2cos (problem 3.3.5)

Time bar (total: 19.1s)

analyze89.0ms (0.5%)

Memory
19.7MiB live, 95.5MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample10.1s (53.1%)

Memory
-14.7MiB live, 11 332.5MiB allocated
Samples
4.0s25 998×0invalid
3.4s5 479×2valid
686.0ms2 493×1valid
79.0ms168×3valid
15.0ms116×0valid
Precisions
Click to see histograms. Total time spent on operations: 6.1s
ival-cos: 2.9s (48.6% of total)
const: 751.0ms (12.4% of total)
ival-add: 398.0ms (6.6% of total)
ival-sub: 388.0ms (6.4% of total)
ival-<=: 365.0ms (6% of total)
adjust: 346.0ms (5.7% of total)
ival-mult: 283.0ms (4.7% of total)
ival-fabs: 250.0ms (4.1% of total)
ival-<: 174.0ms (2.9% of total)
ival-and: 100.0ms (1.6% of total)
exact: 47.0ms (0.8% of total)
ival-assert: 15.0ms (0.2% of total)
Bogosity

preprocess27.0ms (0.1%)

Memory
21.7MiB live, 61.2MiB allocated
Algorithm
egg-herbie
Rules
108×sub-neg
80×accelerator-lowering-fma.f32
80×accelerator-lowering-fma.f64
80×associate--r+
66×cancel-sign-sub-inv
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01841
13837
28135
315235
427835
537035
644835
748535
853135
954635
1055435
067
197
2147
3207
4287
5437
6767
71017
81447
91597
101677
01677
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- (cos (+ x eps)) (cos x))
Outputs
(- (cos (+ x eps)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

explain238.0ms (1.2%)

Memory
-14.2MiB live, 465.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1372(-3.341715800644979e-159 1.0670109309597453e-165)0-(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
50-1(267.25797176322624 5.499816144482922e-13)(cos.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(cos.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))cancellation1391
cos.f64(cos.f64 (+.f64 x eps))sensitivity41
Confusion
Predicted +Predicted -
+1380
-2116
Precision
0.9857142857142858
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+13800
-21115
Precision?
0.9787234042553191
Recall?
1.0
Freqs
test
numberfreq
0116
1137
23
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
131.0ms320×2valid
20.0ms160×1valid
17.0ms22×3valid
1.0ms10×0valid
Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 142.0ms
ival-cos: 108.0ms (75.9% of total)
adjust: 21.0ms (14.8% of total)
ival-sub: 8.0ms (5.6% of total)
ival-add: 5.0ms (3.5% of total)
ival-true: 1.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
52.1%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0%)

Memory
8.2MiB live, 8.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 x)
cost-diff0
(+.f64 x eps)
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Rules
80×accelerator-lowering-fma.f32
80×accelerator-lowering-fma.f64
48×*-lowering-*.f32
48×*-lowering-*.f64
36×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
1918
21418
32018
42818
54318
67618
710118
814418
915918
1016718
016718
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(- (cos (+ x eps)) (cos x))
(cos (+ x eps))
(+ x eps)
x
eps
(cos x)
Outputs
(- (cos (+ x eps)) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos (+ x eps))
(cos.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(cos x)
(cos.f64 x)

localize110.0ms (0.6%)

Memory
4.8MiB live, 160.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x eps)
accuracy100.0%
(cos.f64 x)
accuracy99.8%
(cos.f64 (+.f64 x eps))
accuracy52.4%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Samples
82.0ms160×2valid
10.0ms80×1valid
8.0ms11×3valid
0.0ms0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 88.0ms
ival-cos: 74.0ms (84.2% of total)
adjust: 7.0ms (8% of total)
ival-sub: 4.0ms (4.5% of total)
ival-add: 3.0ms (3.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory
10.3MiB live, 10.3MiB allocated
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
eps
@-inf
(- (cos (+ x eps)) (cos x))
0.0ms
x
@-inf
(- (cos (+ x eps)) (cos x))

rewrite306.0ms (1.6%)

Memory
-16.8MiB live, 653.3MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 936×accelerator-lowering-fma.f32
4 936×accelerator-lowering-fma.f64
4 656×*-lowering-*.f32
4 656×*-lowering-*.f64
2 192×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
15016
237616
3468816
0820116
Stop Event
iter limit
node limit
Counts
4 → 228
Calls
Call 1
Inputs
(- (cos (+ x eps)) (cos x))
(cos (+ x eps))
(+ x eps)
(cos x)
Outputs
(+.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (cos.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(+.f64 (+.f64 (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps))) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))) #s(literal -1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 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 (neg.f64 (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 (+.f64 x eps)) (/.f64 (cos.f64 (+.f64 x eps)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(fma.f64 (cos.f64 (+.f64 x eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(fma.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (/.f64 (cos.f64 (+.f64 x eps)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(fma.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(fma.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(fma.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))) (neg.f64 (cos.f64 x)))
(fma.f64 #s(literal -1 binary64) (cos.f64 x) (cos.f64 (+.f64 x eps)))
(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
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(/.f64 (neg.f64 (*.f64 (neg.f64 (+.f64 x eps)) (-.f64 x eps))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.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 eps eps) (-.f64 x eps)))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.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)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (*.f64 (fma.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) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.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 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)))))
(/.f64 (*.f64 (*.f64 (fma.f64 eps eps (*.f64 x x)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 eps eps (*.f64 x x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #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 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(*.f64 (*.f64 (neg.f64 (+.f64 x eps)) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps))))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x))))))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 eps eps (*.f64 x x)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps (*.f64 x x))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.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 #s(literal 1 binary64) (fma.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 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(cos.f64 x)
(cos.f64 (neg.f64 x))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))

simplify409.0ms (2.1%)

Memory
6.6MiB live, 758.5MiB allocated
Algorithm
egg-herbie
Rules
14 158×accelerator-lowering-fma.f32
14 158×accelerator-lowering-fma.f64
4 148×*-lowering-*.f32
4 148×*-lowering-*.f64
3 720×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105498
1277495
2609495
32398494
47880494
08026474
Stop Event
iter limit
node limit
Counts
84 → 84
Calls
Call 1
Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
Outputs
(- (cos eps) 1)
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(+.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) (fma.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 (sin.f64 x) (neg.f64 eps))
(* 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 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) (fma.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 (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.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 (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps)) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) (fma.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 (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 eps (sin.f64 x)))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) (fma.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)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 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)

eval49.0ms (0.3%)

Memory
20.3MiB live, 114.4MiB allocated
Compiler

Compiled 7 975 to 879 computations (89% saved)

prune42.0ms (0.2%)

Memory
-18.4MiB live, 140.6MiB allocated
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New30210312
Fresh000
Picked011
Done000
Total30211313
Accuracy
99.8%
Counts
313 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
52.4%
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
50.9%
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
50.8%
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
52.1%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
50.9%
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
50.3%
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
99.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
79.9%
(*.f64 (sin.f64 x) (neg.f64 eps))
99.5%
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
99.2%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
Compiler

Compiled 277 to 192 computations (30.7% saved)

simplify550.0ms (2.9%)

Memory
15.5MiB live, 760.5MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
cost-diff0
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
cost-diff0
(-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
cost-diff0
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
cost-diff0
(fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))
cost-diff0
(+.f64 x eps)
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
cost-diff0
(neg.f64 eps)
cost-diff0
(sin.f64 x)
cost-diff0
(*.f64 (sin.f64 x) (neg.f64 eps))
cost-diff0
(cos.f64 eps)
cost-diff0
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
cost-diff0
(fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))
cost-diff0
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
cost-diff128
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))
cost-diff6208
(fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x)))
Rules
16 614×accelerator-lowering-fma.f32
16 614×accelerator-lowering-fma.f64
3 298×*-lowering-*.f32
3 298×*-lowering-*.f64
2 374×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038222
1105220
2264220
3662220
41428220
52730220
64894220
75911220
86775220
97323220
107476220
117715220
08131207
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))))
eps
(+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))
(+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))
(cos x)
x
(+ -1/2 (* eps (* eps 1/24)))
-1/2
(* eps (* eps 1/24))
(* eps 1/24)
1/24
(* eps (* 1/6 (sin x)))
(* 1/6 (sin x))
1/6
(sin x)
(sin (neg x))
(neg x)
(+ (cos eps) -1)
(cos eps)
eps
-1
(* (sin x) (neg eps))
(sin x)
x
(neg eps)
eps
(- (cos (+ x eps)) (+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1))
(cos (+ x eps))
(+ x eps)
x
eps
(+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1)
(* x (+ (* 1/24 (* x x)) -1/2))
(+ (* 1/24 (* x x)) -1/2)
1/24
(* x x)
-1/2
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)
Outputs
(* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))))
(*.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (*.f64 (sin.f64 x) (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)))))
eps
(+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))
(fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (*.f64 (sin.f64 x) (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))))
(+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))
(fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(cos x)
(cos.f64 x)
x
(+ -1/2 (* eps (* eps 1/24)))
(fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* eps (* eps 1/24))
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))
(* eps 1/24)
(*.f64 eps #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
(* eps (* 1/6 (sin x)))
(*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
1/6
#s(literal 1/6 binary64)
(sin x)
(sin.f64 x)
(sin (neg x))
(sin.f64 (neg.f64 x))
(neg x)
(neg.f64 x)
(+ (cos eps) -1)
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(cos eps)
(cos.f64 eps)
eps
-1
#s(literal -1 binary64)
(* (sin x) (neg eps))
(*.f64 (sin.f64 x) (neg.f64 eps))
(sin x)
(sin.f64 x)
x
(neg eps)
(neg.f64 eps)
eps
(- (cos (+ x eps)) (+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1))
(+.f64 (cos.f64 (+.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1)
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* x (+ (* 1/24 (* x x)) -1/2))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(+ (* 1/24 (* x x)) -1/2)
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
1/24
#s(literal 1/24 binary64)
(* x x)
(*.f64 x x)
-1/2
#s(literal -1/2 binary64)
1
#s(literal 1 binary64)
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
(*.f64 (neg.f64 eps) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)))
eps
(- (* eps (* -1/2 (cos x))) (sin x))
(-.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x))
(* eps (* -1/2 (cos x)))
(*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(* -1/2 (cos x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
x
(sin x)
(sin.f64 x)

localize313.0ms (1.6%)

Memory
8.9MiB live, 553.2MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
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 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
accuracy100.0%
(fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))
accuracy99.8%
(cos.f64 (+.f64 x eps))
accuracy53.1%
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
accuracy100.0%
(sin.f64 x)
accuracy100.0%
(neg.f64 eps)
accuracy100.0%
(*.f64 (sin.f64 x) (neg.f64 eps))
accuracy100.0%
(cos.f64 eps)
accuracy53.7%
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
accuracy99.8%
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
accuracy99.8%
(*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
accuracy99.5%
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
accuracy99.4%
(*.f64 eps #s(literal 1/24 binary64))
Samples
154.0ms152×2valid
48.0ms77×1valid
40.0ms24×3valid
1.0ms0valid
Compiler

Compiled 213 to 40 computations (81.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 192.0ms
ival-mult: 56.0ms (29.2% of total)
ival-cos: 55.0ms (28.7% of total)
adjust: 35.0ms (18.2% of total)
ival-add: 21.0ms (10.9% of total)
const: 8.0ms (4.2% of total)
ival-sin: 7.0ms (3.6% of total)
ival-sub: 6.0ms (3.1% of total)
ival-neg: 2.0ms (1% of total)
exact: 1.0ms (0.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series34.0ms (0.2%)

Memory
2.1MiB live, 84.2MiB allocated
Counts
22 → 396
Calls
Call 1
Inputs
#<alt (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))>
#<alt (+ -1/2 (* eps (* eps 1/24)))>
#<alt (* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))))>
#<alt (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))>
#<alt (+ (cos eps) -1)>
#<alt (cos eps)>
#<alt (* (sin x) (neg eps))>
#<alt (sin x)>
#<alt (neg eps)>
#<alt (- (cos (+ x eps)) (+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1))>
#<alt (cos (+ x eps))>
#<alt (+ x eps)>
#<alt (+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1)>
#<alt (* eps (- (* eps (* -1/2 (cos x))) (sin x)))>
#<alt (- (* eps (* -1/2 (cos x))) (sin x))>
#<alt (* eps (* -1/2 (cos x)))>
#<alt (* -1/2 (cos x))>
#<alt (* eps 1/24)>
#<alt (* 1/6 (sin x))>
#<alt (* eps (* 1/6 (sin x)))>
#<alt (* x (+ (* 1/24 (* x x)) -1/2))>
#<alt (cos x)>
Outputs
#<alt (sin (neg x))>
#<alt (+ (sin (neg x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* eps (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt -1/2>
#<alt (- (* 1/24 (pow eps 2)) 1/2)>
#<alt (- (* 1/24 (pow eps 2)) 1/2)>
#<alt (- (* 1/24 (pow eps 2)) 1/2)>
#<alt (* 1/24 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* eps (sin (neg x)))>
#<alt (* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))>
#<alt (* 1/24 (* (pow eps 4) (cos x)))>
#<alt (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 4) (cos x)))>
#<alt (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (- (* 1/24 (pow eps 2)) 1/2)>
#<alt (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)>
#<alt (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/2 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 eps)))) 1/2)>
#<alt (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/2 (- (* 1/24 (pow eps 2)) 1/2)) (* -1/36 (* eps x))))))) 1/2)>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* -1/2 (cos x))>
#<alt (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))>
#<alt (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))>
#<alt (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))>
#<alt (* 1/24 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* 1/24 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt 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)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<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 (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (- (cos x) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<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) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))>
#<alt (* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps x))>
#<alt (* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))>
#<alt (* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))>
#<alt (* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* 1/6 (* eps (sin x)))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))>
#<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

99 calls:

TimeVariablePointExpression
3.0ms
eps
@0
(* (sin x) (neg eps))
3.0ms
eps
@-inf
(* eps (* 1/6 (sin x)))
3.0ms
eps
@0
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
2.0ms
x
@-inf
(+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))
2.0ms
x
@inf
(+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))

rewrite375.0ms (2%)

Memory
-1.3MiB live, 625.2MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 470×accelerator-lowering-fma.f32
5 470×accelerator-lowering-fma.f64
4 518×*-lowering-*.f32
4 518×*-lowering-*.f64
3 364×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038179
1218177
21835177
08386165
Stop Event
iter limit
node limit
Counts
22 → 432
Calls
Call 1
Inputs
(+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x)))
(+ -1/2 (* eps (* eps 1/24)))
(* eps (+ (* eps (+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))) (sin (neg x))))
(+ (* (cos x) (+ -1/2 (* eps (* eps 1/24)))) (* eps (* 1/6 (sin x))))
(+ (cos eps) -1)
(cos eps)
(* (sin x) (neg eps))
(sin x)
(neg eps)
(- (cos (+ x eps)) (+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1))
(cos (+ x eps))
(+ x eps)
(+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1)
(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
(- (* eps (* -1/2 (cos x))) (sin x))
(* eps (* -1/2 (cos x)))
(* -1/2 (cos x))
(* eps 1/24)
(* 1/6 (sin x))
(* eps (* 1/6 (sin x)))
(* x (+ (* 1/24 (* x x)) -1/2))
(cos x)
Outputs
(+.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (sin.f64 (neg.f64 x)))
(+.f64 (sin.f64 (neg.f64 x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) (/.f64 (pow.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) (*.f64 (/.f64 (pow.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))) (/.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))) (fma.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))) (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)))))))
(pow.f64 (/.f64 (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x)) (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal -1 binary64))
(*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))))
(*.f64 (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x))))
(*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(*.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x))
(*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 eps #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) eps)
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal 1/6 binary64))
(*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))
(*.f64 (sin.f64 x) (*.f64 eps #s(literal 1/6 binary64)))
(*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)
(*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/6 binary64))
(*.f64 (*.f64 eps #s(literal 1/6 binary64)) (sin.f64 x))
(+.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x #s(literal -1/2 binary64)))
(+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))) (-.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x #s(literal -1/2 binary64)))) (/.f64 (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64))) (-.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x #s(literal -1/2 binary64)))))
(fma.f64 x #s(literal -1/2 binary64) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) x (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x x)) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/24 binary64)) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) x (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x #s(literal 1/24 binary64)) (*.f64 x x) (*.f64 x #s(literal -1/2 binary64)))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/13824 binary64))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (fma.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (-.f64 (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))) (-.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x #s(literal -1/2 binary64))))
(/.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64))) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) x) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/13824 binary64))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (-.f64 (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64))))) (neg.f64 (-.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) x)) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/576 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/13824 binary64))))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)) (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) x)
(cos.f64 x)

simplify462.0ms (2.4%)

Memory
-9.9MiB live, 509.1MiB allocated
Algorithm
egg-herbie
Rules
13 096×accelerator-lowering-fma.f32
13 096×accelerator-lowering-fma.f64
7 058×*-lowering-*.f32
7 058×*-lowering-*.f64
3 854×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04414006
113493948
239453928
083053682
Stop Event
iter limit
node limit
Counts
396 → 396
Calls
Call 1
Inputs
(sin (neg x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
-1/2
(- (* 1/24 (pow eps 2)) 1/2)
(- (* 1/24 (pow eps 2)) 1/2)
(- (* 1/24 (pow eps 2)) 1/2)
(* 1/24 (pow eps 2))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* 1/24 (pow eps 2))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/2 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 eps)))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/2 (- (* 1/24 (pow eps 2)) 1/2)) (* -1/36 (* eps x))))))) 1/2)
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
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)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (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)
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(- (cos x) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(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) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/6 x)
(* x (+ 1/6 (* -1/36 (pow x 2))))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps x))
(* x (+ (* -1/36 (* eps (pow x 2))) (* 1/6 eps)))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* 1/720 (* eps (pow x 2)))))))
(* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/36 eps) (* (pow x 2) (+ (* -1/30240 (* eps (pow x 2))) (* 1/720 eps)))))))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* 1/6 (* eps (sin x)))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* 1/24 (pow x 2)) 1/2))
(* 1/24 (pow x 3))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
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
(sin (neg x))
(sin.f64 (neg.f64 x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal 1/6 binary64)))) (sin.f64 (neg.f64 x)))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (*.f64 (sin.f64 x) (*.f64 eps #s(literal 1/6 binary64)))) (sin.f64 (neg.f64 x)))
(* 1/24 (* (pow eps 3) (cos x)))
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (cos.f64 x) #s(literal 1/24 binary64)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 1/24 binary64))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 1/24 binary64)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 1/24 binary64)))) (/.f64 (sin.f64 x) (*.f64 eps (*.f64 eps eps)))))
(* 1/24 (* (pow eps 3) (cos x)))
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (cos.f64 x) #s(literal 1/24 binary64)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
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(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/24 (pow x 2)) 1/2))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* x (- (* 1/24 (pow x 2)) 1/2))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* x (- (* 1/24 (pow x 2)) 1/2))
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(* 1/24 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* 1/24 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(*.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(*.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)))
(*.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 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)

eval124.0ms (0.6%)

Memory
2.5MiB live, 191.8MiB allocated
Compiler

Compiled 29 269 to 2 061 computations (93% saved)

prune91.0ms (0.5%)

Memory
21.7MiB live, 219.7MiB allocated
Pruning

28 alts after pruning (25 fresh and 3 done)

PrunedKeptTotal
New84522867
Fresh235
Picked325
Done011
Total85028878
Accuracy
99.9%
Counts
878 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.1%
(fma.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))
52.4%
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
97.9%
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
96.9%
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
52.1%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
50.3%
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
50.2%
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
78.9%
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
78.7%
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
78.9%
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
99.5%
(*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))) eps)
25.1%
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (-.f64 (*.f64 (sin.f64 x) #s(literal -1/6 binary64)) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)) eps)))
99.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
79.9%
(*.f64 (sin.f64 x) (neg.f64 eps))
78.6%
(*.f64 x (neg.f64 eps))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
96.8%
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
98.3%
(*.f64 eps (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
98.5%
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
98.0%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
98.2%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) (sin.f64 x)))
98.3%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
99.2%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
98.5%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
96.8%
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
51.4%
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
Compiler

Compiled 883 to 562 computations (36.4% saved)

simplify358.0ms (1.9%)

Memory
-4.7MiB live, 588.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
cost-diff0
(*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
cost-diff0
(-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x))
cost-diff0
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
cost-diff0
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
cost-diff0
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
cost-diff320
(fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64))
cost-diff320
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64))))
cost-diff0
(*.f64 x #s(literal -1/6 binary64))
cost-diff0
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
cost-diff0
(fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x)
cost-diff128
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
cost-diff192
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
cost-diff0
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
cost-diff0
(fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
cost-diff0
(*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))) eps)
cost-diff6208
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
Rules
13 392×accelerator-lowering-fma.f32
13 392×accelerator-lowering-fma.f64
4 354×+-lowering-+.f64
4 354×+-lowering-+.f32
3 144×--lowering--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063464
1195462
2658458
31925457
45216449
57619449
08074397
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (+ (* eps (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin (neg x))) eps)
(+ (* eps (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin (neg x)))
eps
(+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))
(* 1/6 (sin x))
1/6
(sin x)
x
(* (cos x) (+ (* eps (* eps 1/24)) -1/2))
(cos x)
(+ (* eps (* eps 1/24)) -1/2)
(* eps 1/24)
1/24
-1/2
(sin (neg x))
(neg x)
(+ 1 -1)
1
-1
(* (+ (* x (* x (* x -1/6))) x) (neg eps))
(+ (* x (* x (* x -1/6))) x)
x
(* x (* x -1/6))
(* x -1/6)
-1/6
(neg eps)
eps
(* eps (+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))))
eps
(+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2)))
x
(+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))
(+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))
(+ (* eps (* eps -1/36)) 1/6)
(* eps -1/36)
-1/36
1/6
(* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4))
(+ (* -1/2 (* 1/24 (* eps eps))) 1/4)
-1/2
(* 1/24 (* eps eps))
1/24
(* eps eps)
1/4
(+ (* eps (* eps 1/6)) -1)
(* eps 1/6)
-1
(* eps (+ (* eps (* eps 1/24)) -1/2))
(+ (* eps (* eps 1/24)) -1/2)
(* eps 1/24)
(* eps (- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x)))
eps
(- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x))
(* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2))
(+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)
(* x x)
x
(+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)
(+ (* (* x x) 1/1440) -1/48)
1/1440
-1/48
1/4
-1/2
(sin x)
Outputs
(* (+ (* eps (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin (neg x))) eps)
(*.f64 eps (fma.f64 (sin.f64 x) (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (*.f64 (cos.f64 x) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(+ (* eps (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin (neg x)))
(fma.f64 (sin.f64 x) (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (*.f64 (cos.f64 x) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
eps
(+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))
(fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(* 1/6 (sin x))
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
1/6
#s(literal 1/6 binary64)
(sin x)
(sin.f64 x)
x
(* (cos x) (+ (* eps (* eps 1/24)) -1/2))
(*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(cos x)
(cos.f64 x)
(+ (* eps (* eps 1/24)) -1/2)
(fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(* eps 1/24)
(*.f64 eps #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
-1/2
#s(literal -1/2 binary64)
(sin (neg x))
(sin.f64 (neg.f64 x))
(neg x)
(neg.f64 x)
(+ 1 -1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
-1
#s(literal -1 binary64)
(* (+ (* x (* x (* x -1/6))) x) (neg eps))
(*.f64 eps (*.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
(+ (* x (* x (* x -1/6))) x)
(fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x)
x
(* x (* x -1/6))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* x -1/6)
(*.f64 x #s(literal -1/6 binary64))
-1/6
#s(literal -1/6 binary64)
(neg eps)
(neg.f64 eps)
eps
(* eps (+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(literal -1/48 binary64) (*.f64 x #s(literal -1/36 binary64))) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/6 binary64) x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
eps
(+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2)))
(fma.f64 x (fma.f64 x (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(literal -1/48 binary64) (*.f64 x #s(literal -1/36 binary64))) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/6 binary64) x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
x
(+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))
(fma.f64 x (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(literal -1/48 binary64) (*.f64 x #s(literal -1/36 binary64))) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/6 binary64) x)) (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)))
(+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))
(fma.f64 eps (fma.f64 eps (fma.f64 eps #s(literal -1/48 binary64) (*.f64 x #s(literal -1/36 binary64))) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/6 binary64) x))
(+ (* eps (* eps -1/36)) 1/6)
(fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64))
(* eps -1/36)
(*.f64 eps #s(literal -1/36 binary64))
-1/36
#s(literal -1/36 binary64)
1/6
#s(literal 1/6 binary64)
(* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64)))
(+ (* -1/2 (* 1/24 (* eps eps))) 1/4)
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/4 binary64))
-1/2
#s(literal -1/2 binary64)
(* 1/24 (* eps eps))
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))
1/24
#s(literal 1/24 binary64)
(* eps eps)
(*.f64 eps eps)
1/4
#s(literal 1/4 binary64)
(+ (* eps (* eps 1/6)) -1)
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
-1
#s(literal -1 binary64)
(* eps (+ (* eps (* eps 1/24)) -1/2))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(+ (* eps (* eps 1/24)) -1/2)
(fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(* eps 1/24)
(*.f64 eps #s(literal 1/24 binary64))
(* eps (- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x)))
(*.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
eps
(- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x))
(fma.f64 eps (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x)))
(* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2))
(*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
(* x x)
(*.f64 x x)
x
(+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))) #s(literal 1/4 binary64))
(+ (* (* x x) 1/1440) -1/48)
(fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))
1/1440
#s(literal 1/1440 binary64)
-1/48
#s(literal -1/48 binary64)
1/4
#s(literal 1/4 binary64)
-1/2
#s(literal -1/2 binary64)
(sin x)
(sin.f64 x)

localize205.0ms (1.1%)

Memory
13.1MiB live, 411.8MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))
accuracy100.0%
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
accuracy100.0%
(-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x))
accuracy99.8%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
accuracy99.4%
(*.f64 eps #s(literal -1/36 binary64))
accuracy99.4%
(*.f64 eps #s(literal 1/24 binary64))
accuracy99.4%
(*.f64 eps #s(literal 1/6 binary64))
accuracy99.4%
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64))))
accuracy100.0%
(neg.f64 eps)
accuracy100.0%
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
accuracy99.8%
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
accuracy99.5%
(*.f64 x #s(literal -1/6 binary64))
accuracy100.0%
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
accuracy100.0%
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
accuracy99.8%
(*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))) eps)
accuracy99.5%
(*.f64 #s(literal 1/6 binary64) (sin.f64 x))
accuracy99.4%
(*.f64 eps #s(literal 1/24 binary64))
Samples
125.0ms252×0valid
5.0ms3valid
2.0ms4valid
Compiler

Compiled 425 to 64 computations (84.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 95.0ms
ival-mult: 48.0ms (50.4% of total)
const: 18.0ms (18.9% of total)
ival-add: 17.0ms (17.8% of total)
ival-sin: 5.0ms (5.2% of total)
ival-neg: 2.0ms (2.1% of total)
ival-cos: 2.0ms (2.1% of total)
adjust: 1.0ms (1% of total)
exact: 1.0ms (1% of total)
ival-sub: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series83.0ms (0.4%)

Memory
-33.0MiB live, 48.7MiB allocated
Counts
22 → 372
Calls
Call 1
Inputs
#<alt (+ (* eps (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin (neg x)))>
#<alt (* (+ (* eps (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin (neg x))) eps)>
#<alt (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))>
#<alt (* 1/6 (sin x))>
#<alt (+ 1 -1)>
#<alt (* (+ (* x (* x (* x -1/6))) x) (neg eps))>
#<alt (+ (* x (* x (* x -1/6))) x)>
#<alt (* x (* x -1/6))>
#<alt (* x -1/6)>
#<alt (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))>
#<alt (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)>
#<alt (* eps (+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))))>
#<alt (+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2)))>
#<alt (* eps (- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x)))>
#<alt (- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x))>
#<alt (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2))>
#<alt (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)>
#<alt (* eps 1/24)>
#<alt (neg eps)>
#<alt (* eps 1/6)>
#<alt (* eps -1/36)>
#<alt (+ (* (* x x) 1/1440) -1/48)>
Outputs
#<alt (sin (neg x))>
#<alt (+ (sin (neg x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 3) (cos x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))>
#<alt (* eps (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (* eps (sin (neg x)))>
#<alt (* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))>
#<alt (* 1/24 (* (pow eps 4) (cos x)))>
#<alt (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 4) (cos x)))>
#<alt (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (* -1/2 (cos x))>
#<alt (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))>
#<alt (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))>
#<alt (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))>
#<alt (* 1/24 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))>
#<alt (* 1/24 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))>
#<alt (- (* 1/24 (pow eps 2)) 1/2)>
#<alt (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)>
#<alt (- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/2 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 eps)))) 1/2)>
#<alt (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/2 (- (* 1/24 (pow eps 2)) 1/2)) (* -1/36 (* eps x))))))) 1/2)>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* -1/36 (pow x 2))))>
#<alt (* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))>
#<alt (* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* 1/6 (sin x))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt (* -1 (* eps (+ x (* -1/6 (pow x 3)))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* eps (+ 1/4 (* -1/48 (pow eps 2))))>
#<alt (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))>
#<alt (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))>
#<alt (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))>
#<alt (* x (+ 1/6 (* -1/36 (pow eps 2))))>
#<alt (* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))>
#<alt (* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))>
#<alt (* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))>
#<alt (* x (+ 1/6 (* -1/36 (pow eps 2))))>
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#<alt (* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))>
#<alt (* 1/6 x)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))>
#<alt (+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))>
#<alt (* -1/48 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -1/36 (/ x eps)) 1/48))>
#<alt (* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))>
#<alt (* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))>
#<alt (* -1/48 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))>
#<alt (* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))>
#<alt 1/4>
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#<alt (+ 1/4 (* -1/48 (pow eps 2)))>
#<alt (+ 1/4 (* -1/48 (pow eps 2)))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* (pow eps 4) (+ 1/24 (* -1/48 (pow x 2))))>
#<alt (* (pow eps 4) (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))>
#<alt (* (pow eps 4) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))) (/ 1/2 (pow eps 2))))>
#<alt (* (pow eps 4) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))>
#<alt (* -1 (* (pow eps 4) (- (* 1/48 (pow x 2)) 1/24)))>
#<alt (* (pow eps 4) (+ (* -1 (- (* 1/48 (pow x 2)) 1/24)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))>
#<alt (* (pow eps 4) (+ (* -1 (- (* 1/48 (pow x 2)) 1/24)) (* -1 (/ (+ (* -1 (* x (+ 1/6 (* -1/36 (pow x 2))))) (+ (* -1/4 (/ (pow x 2) eps)) (* 1/2 (/ 1 eps)))) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (- (* 1/48 (pow x 2)) 1/24)) (* -1 (/ (+ (* -1 (* x (+ 1/6 (* -1/36 (pow x 2))))) (* -1 (/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) eps))) eps))))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
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#<alt (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2)))))>
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#<alt (* (pow x 3) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x))))>
#<alt (* (pow x 3) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)) (+ (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3))))))>
#<alt (* eps (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) x)))))>
#<alt (* eps (- (* 1/24 (pow eps 2)) 1/2))>
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#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))>
#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))>
#<alt (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))>
#<alt (* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (+ (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3)))))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))>
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#<alt (* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) x)))))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
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#<alt (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
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#<alt (* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))>
#<alt (* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))>
#<alt (* -1 (* (pow eps 3) (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))>
#<alt (* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))>
#<alt (* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))))>
#<alt (* (pow eps 2) (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
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#<alt (* 1/1440 (* (pow eps 2) (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (* 1/1440 (pow eps 2))))>
#<alt (* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (+ (* 1/1440 (pow eps 2)) (* 1/4 (/ (pow eps 2) (pow x 4))))))>
#<alt (* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (+ (* 1/1440 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 6))))))>
#<alt (* 1/1440 (* (pow eps 2) (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (* 1/1440 (pow eps 2))))>
#<alt (* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (+ (* 1/1440 (pow eps 2)) (* 1/4 (/ (pow eps 2) (pow x 4))))))>
#<alt (* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (+ (* 1/1440 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 6))))))>
#<alt (* -1 (sin x))>
#<alt (- (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (sin x))>
#<alt (- (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (sin x))>
#<alt (- (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (sin x))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* 1/1440 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))>
#<alt (* (pow x 6) (- (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))) (/ (sin x) (pow x 6))))>
#<alt (* 1/1440 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))>
#<alt (* (pow x 6) (- (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))) (/ (sin x) (pow x 6))))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))>
#<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 (* 1/1440 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))))>
#<alt (* 1/1440 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))>
#<alt (* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))))>
#<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 (* 1/1440 (pow x 6))>
#<alt (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))>
#<alt (* 1/1440 (pow x 6))>
#<alt (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt (* -1/36 eps)>
#<alt -1/48>
#<alt (- (* 1/1440 (pow x 2)) 1/48)>
#<alt (- (* 1/1440 (pow x 2)) 1/48)>
#<alt (- (* 1/1440 (pow x 2)) 1/48)>
#<alt (* 1/1440 (pow x 2))>
#<alt (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* 1/1440 (pow x 2))>
#<alt (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))>
Calls

93 calls:

TimeVariablePointExpression
6.0ms
eps
@-inf
(* eps (+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))))
1.0ms
eps
@0
(* (+ (* x (* x (* x -1/6))) x) (neg eps))
1.0ms
eps
@0
(* eps (- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x)))
1.0ms
eps
@inf
(+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))
1.0ms
eps
@-inf
(* eps (- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x)))

rewrite385.0ms (2%)

Memory
15.2MiB live, 549.8MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 334×*-lowering-*.f32
5 334×*-lowering-*.f64
4 770×accelerator-lowering-fma.f32
4 770×accelerator-lowering-fma.f64
2 488×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063317
1369311
23434311
08092272
Stop Event
iter limit
node limit
Counts
22 → 527
Calls
Call 1
Inputs
(+ (* eps (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin (neg x)))
(* (+ (* eps (+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))) (sin (neg x))) eps)
(+ (* eps (* 1/6 (sin x))) (* (cos x) (+ (* eps (* eps 1/24)) -1/2)))
(* 1/6 (sin x))
(+ 1 -1)
(* (+ (* x (* x (* x -1/6))) x) (neg eps))
(+ (* x (* x (* x -1/6))) x)
(* x (* x -1/6))
(* x -1/6)
(+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))
(+ (* -1/2 (* 1/24 (* eps eps))) 1/4)
(* eps (+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2))))
(+ (* x (+ (* x (+ (* x (+ (* eps (* eps -1/36)) 1/6)) (* eps (+ (* -1/2 (* 1/24 (* eps eps))) 1/4)))) (+ (* eps (* eps 1/6)) -1))) (* eps (+ (* eps (* eps 1/24)) -1/2)))
(* eps (- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x)))
(- (* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)) (sin x))
(* eps (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2))
(+ (* (* x x) (+ (* (* x x) (+ (* (* x x) 1/1440) -1/48)) 1/4)) -1/2)
(* eps 1/24)
(neg eps)
(* eps 1/6)
(* eps -1/36)
(+ (* (* x x) 1/1440) -1/48)
Outputs
(+.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) (sin.f64 (neg.f64 x)))
(+.f64 (sin.f64 (neg.f64 x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))
(+.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 eps eps)) (fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(+.f64 (+.f64 (sin.f64 (neg.f64 x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 eps eps))) (*.f64 (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
(-.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x))))))
(fma.f64 eps (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x)))
(fma.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 eps eps) (fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(fma.f64 (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(fma.f64 (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) eps (sin.f64 (neg.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(fma.f64 (*.f64 eps #s(literal 1/6 binary64)) (*.f64 (sin.f64 x) eps) (fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(fma.f64 (*.f64 eps (*.f64 eps #s(literal 1/6 binary64))) (sin.f64 x) (fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))) (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x)))) (-.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))))
(/.f64 (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))) (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (*.f64 (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (*.f64 eps (sin.f64 (neg.f64 x)))))))
(/.f64 (-.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))) (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (neg.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64))) (-.f64 (sin.f64 (neg.f64 x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x))))) (*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x)))) (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x))))))
(pow.f64 (/.f64 (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))) (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x)))) (-.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal -1 binary64))
(*.f64 (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 (neg.f64 x)) (-.f64 (sin.f64 (neg.f64 x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))) (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)))))
(*.f64 (-.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 (neg.f64 x))))))
(+.f64 (*.f64 eps (sin.f64 (neg.f64 x))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
(+.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))) (*.f64 eps (sin.f64 (neg.f64 x))))
(+.f64 (*.f64 (sin.f64 (neg.f64 x)) eps) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) eps))
(+.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))) eps) (*.f64 (sin.f64 (neg.f64 x)) eps))
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(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64)) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64))) (/.f64 #s(literal 1/2304 binary64) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))
(fma.f64 #s(literal 1/1440 binary64) (*.f64 x x) #s(literal -1/48 binary64))
(fma.f64 (*.f64 x #s(literal 1/1440 binary64)) x #s(literal -1/48 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 x x) #s(literal -1/69120 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/2985984000 binary64)) #s(literal -1/110592 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) #s(literal -1/2304 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/2985984000 binary64)) #s(literal -1/110592 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 x x) #s(literal -1/69120 binary64)))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/2985984000 binary64)) #s(literal -1/110592 binary64)) (+.f64 #s(literal 1/2304 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64)) (*.f64 (*.f64 x x) #s(literal -1/69120 binary64)))))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) #s(literal -1/2304 binary64)) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/2985984000 binary64)) #s(literal -1/110592 binary64))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 x x) #s(literal -1/69120 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) #s(literal -1/2304 binary64))) (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64))))
(/.f64 (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64))) (-.f64 #s(literal -1/48 binary64) (*.f64 x (*.f64 x #s(literal 1/1440 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64)) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) #s(literal 1/2304 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64))))
(pow.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 x x) #s(literal -1/69120 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/2985984000 binary64)) #s(literal -1/110592 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) #s(literal -1/2304 binary64))) #s(literal -1 binary64))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/2985984000 binary64)) #s(literal -1/110592 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 x x) #s(literal -1/69120 binary64))))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2073600 binary64) #s(literal -1/2304 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal 1/48 binary64))))

simplify456.0ms (2.4%)

Memory
-22.3MiB live, 452.9MiB allocated
Algorithm
egg-herbie
Rules
11 252×accelerator-lowering-fma.f32
11 252×accelerator-lowering-fma.f64
6 806×*-lowering-*.f32
6 806×*-lowering-*.f64
3 870×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06165795
119915671
268985647
082475140
Stop Event
iter limit
node limit
Counts
372 → 372
Calls
Call 1
Inputs
(sin (neg x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
(* eps (sin (neg x)))
(* eps (+ (sin (neg x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (cos x)) (/ (sin (neg x)) eps)) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* -1/2 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/6 (pow eps 2)) 1)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/2 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* eps (+ (sin (* -1 x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2))))))
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/2 (* x (- (* 1/24 (pow eps 2)) 1/2))) (* 1/6 eps)))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/2 (- (* 1/24 (pow eps 2)) 1/2)) (* -1/36 (* eps x))))))) 1/2)
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))
(* 1/6 x)
(* x (+ 1/6 (* -1/36 (pow x 2))))
(* x (+ 1/6 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/36))))
(* x (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/30240 (pow x 2)))) 1/36))))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* 1/6 (sin x))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
(* -1 (* eps (+ x (* -1/6 (pow x 3)))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* eps (+ 1/4 (* -1/48 (pow eps 2))))
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(+ (* 1/6 x) (* eps (+ 1/4 (* eps (+ (* -1/36 x) (* -1/48 eps))))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* -1/36 (/ x eps)) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (/ 1/4 (pow eps 2))) 1/48))
(* (pow eps 3) (- (+ (* -1/36 (/ x eps)) (+ (* 1/6 (/ x (pow eps 3))) (/ 1/4 (pow eps 2)))) 1/48))
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (+ 1/48 (* 1/36 (/ x eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1/36 x) (* 1/4 (/ 1 eps))) eps)))))
(* -1 (* (pow eps 3) (+ 1/48 (* -1 (/ (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)) eps)))))
1/4
(+ 1/4 (* -1/48 (pow eps 2)))
(+ 1/4 (* -1/48 (pow eps 2)))
(+ 1/4 (* -1/48 (pow eps 2)))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* (pow eps 4) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 4) (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))) (/ 1/2 (pow eps 2))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))
(* -1 (* (pow eps 4) (- (* 1/48 (pow x 2)) 1/24)))
(* (pow eps 4) (+ (* -1 (- (* 1/48 (pow x 2)) 1/24)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))
(* (pow eps 4) (+ (* -1 (- (* 1/48 (pow x 2)) 1/24)) (* -1 (/ (+ (* -1 (* x (+ 1/6 (* -1/36 (pow x 2))))) (+ (* -1/4 (/ (pow x 2) eps)) (* 1/2 (/ 1 eps)))) eps))))
(* (pow eps 4) (+ (* -1 (- (* 1/48 (pow x 2)) 1/24)) (* -1 (/ (+ (* -1 (* x (+ 1/6 (* -1/36 (pow x 2))))) (* -1 (/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) eps))) eps))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2)))))
(* (pow x 3) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))
(* (pow x 3) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)) (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* (pow x 3) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)) (+ (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3))))))
(* eps (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) x)))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* (pow x 3) (+ 1/6 (+ (* -1/36 (pow eps 2)) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/36 (pow eps 2)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (+ (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 3)))))) (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (+ 1/6 (* -1/36 (pow eps 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))) x)))))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2))))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(* (pow eps 3) (+ 1/24 (* -1/48 (pow x 2))))
(* (pow eps 3) (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)))) (/ 1/2 (pow eps 2))))
(* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/4 (/ (pow x 2) (pow eps 2))) (+ (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 3)))))) (/ 1/2 (pow eps 2))))
(* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) eps)) (* 1/48 (pow x 2))) 1/24)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))))
(* (pow eps 2) (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* (pow eps 2) (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/1440 (* (pow eps 2) (pow x 6)))
(* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (* 1/1440 (pow eps 2))))
(* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (+ (* 1/1440 (pow eps 2)) (* 1/4 (/ (pow eps 2) (pow x 4))))))
(* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (+ (* 1/1440 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 6))))))
(* 1/1440 (* (pow eps 2) (pow x 6)))
(* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (* 1/1440 (pow eps 2))))
(* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (+ (* 1/1440 (pow eps 2)) (* 1/4 (/ (pow eps 2) (pow x 4))))))
(* (pow x 6) (+ (* -1/48 (/ (pow eps 2) (pow x 2))) (+ (* 1/1440 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 4))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 6))))))
(* -1 (sin x))
(- (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (sin x))
(- (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (sin x))
(- (* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (sin x))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* 1/1440 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))
(* (pow x 6) (- (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))) (/ (sin x) (pow x 6))))
(* 1/1440 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))
(* (pow x 6) (- (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))) (/ (sin x) (pow x 6))))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))
(* -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))))))))
(* 1/1440 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))))
(* 1/1440 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))))
-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)
(* 1/1440 (pow x 6))
(* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))
(* 1/1440 (pow x 6))
(* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
(* -1/36 eps)
-1/48
(- (* 1/1440 (pow x 2)) 1/48)
(- (* 1/1440 (pow x 2)) 1/48)
(- (* 1/1440 (pow x 2)) 1/48)
(* 1/1440 (pow x 2))
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(* 1/1440 (pow x 2))
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
Outputs
(sin (neg x))
(sin.f64 (neg.f64 x))
(+ (sin (neg x)) (* -1/2 (* eps (cos x))))
(-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(-.f64 (*.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))
(+ (sin (neg x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 (neg.f64 x)))
(* 1/24 (* (pow eps 3) (cos x)))
(*.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (/.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (/.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (+ (* 1/6 (/ (sin x) eps)) (/ (sin (neg x)) (pow eps 3))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (/.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps))) (/.f64 (sin.f64 x) (*.f64 eps (*.f64 eps eps)))))
(* 1/24 (* (pow eps 3) (cos x)))
(*.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(*.f64 (fma.f64 (cos.f64 x) #s(literal -1/24 binary64) (/.f64 (*.f64 (sin.f64 x) #s(literal -1/6 binary64)) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin (neg x)) eps)) (* 1/2 (cos x))) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(*.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/2 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/6 (pow eps 2))) 1)))
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x eps)) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/2 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(+ (sin (neg x)) (* eps (+ (* 1/6 (* eps (sin x))) (* (cos x) (- (* 1/24 (pow eps 2)) 1/2)))))
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(*.f64 eps (*.f64 #s(literal 1/1440 binary64) (pow.f64 x #s(literal 6 binary64))))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (* 1/1440 eps)))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (/.f64 #s(literal -1/48 binary64) (*.f64 x x)) (*.f64 eps #s(literal 1/1440 binary64))))
(* (pow x 6) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4))))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal -1/48 binary64) (*.f64 x x)) (*.f64 eps #s(literal 1/1440 binary64)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 6))) (+ (* -1/48 (/ eps (pow x 2))) (+ (* 1/1440 eps) (* 1/4 (/ eps (pow x 4)))))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 6 binary64))) (fma.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal -1/48 binary64) (*.f64 x x)) (*.f64 eps #s(literal 1/1440 binary64))))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
(* 1/1440 (pow x 6))
(*.f64 #s(literal 1/1440 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x))))
(* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x)))))
(* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (-.f64 (/.f64 #s(literal -1/48 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))))))
(* 1/1440 (pow x 6))
(*.f64 #s(literal 1/1440 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x))))
(* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x)))))
(* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (-.f64 (/.f64 #s(literal -1/48 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))))))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
(* -1/36 eps)
(*.f64 eps #s(literal -1/36 binary64))
-1/48
#s(literal -1/48 binary64)
(- (* 1/1440 (pow x 2)) 1/48)
(fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))
(- (* 1/1440 (pow x 2)) 1/48)
(fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))
(- (* 1/1440 (pow x 2)) 1/48)
(fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64))
(* 1/1440 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/1440 binary64))
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x))) x) x)
(* 1/1440 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/1440 binary64))
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (+.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 x x))) x) x)

eval136.0ms (0.7%)

Memory
24.4MiB live, 255.8MiB allocated
Compiler

Compiled 52 518 to 2 900 computations (94.5% saved)

prune144.0ms (0.8%)

Memory
11.2MiB live, 246.5MiB allocated
Pruning

37 alts after pruning (32 fresh and 5 done)

PrunedKeptTotal
New89617913
Fresh51520
Picked325
Done033
Total90437941
Accuracy
99.9%
Counts
941 → 37
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) eps (*.f64 (sin.f64 (neg.f64 x)) eps))
99.1%
(fma.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))
52.4%
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
97.9%
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
96.9%
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
52.1%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
50.3%
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
78.9%
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
78.7%
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
78.9%
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
98.3%
(*.f64 (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))) eps)
99.5%
(*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))) eps)
98.5%
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))) eps)
34.9%
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) eps)
99.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
51.5%
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
96.0%
(*.f64 (*.f64 eps eps) (-.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
79.9%
(*.f64 (sin.f64 x) (neg.f64 eps))
78.9%
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
78.6%
(*.f64 x (neg.f64 eps))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
97.5%
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
96.8%
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
97.7%
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
98.0%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
98.2%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
98.3%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (sin.f64 x)))
99.2%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
98.5%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
96.8%
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
78.9%
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
51.4%
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
50.1%
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
50.2%
#s(literal 0 binary64)
Compiler

Compiled 1 194 to 748 computations (37.4% saved)

simplify337.0ms (1.8%)

Memory
-20.0MiB live, 428.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
cost-diff0
(*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
cost-diff0
(-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x))
cost-diff0
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
cost-diff0
(*.f64 eps #s(literal 1/6 binary64))
cost-diff128
(fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps))
cost-diff320
(fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64))))
cost-diff320
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
cost-diff0
(*.f64 x #s(literal 1/6 binary64))
cost-diff0
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
cost-diff0
(*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
cost-diff0
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
cost-diff0
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff192
(+.f64 eps #s(literal 0 binary64))
cost-diff320
(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
Rules
14 048×accelerator-lowering-fma.f32
14 048×accelerator-lowering-fma.f64
3 382×*-lowering-*.f32
3 382×*-lowering-*.f64
2 314×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045257
1122257
2461251
31107241
42138239
53236239
65696239
77204239
08057217
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
(* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
(sin (* (+ eps 0) 1/2))
(* (+ eps 0) 1/2)
(+ eps 0)
eps
0
1/2
(sin (* (+ x (+ x eps)) 1/2))
(* (+ x (+ x eps)) 1/2)
(+ x (+ x eps))
x
(+ x eps)
-2
0
(* x (* eps (+ (* x (* x 1/6)) -1)))
x
(* eps (+ (* x (* x 1/6)) -1))
eps
(+ (* x (* x 1/6)) -1)
(* x 1/6)
1/6
-1
(+ (* x (+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))) (* -1/2 (* eps eps)))
x
(+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))
(+ (* x (* eps 1/6)) (* eps (* eps 1/4)))
(* eps 1/6)
eps
1/6
(* eps (* eps 1/4))
(* eps 1/4)
1/4
(neg eps)
(* -1/2 (* eps eps))
-1/2
(* eps eps)
(* eps (- (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)) (sin x)))
eps
(- (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)) (sin x))
(* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2))
(+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)
(* x x)
x
(+ (* (* x x) -1/48) 1/4)
-1/48
1/4
-1/2
(sin x)
Outputs
(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
(*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin (* (+ eps 0) 1/2))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* (+ eps 0) 1/2)
(*.f64 eps #s(literal 1/2 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
1/2
#s(literal 1/2 binary64)
(sin (* (+ x (+ x eps)) 1/2))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* (+ x (+ x eps)) 1/2)
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (+ x eps))
(+.f64 eps (+.f64 x x))
x
(+ x eps)
(+.f64 eps x)
-2
#s(literal -2 binary64)
0
#s(literal 0 binary64)
(* x (* eps (+ (* x (* x 1/6)) -1)))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
x
(* eps (+ (* x (* x 1/6)) -1))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
eps
(+ (* x (* x 1/6)) -1)
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)
(+ (* x (+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))) (* -1/2 (* eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
x
(+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))
(*.f64 eps (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))
(+ (* x (* eps 1/6)) (* eps (* eps 1/4)))
(*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
eps
1/6
#s(literal 1/6 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)
(neg eps)
(neg.f64 eps)
(* -1/2 (* eps eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(* eps eps)
(*.f64 eps eps)
(* eps (- (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)) (sin x)))
(neg.f64 (*.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) (sin.f64 x))))
eps
(- (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)) (sin x))
(-.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) (sin.f64 x))
(* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))
(* x x)
(*.f64 x x)
x
(+ (* (* x x) -1/48) 1/4)
(fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))
-1/48
#s(literal -1/48 binary64)
1/4
#s(literal 1/4 binary64)
-1/2
#s(literal -1/2 binary64)
(sin x)
(sin.f64 x)

localize134.0ms (0.7%)

Memory
4.5MiB live, 232.8MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
accuracy100.0%
(-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x))
accuracy100.0%
(*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
accuracy99.8%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
accuracy100.0%
(*.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
accuracy100.0%
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
accuracy99.8%
(fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64))))
accuracy99.4%
(*.f64 eps #s(literal 1/6 binary64))
accuracy100.0%
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
accuracy100.0%
(*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
accuracy100.0%
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
accuracy99.5%
(*.f64 x #s(literal 1/6 binary64))
accuracy100.0%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
accuracy99.8%
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
accuracy99.8%
(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
accuracy99.6%
(+.f64 x (+.f64 x eps))
Samples
76.0ms254×0valid
3.0ms4valid
Compiler

Compiled 253 to 47 computations (81.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 57.0ms
ival-mult: 30.0ms (52.9% of total)
ival-add: 11.0ms (19.4% of total)
const: 6.0ms (10.6% of total)
ival-sin: 6.0ms (10.6% of total)
ival-sub: 1.0ms (1.8% of total)
exact: 1.0ms (1.8% of total)
ival-neg: 1.0ms (1.8% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series39.0ms (0.2%)

Memory
-18.0MiB live, 69.8MiB allocated
Counts
19 → 384
Calls
Call 1
Inputs
#<alt (* (+ x (+ x eps)) 1/2)>
#<alt (+ eps 0)>
#<alt (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)>
#<alt (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))>
#<alt (* x (* eps (+ (* x (* x 1/6)) -1)))>
#<alt (* eps (+ (* x (* x 1/6)) -1))>
#<alt (+ (* x (* x 1/6)) -1)>
#<alt (* x 1/6)>
#<alt (+ (* x (+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))) (* -1/2 (* eps eps)))>
#<alt (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))>
#<alt (+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))>
#<alt (* eps 1/6)>
#<alt (* eps (- (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)) (sin x)))>
#<alt (- (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)) (sin x))>
#<alt (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2))>
#<alt (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)>
#<alt (+ x (+ x eps))>
#<alt (sin (* (+ x (+ x eps)) 1/2))>
#<alt (* -1/2 (* eps eps))>
Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<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 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt -1>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 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 (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (/ eps (pow x 2))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))>
#<alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))>
#<alt (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))>
#<alt (* 1/6 (* eps x))>
#<alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* 1/6 (* eps x))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* 1/6 (* eps x))>
#<alt (* eps (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* eps (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* eps (+ (* 1/6 x) (* 1/4 eps)))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* -1 eps)>
#<alt (- (* 1/4 (* (pow eps 2) x)) eps)>
#<alt (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)>
#<alt (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* 1/6 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))>
#<alt (* eps (- (* 1/6 (pow x 2)) 1))>
#<alt (* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))>
#<alt (* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))>
#<alt (* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))))>
#<alt (* (pow eps 2) (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* -1/48 (* (pow eps 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/48 (pow eps 2)) (* 1/4 (/ (pow eps 2) (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/48 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 4)))))>
#<alt (* (pow x 4) (+ (* -1/48 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 4)))))>
#<alt (* -1/48 (* (pow eps 2) (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/48 (pow eps 2)) (* 1/4 (/ (pow eps 2) (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/48 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 4)))))>
#<alt (* (pow x 4) (+ (* -1/48 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 4)))))>
#<alt (* -1 (sin x))>
#<alt (- (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (sin x))>
#<alt (- (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (sin x))>
#<alt (- (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (sin x))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* -1/48 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))>
#<alt (* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))>
#<alt (* -1/48 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))>
#<alt (* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<alt (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))>
#<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) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (* -1/48 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))>
#<alt (* -1/48 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))>
#<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 (* -1/48 (pow x 2)))) 1/2)>
#<alt (* -1/48 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) 1/48))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))>
#<alt (* -1/48 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) 1/48))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<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 (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 (* -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))>
Calls

96 calls:

TimeVariablePointExpression
8.0ms
eps
@inf
(* x (* eps (+ (* x (* x 1/6)) -1)))
3.0ms
eps
@-inf
(* x (* eps (+ (* x (* x 1/6)) -1)))
1.0ms
x
@0
(sin (* (+ x (+ x eps)) 1/2))
1.0ms
x
@inf
(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms
eps
@inf
(+ (* x (+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))) (* -1/2 (* eps eps)))

rewrite439.0ms (2.3%)

Memory
22.0MiB live, 621.5MiB allocated
Algorithm
batch-egg-rewrite
Rules
3 782×*-lowering-*.f32
3 782×*-lowering-*.f64
3 588×/-lowering-/.f32
3 588×/-lowering-/.f64
3 424×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045202
1249202
22570202
08880180
Stop Event
iter limit
node limit
Counts
19 → 966
Calls
Call 1
Inputs
(* (+ x (+ x eps)) 1/2)
(+ eps 0)
(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
(* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
(* x (* eps (+ (* x (* x 1/6)) -1)))
(* eps (+ (* x (* x 1/6)) -1))
(+ (* x (* x 1/6)) -1)
(* x 1/6)
(+ (* x (+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))) (* -1/2 (* eps eps)))
(+ (* x (* eps 1/6)) (* eps (* eps 1/4)))
(+ (* x (+ (* x (* eps 1/6)) (* eps (* eps 1/4)))) (neg eps))
(* eps 1/6)
(* eps (- (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)) (sin x)))
(- (* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)) (sin x))
(* eps (+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2))
(+ (* (* x x) (+ (* (* x x) -1/48) 1/4)) -1/2)
(+ x (+ x eps))
(sin (* (+ x (+ x eps)) 1/2))
(* -1/2 (* eps eps))
Outputs
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x)) (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x eps) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x x) (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 (+.f64 x eps) #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (+.f64 x x) #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 x x (*.f64 eps eps)) (+.f64 x eps) (*.f64 x (*.f64 x x)))) (fma.f64 x x (*.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))) (-.f64 x (+.f64 x eps)))
(/.f64 (*.f64 (fma.f64 (fma.f64 x x (*.f64 eps eps)) (+.f64 x eps) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (fma.f64 x x (*.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps)))))
(/.f64 (*.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) #s(literal 1/2 binary64)) (-.f64 x (+.f64 x eps)))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 x x (*.f64 eps eps)) (+.f64 x eps) (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 x x (*.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps))))))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))))) (neg.f64 (-.f64 x (+.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (fma.f64 x x (*.f64 eps eps)) (+.f64 x eps) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 x x (*.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps))))))
(/.f64 (neg.f64 (*.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) #s(literal 1/2 binary64))) (neg.f64 (-.f64 x (+.f64 x eps))))
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(/.f64 (neg.f64 (-.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 x x))) (neg.f64 (-.f64 x (+.f64 x eps))))
(/.f64 (neg.f64 (-.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 eps eps))) (neg.f64 (-.f64 (+.f64 x x) eps)))
(pow.f64 (/.f64 (fma.f64 x x (*.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps)))) (fma.f64 (fma.f64 x x (*.f64 eps eps)) (+.f64 x eps) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (+.f64 x eps)) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))) #s(literal -1 binary64))
(*.f64 (fma.f64 (fma.f64 x x (*.f64 eps eps)) (+.f64 x eps) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 (+.f64 x eps) (-.f64 x (+.f64 x eps))))))
(*.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 x eps))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))))
(+.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
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(fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)))
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(fma.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)))
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(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)))
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(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) eps (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(/.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps eps)) eps)
(/.f64 (neg.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps (*.f64 eps eps)))) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps eps))) eps)
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)

simplify631.0ms (3.3%)

Memory
24.0MiB live, 572.6MiB allocated
Algorithm
egg-herbie
Rules
15 806×accelerator-lowering-fma.f32
15 806×accelerator-lowering-fma.f64
6 366×*-lowering-*.f32
6 366×*-lowering-*.f64
3 836×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03684476
111554252
233034137
085193813
Stop Event
iter limit
node limit
Counts
384 → 384
Calls
Call 1
Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
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)
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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))
(* (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 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
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(* eps (* x (- (* 1/6 (pow x 2)) 1)))
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(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
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(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
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(* eps (- (* 1/6 (pow x 2)) 1))
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(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
-1
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(* 1/6 (pow x 2))
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(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
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(* 1/6 x)
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(* 1/6 x)
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(* 1/6 x)
(* 1/6 x)
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(* -1/2 (pow eps 2))
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(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/6 (* eps (pow x 3)))
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(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
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(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2))
(* 1/4 (pow eps 2))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))
(* 1/6 (* eps x))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* 1/6 (* eps x))
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(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* 1/6 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* 1/4 (pow eps 2))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 (pow eps 2))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps))))
(* -1 eps)
(- (* 1/4 (* (pow eps 2) x)) eps)
(- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)
(- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps)
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* 1/4 (* (pow eps 2) x))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* 1/4 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))))
(* (pow eps 2) (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* (pow eps 2) (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/48 (* (pow eps 2) (pow x 4)))
(* (pow x 4) (+ (* -1/48 (pow eps 2)) (* 1/4 (/ (pow eps 2) (pow x 2)))))
(* (pow x 4) (+ (* -1/48 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 4)))))
(* (pow x 4) (+ (* -1/48 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 4)))))
(* -1/48 (* (pow eps 2) (pow x 4)))
(* (pow x 4) (+ (* -1/48 (pow eps 2)) (* 1/4 (/ (pow eps 2) (pow x 2)))))
(* (pow x 4) (+ (* -1/48 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 4)))))
(* (pow x 4) (+ (* -1/48 (pow eps 2)) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (/ (* eps (- (* -1/2 eps) (sin x))) (pow x 4)))))
(* -1 (sin x))
(- (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (sin x))
(- (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (sin x))
(- (* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (sin x))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* eps (- (+ (* -1 (/ (sin x) eps)) (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (/ (sin x) eps))))
(* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* -1/48 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))
(* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))
(* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))
(* -1/48 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))
(* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))
(* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(* -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) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(* -1/48 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))
(* -1/48 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))
-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 (* -1/48 (pow x 2)))) 1/2)
(* -1/48 (pow x 4))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) 1/48))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))
(* -1/48 (pow x 4))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) 1/48))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(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))))
(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))))
(* -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))
Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(neg.f64 (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(neg.f64 (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(neg.f64 (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (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 (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.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))))))
(fma.f64 x (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* 1/2 (* eps (sin x)))
(*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (*.f64 (cos.f64 x) #s(literal 1/4 binary64)))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(*.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/12 binary64) (*.f64 (cos.f64 x) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
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(*.f64 eps (-.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
(* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (/ (sin x) eps))))
(*.f64 eps (-.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
(* -1 (* eps (+ (* -1 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)) (/ (sin x) eps))))
(*.f64 eps (-.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64)))
(* -1/48 (* eps (pow x 4)))
(*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))
(* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(* -1/48 (* eps (pow x 4)))
(*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))
(* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))) (/ (sin x) (pow x 4))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* eps (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(*.f64 eps (fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(* -1/48 (* eps (pow x 4)))
(*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))
(* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(* -1/48 (* eps (pow x 4)))
(*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))
(* (pow x 4) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/48 eps) (* 1/4 (/ eps (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 eps (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (pow x 2)) 1/2)
(fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(fma.f64 x (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))
(* -1/48 (pow x 4))
(*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) 1/48))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* -1/48 (pow x 4))
(*.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) 1/48))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* (pow x 4) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 4)))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
eps
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps x) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps x) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps x) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps x) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps x) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps x) eps) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/8 binary64)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (pow eps 2))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))

eval231.0ms (1.2%)

Memory
-36.2MiB live, 208.0MiB allocated
Compiler

Compiled 51 101 to 3 952 computations (92.3% saved)

prune237.0ms (1.2%)

Memory
11.3MiB live, 250.9MiB allocated
Pruning

42 alts after pruning (34 fresh and 8 done)

PrunedKeptTotal
New1 336141 350
Fresh72027
Picked235
Done055
Total1 345421 387
Accuracy
100.0%
Counts
1 387 → 42
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.2%
(fma.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
99.1%
(fma.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))
52.4%
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
97.6%
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) (*.f64 (neg.f64 (*.f64 eps #s(literal 1/4 binary64))) eps)) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
97.9%
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
97.7%
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
96.9%
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
52.1%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
50.3%
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
78.9%
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
78.7%
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
78.9%
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
78.9%
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
98.3%
(*.f64 (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))) eps)
99.5%
(*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))) eps)
98.5%
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))) eps)
99.8%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
99.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/8 binary64)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))) #s(literal -2 binary64))
40.8%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (fma.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
99.6%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
51.5%
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
51.5%
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
96.0%
(*.f64 (*.f64 eps eps) (-.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
79.9%
(*.f64 (sin.f64 x) (neg.f64 eps))
78.9%
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
50.1%
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
78.6%
(*.f64 x (neg.f64 eps))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
96.8%
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
97.7%
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
98.0%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
98.2%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
98.3%
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (sin.f64 x)))
99.2%
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
98.5%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
96.8%
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
51.4%
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
50.1%
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
50.2%
#s(literal 0 binary64)
Compiler

Compiled 1 743 to 741 computations (57.5% saved)

regimes77.0ms (0.4%)

Memory
-9.6MiB live, 70.0MiB allocated
Counts
64 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) (*.f64 (neg.f64 (*.f64 eps #s(literal 1/4 binary64))) eps)) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))) eps)
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) eps (*.f64 (sin.f64 (neg.f64 x)) eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(*.f64 (*.f64 eps eps) (-.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
(*.f64 (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))) eps)
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(fma.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (fma.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))) eps)
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/8 binary64)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (-.f64 (*.f64 (sin.f64 x) #s(literal -1/6 binary64)) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)) eps)))
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) eps)
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
Calls

3 calls:

34.0ms
eps
16.0ms
x
13.0ms
(-.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)

regimes70.0ms (0.4%)

Memory
35.4MiB live, 74.4MiB allocated
Counts
63 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) (*.f64 (neg.f64 (*.f64 eps #s(literal 1/4 binary64))) eps)) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))) eps)
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) eps (*.f64 (sin.f64 (neg.f64 x)) eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(*.f64 (*.f64 eps eps) (-.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
(*.f64 (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))) eps)
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(fma.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (fma.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(*.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (sin.f64 (neg.f64 x))) eps)
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/8 binary64)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) (/.f64 (-.f64 (*.f64 (sin.f64 x) #s(literal -1/6 binary64)) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (sin.f64 x) eps)) eps)) eps)))
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal -1/24 binary64)) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) eps)
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
Calls

3 calls:

38.0ms
eps
16.0ms
x
13.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.6%1x
99.6%1eps
99.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes78.0ms (0.4%)

Memory
-8.8MiB live, 70.0MiB allocated
Counts
53 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) (*.f64 (neg.f64 (*.f64 eps #s(literal 1/4 binary64))) eps)) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))) eps)
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) eps (*.f64 (sin.f64 (neg.f64 x)) eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(*.f64 (*.f64 eps eps) (-.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
(*.f64 (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))) eps)
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
Outputs
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
Calls

3 calls:

36.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
26.0ms
eps
14.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes98.0ms (0.5%)

Memory
-25.0MiB live, 65.4MiB allocated
Counts
52 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) (*.f64 (neg.f64 (*.f64 eps #s(literal 1/4 binary64))) eps)) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
(*.f64 (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))) eps)
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (*.f64 eps (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) eps (*.f64 (sin.f64 (neg.f64 x)) eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(*.f64 (*.f64 eps eps) (-.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (/.f64 (sin.f64 x) eps)))
(*.f64 (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)) (*.f64 eps #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))) eps)
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
Outputs
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
Calls

3 calls:

44.0ms
x
38.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
14.0ms
eps
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes37.0ms (0.2%)

Memory
10.4MiB live, 49.5MiB allocated
Counts
39 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) (*.f64 (neg.f64 (*.f64 eps #s(literal 1/4 binary64))) eps)) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (sin.f64 x)))
Outputs
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
Calls

3 calls:

17.0ms
eps
10.0ms
x
8.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes36.0ms (0.2%)

Memory
4.1MiB live, 43.3MiB allocated
Counts
35 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/1440 binary64)) #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 x eps) #s(literal 1/6 binary64) (*.f64 (neg.f64 (*.f64 eps #s(literal 1/4 binary64))) eps)) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/36 binary64)) #s(literal 1/6 binary64)) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/4 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
Outputs
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
Calls

3 calls:

17.0ms
eps
10.0ms
x
8.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.9%1x
97.9%1eps
97.9%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes34.0ms (0.2%)

Memory
-17.8MiB live, 24.0MiB allocated
Counts
23 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) (neg.f64 eps))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))))
Outputs
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
Calls

3 calls:

21.0ms
x
7.0ms
eps
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.7%1x
97.7%1eps
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory
19.9MiB live, 19.9MiB allocated
Counts
20 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
Outputs
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
Calls

3 calls:

6.0ms
x
6.0ms
eps
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.7%1eps
97.7%1x
97.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes42.0ms (0.2%)

Memory
-19.6MiB live, 19.6MiB allocated
Counts
19 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x (*.f64 x eps))))
(*.f64 x (*.f64 eps (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 eps (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 x eps))
(*.f64 (fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) (neg.f64 eps))
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
Outputs
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
Calls

3 calls:

32.0ms
eps
6.0ms
x
4.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
96.9%1x
96.9%1eps
96.9%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0%)

Memory
10.9MiB live, 10.9MiB allocated
Counts
8 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))
Outputs
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
Calls

3 calls:

3.0ms
x
3.0ms
eps
2.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
96.8%1x
96.8%1eps
96.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory
9.1MiB live, 9.1MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 x (neg.f64 eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))
Outputs
(*.f64 x (neg.f64 eps))
Calls

3 calls:

2.0ms
x
2.0ms
eps
2.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
78.6%1eps
78.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
78.6%1x
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory
7.8MiB live, 7.8MiB allocated
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

3 calls:

1.0ms
x
1.0ms
eps
1.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
50.2%1eps
50.2%1x
50.2%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify41.0ms (0.2%)

Memory
-27.1MiB live, 12.7MiB allocated
Algorithm
egg-herbie
Rules
56×*-commutative_binary64
16×+-commutative_binary64
16×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066144
1103144
2120144
3131144
4136144
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 x (neg.f64 eps))
#s(literal 0 binary64)
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (sin.f64 (neg.f64 x))))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(fma.f64 x (fma.f64 x (*.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(fma.f64 x (neg.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(*.f64 eps (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 x (neg.f64 eps))
(*.f64 eps (neg.f64 x))
#s(literal 0 binary64)

soundness1.3s (6.8%)

Memory
18.8MiB live, 814.7MiB allocated
Rules
15 806×accelerator-lowering-fma.f32
15 806×accelerator-lowering-fma.f64
14 158×accelerator-lowering-fma.f32
14 158×accelerator-lowering-fma.f64
13 096×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
15016
237616
3468816
0820116
045202
1249202
22570202
08880180
0105498
1277495
2609495
32398494
47880494
08026474
03684476
111554252
233034137
085193813
063317
1369311
23434311
08092272
04414006
113493948
239453928
083053682
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 464 to 274 computations (40.9% saved)

preprocess72.0ms (0.4%)

Memory
-12.9MiB live, 69.6MiB allocated
Compiler

Compiled 378 to 182 computations (51.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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