Details

Time bar (total: 8.0s)

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)

sample5.1s (64%)

Results
2.5s3583×body1024valid
1.5s1250×body2048valid
671.0ms1449×body512valid
202.0ms616×body256valid
198.0ms1354×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

prune2.0ms (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))

series11.0ms (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))

rewrite66.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
151×egg-rr
Counts
2 → 151
Calls

2 calls:

60.0ms
((sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
117317
2253917
3535917
000
100

simplify104.0ms (1.3%)

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

prune152.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1719180
Fresh000
Picked101
Done000
Total1729181
Error
0.1b
Counts
181 → 9
Alt Table
StatusErrorProgram
23.1b
(-.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))
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)) (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))
22.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.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)))
22.6b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.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
(-.f64 (log.f64 (*.f64 (exp.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (exp.f64 (*.f64 (sin.f64 x) (cos.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 3649 to 1128 computations (69.1% saved)

localize11.0ms (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))

series42.0ms (0.5%)

Counts
4 → 68
Calls

4 calls:

18.0ms
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
14.0ms
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
9.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
2.0ms
(cos.f64 x)

rewrite99.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
149×egg-rr
Counts
4 → 149
Calls

2 calls:

96.0ms
((-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (cos.f64 x))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01048
120748
2259828
3464928
4513528
000
100

simplify90.0ms (1.1%)

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
217 → 203
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0951230
12971199
28891112
329061102
450391102

prune172.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1994203
Fresh358
Picked101
Done000
Total2039212
Error
0.1b
Counts
212 → 9
Alt Table
StatusErrorProgram
29.6b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 2) (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)) (fma.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 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.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)))
22.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (expm1.f64 (log1p.f64 (*.f64 (cos.f64 x) (sin.f64 eps))))) (sin.f64 x))
0.3b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
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
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 3990 to 1334 computations (66.6% 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)

series29.0ms (0.4%)

Counts
3 → 60
Calls

3 calls:

16.0ms
(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)

rewrite92.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
113×egg-rr
Counts
3 → 113
Calls

2 calls:

90.0ms
((+.f64 (cos.f64 eps) -1) (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01136
122736
2275130
3474330
4554430
000
100

simplify70.0ms (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

prune220.0ms (2.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1738181
Fresh628
Picked101
Done000
Total18010190
Error
0.0b
Counts
190 → 10
Alt Table
StatusErrorProgram
0.4b
(fma.f64 (sin.f64 eps) (log.f64 (exp.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
20.4b
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) 3) (pow.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) 3)) (fma.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (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))))))
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) (*.f64 (sin.f64 x) (/.f64 1 (/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2))))))
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)))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (+.f64 (cos.f64 eps) -1)) 3)))
0.5b
(fma.f64 (sin.f64 eps) (cbrt.f64 (pow.f64 (cos.f64 x) 3)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
23.0b
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 (cbrt.f64 (sin.f64 x)) (cos.f64 eps)) (neg.f64 (sin.f64 x))))
22.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (expm1.f64 (log1p.f64 (*.f64 (cos.f64 x) (sin.f64 eps))))) (sin.f64 x))
0.4b
(fma.f64 (sin.f64 eps) (expm1.f64 (log1p.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
Compiler

Compiled 3775 to 1641 computations (56.5% saved)

localize11.0ms (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 (+.f64 (cos.f64 eps) -1) (sin.f64 x))
0.1b
(*.f64 (sin.f64 eps) (cos.f64 x))
1.9b
(+.f64 (cos.f64 eps) -1)

series37.0ms (0.5%)

Counts
3 → 64
Calls

3 calls:

17.0ms
(+.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
101×egg-rr
Counts
3 → 101
Calls

2 calls:

95.0ms
((*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) (+.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01238
125838
2335538
3497838
4495838
000
100

simplify65.0ms (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

prune276.0ms (3.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1885193
Fresh369
Picked011
Done000
Total19112203
Error
0.0b
Counts
203 → 12
Alt Table
StatusErrorProgram
0.8b
(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)))
1.5b
(*.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)))) (pow.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)))) 2))
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) (*.f64 (sin.f64 x) (/.f64 1 (/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2))))))
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)))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (+.f64 (cos.f64 eps) -1)) 3)))
0.5b
(fma.f64 (sin.f64 eps) (cbrt.f64 (pow.f64 (cos.f64 x) 3)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
20.4b
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) 3) (pow.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) 3)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) 2) (-.f64 (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))))))
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)))
22.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (expm1.f64 (log1p.f64 (*.f64 (cos.f64 x) (sin.f64 eps))))) (sin.f64 x))
0.4b
(fma.f64 (sin.f64 eps) (expm1.f64 (log1p.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.4b
(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)))))
Compiler

Compiled 4231 to 1938 computations (54.2% saved)

regimes999.0ms (12.5%)

Accuracy

Total 0.3b remaining (80.1%)

Threshold costs 0.3b (80.1%)

Counts
298 → 1
Compiler

Compiled 15313 to 10323 computations (32.6% saved)

simplify3.0ms (0%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01224
11523
21623
31823
41923
52023
62023

end200.0ms (2.5%)

Compiler

Compiled 308 to 199 computations (35.4% saved)

Profiling

Loading profile data...