Details

Time bar (total: 8.8s)

analyze2.0ms (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)

sample6.2s (70.3%)

Results
3.0s3677×body1024valid
1.9s1180×body2048valid
736.0ms1447×body512valid
269.0ms1343×body128valid
196.0ms607×body256valid
6.0msbody4096valid
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
33.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
33.7b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.5b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.8b
(sin.f64 (+.f64 x eps))

series16.0ms (0.2%)

Counts
2 → 48
Calls

2 calls:

11.0ms
(-.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
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:

63.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
63.0ms
(sin.f64 (+.f64 x eps))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
117317
2253917
3535917
000
100

simplify62.0ms (0.7%)

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

prune141.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1737180
Fresh000
Picked101
Done000
Total1747181
Error
0.1b
Counts
181 → 7
Alt Table
StatusErrorProgram
20.8b
(-.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))
17.2b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
17.2b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
35.7b
(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)))))
26.2b
(-.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))
38.5b
(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)))
17.6b
(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)))
Compiler

Compiled 3569 to 1094 computations (69.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 eps)
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))
3.0b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series44.0ms (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))
15.0ms
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
10.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
2.0ms
(sin.f64 eps)

rewrite108.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
960×prod-diff_binary64
281×fma-def_binary64
198×expm1-udef_binary64
198×log1p-udef_binary64
151×fma-neg_binary64
Counts
4 → 150
Calls

4 calls:

103.0ms
(sin.f64 eps)
103.0ms
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
103.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
103.0ms
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01048
120748
2259828
3464928
4513528
000
100

simplify82.0ms (0.9%)

Algorithm
egg-herbie
Rules
441×cancel-sign-sub-inv_binary64
440×fma-def_binary64
382×distribute-rgt-neg-in_binary64
371×sub-neg_binary64
364×distribute-lft-neg-in_binary64
Counts
218 → 204
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0941234
12921193
28831116
328731108
448511108
550341108

prune157.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1995204
Fresh156
Picked101
Done000
Total20110211
Error
0.1b
Counts
211 → 10
Alt Table
StatusErrorProgram
20.8b
(-.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))
17.4b
(fma.f64 (*.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (cos.f64 eps)) 2)) (cbrt.f64 (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
17.3b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (log1p.f64 (expm1.f64 (sin.f64 eps))))) (sin.f64 x))
17.6b
(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)))
17.2b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
37.6b
(fma.f64 (*.f64 (sin.f64 x) (sqrt.f64 (cos.f64 eps))) (sqrt.f64 (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
35.7b
(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)))))
26.2b
(-.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))
38.5b
(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)))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
Compiler

Compiled 4101 to 1392 computations (66.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 eps)
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)))
1.4b
(+.f64 (cos.f64 eps) -1)

series30.0ms (0.3%)

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)

rewrite93.0ms (1.1%)

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:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01136
122736
2275130
3474330
4554430
000
100

simplify62.0ms (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
173 → 155
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01061102
13211032
21019986
33708986
44957986

prune206.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1775182
Fresh549
Picked011
Done000
Total18210192
Error
0.1b
Counts
192 → 10
Alt Table
StatusErrorProgram
38.8b
(fma.f64 (pow.f64 (pow.f64 (sin.f64 eps) 3) 1/3) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
20.8b
(-.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))
2.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)))) 1))
0.3b
(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))))))
17.3b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (log1p.f64 (expm1.f64 (sin.f64 eps))))) (sin.f64 x))
17.6b
(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)))
0.6b
(fma.f64 (sin.f64 eps) (cos.f64 x) (pow.f64 (cbrt.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))) 3))
17.2b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
1.6b
(fma.f64 (pow.f64 (cbrt.f64 (sin.f64 eps)) 3) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
Compiler

Compiled 3788 to 1633 computations (56.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2)))
0.3b
(pow.f64 (sin.f64 eps) 2)
0.5b
(+.f64 (cos.f64 eps) 1)
0.6b
(/.f64 1 (/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2))))

series51.0ms (0.6%)

Counts
4 → 40
Calls

4 calls:

28.0ms
(/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2)))
16.0ms
(/.f64 1 (/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2))))
3.0ms
(pow.f64 (sin.f64 eps) 2)
3.0ms
(+.f64 (cos.f64 eps) 1)

rewrite71.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
917×log1p-expm1-u_binary64
917×expm1-log1p-u_binary64
172×egg-rr
147×prod-diff_binary64
113×add-sqr-sqrt_binary64
Counts
4 → 172
Calls

4 calls:

68.0ms
(/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2)))
68.0ms
(pow.f64 (sin.f64 eps) 2)
68.0ms
(+.f64 (cos.f64 eps) 1)
68.0ms
(/.f64 1 (/.f64 (+.f64 (cos.f64 eps) 1) (neg.f64 (pow.f64 (sin.f64 eps) 2))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01147
123927
2240827
3579327
000
100

simplify97.0ms (1.1%)

Algorithm
egg-herbie
Rules
573×cancel-sign-sub-inv_binary64
482×distribute-rgt-neg-in_binary64
480×fma-neg_binary64
440×sub-neg_binary64
400×times-frac_binary64
Counts
212 → 208
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
067568
1179548
2481530
31423498
43193498
54393498
64974498
74899498

prune271.0ms (3.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2080208
Fresh088
Picked011
Done011
Total20810218
Error
0.1b
Counts
218 → 10
Alt Table
StatusErrorProgram
38.8b
(fma.f64 (pow.f64 (pow.f64 (sin.f64 eps) 3) 1/3) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
20.8b
(-.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))
2.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)))) 1))
0.3b
(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))))))
17.3b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (log1p.f64 (expm1.f64 (sin.f64 eps))))) (sin.f64 x))
17.6b
(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)))
0.6b
(fma.f64 (sin.f64 eps) (cos.f64 x) (pow.f64 (cbrt.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))) 3))
17.2b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
1.6b
(fma.f64 (pow.f64 (cbrt.f64 (sin.f64 eps)) 3) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
Compiler

Compiled 5037 to 2750 computations (45.4% saved)

regimes812.0ms (9.2%)

Accuracy

Total 0.1b remaining (51.5%)

Threshold costs 0.1b (51.5%)

Counts
256 → 1
Compiler

Compiled 12808 to 8627 computations (32.6% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
+-commutative_binary64
sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01326
12126
23226
34226
44926
55326
65426
75426

end177.0ms (2%)

Compiler

Compiled 255 to 156 computations (38.8% saved)

Profiling

Loading profile data...