Details

Time bar (total: 8.2s)

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 (65.3%)

Results
2.6s3605×body1024valid
1.7s1229×body2048valid
583.0ms1447×body512valid
209.0ms1370×body128valid
178.0ms602×body256valid
8.0msbody4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify10.0ms (0.1%)

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
36.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
36.4b
(-.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
1.0b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.9b
(sin.f64 (+.f64 x eps))

series12.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
(sin.f64 (+.f64 x eps))

rewrite65.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
471×fma-def_binary64
446×log-prod_binary64
214×fma-neg_binary64
179×expm1-udef_binary64
179×log1p-udef_binary64
Counts
2 → 151
Calls

2 calls:

61.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
61.0ms
(sin.f64 (+.f64 x eps))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
117317
2253917
3535917
000
100

simplify67.0ms (0.8%)

Algorithm
egg-herbie
Rules
830×sub-neg_binary64
730×fma-neg_binary64
266×cancel-sign-sub-inv_binary64
264×associate-+l-_binary64
245×distribute-rgt-neg-in_binary64
Counts
199 → 180
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
053602
1170587
2523572
31688569
44695565
55641565

prune140.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New17010180
Fresh000
Picked101
Done000
Total17110181
Error
0.2b
Counts
181 → 10
Alt Table
StatusErrorProgram
21.1b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps)))) (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
21.1b
(-.f64 (fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
24.7b
(-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 3) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) 3)) (fma.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))))) (sin.f64 x))
33.3b
(fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (+.f64 (*.f64 (*.f64 eps eps) -1/2) (*.f64 1/24 (pow.f64 eps 4)))))
21.0b
(-.f64 (fma.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps)))) (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
41.1b
(fma.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
20.4b
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
44.3b
(fma.f64 (sqrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (sqrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
21.0b
(fma.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 (cbrt.f64 (sin.f64 x)) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
20.5b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 3735 to 1164 computations (68.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sin.f64 x) (cos.f64 eps))
0.1b
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps)))
2.3b
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))

series42.0ms (0.5%)

Counts
3 → 56
Calls

3 calls:

18.0ms
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
15.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps)))
9.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))

rewrite75.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
530×log-prod_binary64
356×fma-def_binary64
207×expm1-udef_binary64
207×log1p-udef_binary64
204×fma-neg_binary64
Counts
3 → 152
Calls

3 calls:

72.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))
72.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps)))
72.0ms
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01045
121425
2276625
3548625
000
100

simplify84.0ms (1%)

Algorithm
egg-herbie
Rules
404×fma-def_binary64
376×distribute-rgt-neg-in_binary64
369×cancel-sign-sub-inv_binary64
366×distribute-lft-neg-in_binary64
337×sub-neg_binary64
Counts
208 → 199
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0861114
12601092
27891018
325641004
447541004
551041004

prune186.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1918199
Fresh459
Picked101
Done000
Total19613209
Error
0.1b
Counts
209 → 13
Alt Table
StatusErrorProgram
21.4b
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)))) (sin.f64 x))
24.7b
(-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) 3) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 3)) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 2) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))))) (sin.f64 x))
1.5b
(fma.f64 (*.f64 (cos.f64 x) (pow.f64 (cbrt.f64 (sin.f64 eps)) 2)) (cbrt.f64 (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
0.4b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
21.1b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps)))) (cbrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
33.3b
(fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (+.f64 (*.f64 (*.f64 eps eps) -1/2) (*.f64 1/24 (pow.f64 eps 4)))))
15.0b
(fma.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
1.5b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
0.7b
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (*.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
0.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
44.3b
(fma.f64 (sqrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (sqrt.f64 (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
21.0b
(fma.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 (cbrt.f64 (sin.f64 x)) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
20.5b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 4132 to 1371 computations (66.8% 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)))
2.4b
(+.f64 (cos.f64 eps) -1)

series35.0ms (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)))
15.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
2.0ms
(+.f64 (cos.f64 eps) -1)

rewrite99.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
887×prod-diff_binary64
209×expm1-udef_binary64
209×log1p-udef_binary64
189×fma-def_binary64
184×log-pow_binary64
Counts
3 → 113
Calls

3 calls:

92.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
92.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
92.0ms
(+.f64 (cos.f64 eps) -1)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01136
122736
2275130
3474330
4554430
000
100

simplify71.0ms (0.9%)

Algorithm
egg-herbie
Rules
638×fma-def_binary64
574×sub-neg_binary64
424×cancel-sign-sub-inv_binary64
403×distribute-rgt-neg-in_binary64
387×distribute-lft-neg-in_binary64
Counts
173 → 155
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01061102
13211032
21019986
33708986
44957986

prune203.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1487155
Fresh8412
Picked101
Done000
Total15711168
Error
0.0b
Counts
168 → 11
Alt Table
StatusErrorProgram
15.4b
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) 2)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))))
32.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 1/24 (pow.f64 eps 4) (fma.f64 1/40320 (pow.f64 eps 8) (fma.f64 -1/2 (*.f64 eps eps) (*.f64 (pow.f64 eps 6) -1/720))))))
1.5b
(fma.f64 (*.f64 (cos.f64 x) (pow.f64 (cbrt.f64 (sin.f64 eps)) 2)) (cbrt.f64 (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (-.f64 (/.f64 (pow.f64 (cos.f64 eps) 2) (+.f64 (cos.f64 eps) 1)) (/.f64 1 (+.f64 (cos.f64 eps) 1)))))
15.0b
(fma.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
0.3b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 eps) 2) (-.f64 -1 (cos.f64 eps)))))
1.5b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
0.3b
(+.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
0.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))))))
0.7b
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (*.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
28.2b
(log.f64 (*.f64 (pow.f64 (exp.f64 (+.f64 (cos.f64 eps) -1)) (sin.f64 x)) (exp.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))))
Compiler

Compiled 3391 to 1464 computations (56.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
0.1b
(*.f64 (sin.f64 eps) (cos.f64 x))
0.2b
(*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))
2.4b
(+.f64 (cos.f64 eps) -1)

series46.0ms (0.6%)

Counts
3 → 64
Calls

3 calls:

19.0ms
(+.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
11.0ms
(*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))
9.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))

rewrite97.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
492×fma-def_binary64
277×fma-neg_binary64
244×expm1-udef_binary64
244×log1p-udef_binary64
135×add-sqr-sqrt_binary64
Counts
3 → 101
Calls

3 calls:

94.0ms
(+.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
94.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))
94.0ms
(*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01238
125838
2335538
3497838
4495838
000
100

simplify67.0ms (0.8%)

Algorithm
egg-herbie
Rules
741×fma-def_binary64
677×sub-neg_binary64
471×cancel-sign-sub-inv_binary64
372×associate-*r*_binary64
344×associate-*l*_binary64
Counts
165 → 149
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01181234
13731158
211991092
345081092
451571092

prune248.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1885193
Fresh6410
Picked101
Done000
Total1959204
Error
0.0b
Counts
204 → 9
Alt Table
StatusErrorProgram
0.4b
(+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (-.f64 -1 (cos.f64 eps))) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
1.5b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
0.7b
(fma.f64 (*.f64 (sin.f64 eps) (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)))
0.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))))))
0.5b
(log1p.f64 (expm1.f64 (fma.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x)))))
15.0b
(fma.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
30.1b
(pow.f64 (sqrt.f64 (fma.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x)))) 2)
1.5b
(fma.f64 (*.f64 (cos.f64 x) (pow.f64 (cbrt.f64 (sin.f64 eps)) 2)) (cbrt.f64 (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
15.4b
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) 2) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) 2)) (-.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))))
Compiler

Compiled 4152 to 1856 computations (55.3% saved)

regimes1.1s (13.1%)

Accuracy

Total 0.3b remaining (80.6%)

Threshold costs 0.3b (80.6%)

Counts
312 → 1
Compiler

Compiled 16891 to 11520 computations (31.8% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
mul-1-neg_binary64
sub-neg_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01223
11623
21823
31923
42023
52023

end167.0ms (2%)

Compiler

Compiled 229 to 143 computations (37.6% saved)

Profiling

Loading profile data...