Details

Time bar (total: 7.6s)

analyze1.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1
Compiler

Compiled 10 to 7 computations (30% saved)

sample5.3s (69.6%)

Results
2.5s3622×body1024valid
1.8s1279×body2048valid
555.0ms1421×body512valid
202.0ms1338×body128valid
165.0ms589×body256valid
17.0msbody4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify13.0ms (0.2%)

Algorithm
egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11011
21511
32211
42911
54611
67211
79311
811011
912011
1012411
1112611
1211211

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
40.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
40.7b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.5b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.1b
(sin.f64 (+.f64 x eps))

series11.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
(sin.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
add-log-exp_binary64
Counts
2 → 42
Calls

2 calls:

5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
(sin.f64 (+.f64 x eps))

simplify98.0ms (1.3%)

Algorithm
egg-herbie
Rules
639×fma-neg_binary64
483×fma-def_binary64
351×cancel-sign-sub-inv_binary64
291×sub-neg_binary64
284×associate-+l-_binary64
Counts
90 → 92
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01281256
12971180
29601116
324261108
447761108
549531108
648391108

prune69.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New89392
Fresh000
Picked101
Done000
Total90393
Error
0.3b
Counts
93 → 3
Alt Table
StatusErrorProgram
30.9b
(+.f64 (*.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6))) (*.f64 (sin.f64 x) (-.f64 (*.f64 1/24 (pow.f64 eps 4)) (*.f64 1/2 (*.f64 eps eps)))))
23.4b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
23.5b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 1671 to 515 computations (69.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
0.2b
(*.f64 (sin.f64 x) (cos.f64 eps))
2.5b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series53.0ms (0.7%)

Counts
4 → 72
Calls

4 calls:

19.0ms
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
14.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
10.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
9.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
11×add-log-exp_binary64
prod-diff_binary64
Counts
4 → 87
Calls

4 calls:

8.0ms
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
4.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
3.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))
3.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))

simplify133.0ms (1.7%)

Algorithm
egg-herbie
Rules
418×fma-neg_binary64
276×distribute-rgt-in_binary64
249×distribute-rgt-neg-in_binary64
245×distribute-lft-in_binary64
226×associate-*r*_binary64
Counts
159 → 189
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02403009
16162802
221902695
347982695
449722695
549112695

prune201.0ms (2.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New17712189
Fresh112
Picked101
Done000
Total17913192
Error
0.1b
Counts
192 → 13
Alt Table
StatusErrorProgram
23.6b
(-.f64 (+.f64 (*.f64 (*.f64 (sin.f64 x) (*.f64 (cbrt.f64 (cos.f64 eps)) (cbrt.f64 (cos.f64 eps)))) (cbrt.f64 (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
27.6b
(cbrt.f64 (*.f64 (*.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
30.4b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (log.f64 (exp.f64 (*.f64 (cos.f64 x) (sin.f64 eps))))) (sin.f64 x))
44.2b
(fma.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
24.2b
(-.f64 (+.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) 3)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
24.1b
(+.f64 (fma.f64 1 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))
30.9b
(fma.f64 1/24 (*.f64 (sin.f64 x) (pow.f64 eps 4)) (fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) -1/2))))
0.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
53.7b
(+.f64 (fma.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (*.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)))))
29.5b
(*.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
1.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
24.1b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))) (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
23.5b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 5171 to 1484 computations (71.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
0.2b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
1.5b
(+.f64 (cos.f64 eps) -1)

series33.0ms (0.4%)

Counts
3 → 60
Calls

3 calls:

18.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
13.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
2.0ms
(+.f64 (cos.f64 eps) -1)

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
add-cube-cbrt_binary64
associate-*r*_binary64
add-cbrt-cube_binary64
Counts
3 → 54
Calls

3 calls:

6.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
3.0ms
(+.f64 (cos.f64 eps) -1)
0.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))

simplify83.0ms (1.1%)

Algorithm
egg-herbie
Rules
786×fma-def_binary64
629×sub-neg_binary64
442×cancel-sign-sub-inv_binary64
294×distribute-rgt-in_binary64
256×distribute-lft-in_binary64
Counts
114 → 131
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01721922
14731753
215081707
345791707
452931707

prune172.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1265131
Fresh7512
Picked101
Done000
Total13410144
Error
0.1b
Counts
144 → 10
Alt Table
StatusErrorProgram
0.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
1.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))))
16.8b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (+.f64 (sqrt.f64 (cos.f64 eps)) 1)) (-.f64 (sqrt.f64 (cos.f64 eps)) 1)))
29.5b
(*.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
0.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
30.9b
(fma.f64 1/24 (*.f64 (sin.f64 x) (pow.f64 eps 4)) (fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) -1/2))))
44.2b
(fma.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
0.3b
(fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
24.1b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))) (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
23.5b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 3071 to 1427 computations (53.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
1.5b
(-.f64 (cos.f64 eps) 1)

series20.0ms (0.3%)

Counts
2 → 28
Calls

2 calls:

17.0ms
(fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
2.0ms
(-.f64 (cos.f64 eps) 1)

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
add-log-exp_binary64
Counts
2 → 43
Calls

2 calls:

4.0ms
(-.f64 (cos.f64 eps) 1)
0.0ms
(fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))

simplify75.0ms (1%)

Algorithm
egg-herbie
Rules
988×fma-neg_binary64
389×distribute-rgt-neg-in_binary64
367×distribute-lft-neg-in_binary64
322×fma-def_binary64
281×neg-mul-1_binary64
Counts
71 → 90
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01171271
12681031
27471021
326761021
447191021
549571021

prune220.0ms (2.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1257132
Fresh459
Picked101
Done000
Total13012142
Error
0.0b
Counts
142 → 12
Alt Table
StatusErrorProgram
30.9b
(fma.f64 1/24 (*.f64 (sin.f64 x) (pow.f64 eps 4)) (fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) -1/2))))
22.6b
(fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (cbrt.f64 (*.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 x)) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (sin.f64 eps)))))
0.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
1.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))))
0.4b
(fma.f64 (log.f64 (/.f64 (exp.f64 (cos.f64 eps)) (exp.f64 1))) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
16.8b
(fma.f64 (fma.f64 (sqrt.f64 (cos.f64 eps)) (sqrt.f64 (cos.f64 eps)) -1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
44.2b
(fma.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
0.8b
(fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (*.f64 (sin.f64 eps) (cbrt.f64 (cos.f64 x)))))
18.5b
(fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sin.f64 eps) (sqrt.f64 (cos.f64 x)))))
33.4b
(fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) (sqrt.f64 (sin.f64 eps))) (sqrt.f64 (sin.f64 eps))))
29.5b
(*.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
0.4b
(+.f64 (*.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps)))
Compiler

Compiled 2879 to 1275 computations (55.7% saved)

regimes846.0ms (11.1%)

Accuracy

Total 0.3b remaining (73.9%)

Threshold costs 0.3b (73.9%)

Counts
249 → 1
Compiler

Compiled 15270 to 9401 computations (38.4% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11719
21819
31619

end206.0ms (2.7%)

Compiler

Compiled 312 to 188 computations (39.7% saved)

Profiling

Loading profile data...