Details

Time bar (total: 10.0s)

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)

sample6.4s (63.5%)

Results
3.1s3583×body1024valid
2.1s1250×body2048valid
621.0ms1449×body512valid
295.0ms616×body256valid
200.0ms1354×body128valid
9.0msbody4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify11.0ms (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

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
37.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
37.1b
(-.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
1.2b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.2b
(sin.f64 (+.f64 x eps))

series12.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
(sin.f64 (+.f64 x eps))

rewrite110.0ms (1.1%)

Algorithm
egg-rewrite
Rules
112×egg
24×egg
Counts
2 → 136
Calls

2 calls:

62.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
46.0ms
(sin.f64 (+.f64 x eps))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11156
215546
350996
0711
117311
2253911
3535911

simplify79.0ms (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
184 → 165
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
053602
1170587
2523572
31688569
44695565
55641565

prune123.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1587165
Fresh000
Picked101
Done000
Total1597166
Error
0.1b
Counts
166 → 7
Alt Table
StatusErrorProgram
24.6b
(-.f64 (/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.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))
27.1b
(-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 3) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) 3)) (+.f64 (*.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))
44.0b
(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)))
23.0b
(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)))
30.9b
(fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 eps (*.f64 (*.f64 eps (sin.f64 x)) -1/2)))
22.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
22.5b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 3341 to 1036 computations (69% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
0.1b
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
2.9b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series47.0ms (0.5%)

Counts
4 → 68
Calls

4 calls:

19.0ms
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
16.0ms
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
11.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
2.0ms
(cos.f64 x)

rewrite264.0ms (2.6%)

Algorithm
egg-rewrite
Rules
94×egg
48×egg
33×egg
23×egg
Counts
4 → 198
Calls

4 calls:

94.0ms
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
73.0ms
(cos.f64 x)
48.0ms
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
45.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01021
120721
2259811
3464911
4513511
068
11168
213388
350968
0916
117516
2203416
3533116
033
1583
26553
347333
455973

simplify69.0ms (0.7%)

Algorithm
egg-herbie
Rules
431×fma-def_binary64
422×distribute-rgt-neg-in_binary64
405×distribute-lft-neg-in_binary64
393×cancel-sign-sub-inv_binary64
379×sub-neg_binary64
Counts
266 → 250
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0951230
12971199
28891112
329061102
450391102

prune210.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2455250
Fresh246
Picked101
Done000
Total2489257
Error
0.1b
Counts
257 → 9
Alt Table
StatusErrorProgram
30.9b
(fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 eps (*.f64 (*.f64 eps (sin.f64 x)) -1/2)))
29.7b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)))) (sin.f64 x))
44.0b
(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)))
23.0b
(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)))
27.1b
(-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 3) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) 3)) (+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) 2) (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))))) (sin.f64 x))
22.6b
(-.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.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 (cos.f64 eps) -1)))
22.5b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
22.6b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 x))))) (sin.f64 eps))) (sin.f64 x))
Compiler

Compiled 5193 to 1666 computations (67.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
0.1b
(*.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)))
1.9b
(+.f64 (cos.f64 eps) -1)

series32.0ms (0.3%)

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)))
11.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
2.0ms
(+.f64 (cos.f64 eps) -1)

rewrite226.0ms (2.2%)

Algorithm
egg-rewrite
Rules
53×egg
51×egg
40×egg
Counts
3 → 144
Calls

3 calls:

91.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
82.0ms
(+.f64 (cos.f64 eps) -1)
51.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11046
212496
347976
453116
01119
122719
2275113
3474313
4554413
0811
116811
2205411
3552311

simplify67.0ms (0.7%)

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
204 → 185
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01061102
13211032
21019986
33708986
44957986

prune279.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2169225
Fresh628
Picked101
Done000
Total22311234
Error
0.0b
Counts
234 → 11
Alt Table
StatusErrorProgram
33.6b
(fma.f64 (sqrt.f64 (sin.f64 eps)) (*.f64 (sqrt.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.5b
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 eps) -1)) 2) (*.f64 (cbrt.f64 (+.f64 (cos.f64 eps) -1)) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
1.4b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x))) (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (cbrt.f64 (*.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) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (sin.f64 x))))
0.5b
(fma.f64 (sin.f64 eps) (cbrt.f64 (pow.f64 (cos.f64 x) 3)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.4b
(fma.f64 (sin.f64 eps) (expm1.f64 (log1p.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
23.0b
(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)))
0.8b
(fma.f64 (*.f64 (sin.f64 eps) (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
29.7b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)))) (sin.f64 x))
20.4b
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) 3) (pow.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)) 3)) (fma.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)) 2) (*.f64 (*.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) (*.f64 (sin.f64 x) (/.f64 1 (/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2))))))
Compiler

Compiled 4747 to 2176 computations (54.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
0.1b
(*.f64 (sin.f64 x) (cos.f64 eps))
0.2b
(fma.f64 (sin.f64 eps) (cos.f64 x) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (sin.f64 x))))
1.9b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (sin.f64 x)))

series42.0ms (0.4%)

Counts
3 → 56
Calls

3 calls:

17.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (sin.f64 x))))
14.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (sin.f64 x)))
11.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))

rewrite196.0ms (2%)

Algorithm
egg-rewrite
Rules
55×egg
55×egg
33×egg
Counts
3 → 143
Calls

3 calls:

75.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))
63.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (sin.f64 x))))
55.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (sin.f64 x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
117911
2212711
3503811
01121
123819
2282311
3549211
068
11238
215368
349528
450648

simplify134.0ms (1.3%)

Algorithm
egg-herbie
Rules
703×fma-def_binary64
615×sub-neg_binary64
460×cancel-sign-sub-inv_binary64
393×distribute-rgt-neg-in_binary64
265×associate-*r*_binary64
Counts
199 → 188
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01051202
13311162
210531023
338951023
448191023
549841023
649991023
749601023

prune249.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2280228
Fresh01010
Picked011
Done000
Total22811239
Error
0.0b
Counts
239 → 11
Alt Table
StatusErrorProgram
33.6b
(fma.f64 (sqrt.f64 (sin.f64 eps)) (*.f64 (sqrt.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.5b
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (cos.f64 eps) -1)) 2) (*.f64 (cbrt.f64 (+.f64 (cos.f64 eps) -1)) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
1.4b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x))) (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (cbrt.f64 (*.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) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (sin.f64 x))))
0.5b
(fma.f64 (sin.f64 eps) (cbrt.f64 (pow.f64 (cos.f64 x) 3)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.4b
(fma.f64 (sin.f64 eps) (expm1.f64 (log1p.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
23.0b
(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)))
0.8b
(fma.f64 (*.f64 (sin.f64 eps) (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
29.7b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)))) (sin.f64 x))
20.4b
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) 3) (pow.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)) 3)) (fma.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)) 2) (*.f64 (*.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) (*.f64 (sin.f64 x) (/.f64 1 (/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2))))))
Compiler

Compiled 4695 to 1508 computations (67.9% saved)

regimes1.3s (12.8%)

Accuracy

Total 0.3b remaining (82%)

Threshold costs 0.3b (82%)

Counts
323 → 1
Compiler

Compiled 16232 to 10918 computations (32.7% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01322
11822
21722

end192.0ms (1.9%)

Compiler

Compiled 299 to 181 computations (39.5% saved)

Profiling

Loading profile data...