64 eps #s(literal -1/120 binary64)) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/6 binary64))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (*.f64 eps #s(literal -1/120 binary64)) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/6 binary64))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (*.f64 eps #s(literal -1/120 binary64)) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/6 binary64))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(* eps (* (pow x 3) (+ 1/6 (* -1/120 (pow x 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (*.f64 x (*.f64 x x))))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)

eval103.0ms (0.6%)

Compiler

Compiled 33869 to 2410 computations (92.9% saved)

prune95.0ms (0.6%)

Pruning

29 alts after pruning (26 fresh and 3 done)

PrunedKeptTotal
New9738981
Fresh31821
Picked325
Done011
Total979291008
Accuracy
100.0%
Counts
1008 → 29
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.7%
(fma.f64 (-.f64 #s(literal 0 binary64) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
45.9%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (*.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))))))) #s(literal 1 binary64))) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
76.6%
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))
76.2%
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
75.1%
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
98.7%
(+.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
98.7%
(+.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) eps) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
98.6%
(+.f64 (*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
97.6%
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 eps x)))
98.4%
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
99.8%
(*.f64 (+.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 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
99.7%
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
99.7%
(*.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))
99.5%
(*.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))
99.8%
(*.f64 (*.f64 eps (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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)))))))))) #s(literal -2 binary64))
95.8%
(*.f64 (*.f64 eps eps) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))
95.7%
(*.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)))))
45.1%
(*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))
75.7%
(*.f64 eps (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x))
✓97.6%
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
98.8%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))))
98.3%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
✓99.1%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
97.6%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
98.7%
(*.f64 eps (+.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))))))
99.6%
(*.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)))))
98.4%
(*.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))))))))
99.0%
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
✓44.7%
#s(literal 0 binary64)
Compiler

Compiled 1382 to 602 computations (56.4% saved)

regimes41.0ms (0.2%)

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

3 calls:

13.0ms
x
13.0ms
eps
10.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.1%)

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

2 calls:

11.0ms
eps
11.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes24.0ms (0.1%)

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

2 calls:

10.0ms
x
10.0ms
eps
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes24.0ms (0.1%)

Counts
39 → 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 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.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 eps (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 eps x)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 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 eps (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))
(*.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 eps (+.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (*.f64 x (*.f64 x 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 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))) (*.f64 x x)))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(+.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) eps) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))))
(+.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
(fma.f64 (-.f64 #s(literal 0 binary64) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(*.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))
(fma.f64 (-.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (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 #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 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 eps (*.f64 (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 eps (*.f64 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 (*.f64 eps 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 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 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))
Calls

2 calls:

11.0ms
eps
10.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes22.0ms (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 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.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 eps (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 eps x)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 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 eps (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))
(*.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 eps (+.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (*.f64 x (*.f64 x 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 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))) (*.f64 x x)))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(+.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) eps) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))))
(+.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
(fma.f64 (-.f64 #s(literal 0 binary64) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(*.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))
(fma.f64 (-.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (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 #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 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
Outputs
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
Calls

2 calls:

10.0ms
x
9.0ms
eps
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0.1%)

Counts
36 → 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 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.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 eps (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 eps x)))
(*.f64 eps (-.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
(*.f64 eps (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 #s(literal 1/4 binary64) x))))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 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 eps (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)))
(*.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 eps (+.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (*.f64 x (*.f64 x 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 x (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1/120 binary64)))))))))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 eps (+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))) (*.f64 x x)))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(+.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) eps) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))))
(+.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) x) eps)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 eps (*.f64 eps (-.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps))))
(fma.f64 (-.f64 #s(literal 0 binary64) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(*.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))
(fma.f64 (-.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) eps) x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (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 #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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
Calls

2 calls:

9.0ms
eps
9.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes32.0ms (0.2%)

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

2 calls:

21.0ms
eps
9.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.1%)

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

2 calls:

9.0ms
x
8.0ms
eps
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

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

2 calls:

8.0ms
eps
8.0ms
x
Results
AccuracySegmentsBranch
99.1%1x
99.1%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

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

2 calls:

8.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
98.8%1x
98.8%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes14.0ms (0.1%)

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

2 calls:

6.0ms
eps
6.0ms
x
Results
AccuracySegmentsBranch
98.7%1x
98.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

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

2 calls:

6.0ms
eps
6.0ms
x
Results
AccuracySegmentsBranch
98.7%1x
98.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes12.0ms (0.1%)

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

2 calls:

5.0ms
x
5.0ms
eps
Results
AccuracySegmentsBranch
98.7%1x
98.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

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

2 calls:

5.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
98.4%1x
98.4%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

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

2 calls:

5.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
98.3%1x
98.3%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0%)

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

2 calls:

3.0ms
eps
3.0ms
x
Results
AccuracySegmentsBranch
97.6%1x
97.6%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

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

2 calls:

3.0ms
eps
3.0ms
x
Results
AccuracySegmentsBranch
97.6%1x
97.6%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (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 #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
75.1%1x
75.1%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Counts
3 → 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)))
Outputs
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
Calls

2 calls:

2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
46.3%1eps
46.3%1x
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
eps
1.0ms
x
Results
AccuracySegmentsBranch
44.7%1x
44.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify27.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
178×*-commutative_binary64
104×+-commutative_binary64
54×sub-neg_binary64
48×neg-mul-1_binary64
44×neg-sub0_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0118340
1229339
2264338
3293338
4324338
5356338
6375338
7389338
8399338
9413338
10425338
11431338
12434338
13435338
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (+.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 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
(*.f64 (*.f64 eps (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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)))))))))) #s(literal -2 binary64))
(*.f64 (+.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 eps (*.f64 (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 eps (*.f64 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 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 eps (*.f64 (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 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.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 (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))))
(+.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) eps) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(*.f64 eps (+.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #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 x #s(literal -1/6 binary64)))))))
(+.f64 (*.f64 eps (*.f64 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 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
#s(literal 0 binary64)
Outputs
(*.f64 (+.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 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
(*.f64 (*.f64 eps (*.f64 (sin.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.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)))))))))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 eps (*.f64 (+.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 #s(literal 1/2 binary64) eps))))))
(*.f64 (+.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 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
(*.f64 (*.f64 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))) (+.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 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 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 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
(*.f64 (*.f64 eps (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) eps)))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) eps))
(-.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 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 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))))))
(+.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) eps) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 x (*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x #s(literal -1/120 binary64)))))) (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))) x)))
(+.f64 (*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 eps (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64)))))))
(*.f64 eps (+.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))))))
(*.f64 eps (+.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 x (*.f64 x x)))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #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 x #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 x #s(literal -1/6 binary64)))))))
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 eps x)))
(-.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 #s(literal 0 binary64) (*.f64 eps x))
(*.f64 eps (-.f64 #s(literal 0 binary64) x))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
#s(literal 0 binary64)

soundness2.2s (12.9%)

Rules
6066×*-lowering-*.f32
6066×*-lowering-*.f64
5588×*-lowering-*.f32
5588×*-lowering-*.f64
5404×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105481
1304458
2777457
32938457
08476457
044202
1226184
22007184
08329184
049221
1285199
22521199
09885199
03644879
112404095
243404016
084214016
04064425
114133621
248433531
081943531
04033429
113743052
244283027
080303027
0616
15016
241216
3524716
0806216
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 1065 to 623 computations (41.5% saved)

preprocess93.0ms (0.5%)

Compiler

Compiled 730 to 266 computations (63.6% saved)

end0.0ms (0%)

Profiling

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