Details

Time bar (total: 7.3s)

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)

sample4.9s (66.6%)

Results
2.3s3582×body1024valid
1.6s1297×body2048valid
572.0ms1383×body512valid
189.0ms1349×body128valid
167.0ms644×body256valid
4.0msbody4096valid
Compiler

Compiled 20 to 14 computations (30% saved)

preprocess22.0ms (0.3%)

Algorithm
egg-herbie
Rules
76×fma-def_binary64
57×fma-neg_binary64
27×cancel-sign-sub-inv_binary64
24×sub-neg_binary64
18×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
11722
22522
33822
45322
58122
614122
720022
828222
935322
1040522
1140922
022
Stop Event
saturated
saturated
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11011
21511
32211
43111
54811
68611
712411
817211
920811
1023411
1123611
Stop Event
saturated
Counts
1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
34.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
34.2b
(-.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
0.8b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.9b
(sin.f64 (+.f64 x eps))

series9.0ms (0.1%)

Counts
2 → 48
Calls

12 calls:

1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
eps
0
1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
eps
-inf
1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
eps
inf
1.0ms
(sin.f64 (+.f64 x eps))
x
0
1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
x
0

rewrite59.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
471×fma-def_binary64
445×log-prod_binary64
214×fma-neg_binary64
179×expm1-udef_binary64
179×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
117317
2273717
Stop Event
node limit
Counts
2 → 151

simplify32.0ms (0.4%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
053602
1172587
2566572
32209569
Stop Event
node limit
Counts
199 → 180

prune148.0ms (2%)

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
19.8b
(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)))
20.1b
(-.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))
19.8b
(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)))
32.3b
(fma.f64 (cos.f64 x) (-.f64 eps (*.f64 1/6 (pow.f64 eps 3))) (*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps -1/2))))
32.3b
(-.f64 (*.f64 eps (cos.f64 x)) (+.f64 (*.f64 1/6 (*.f64 (pow.f64 eps 3) (cos.f64 x))) (*.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x)))))
40.5b
(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)))
19.8b
(-.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))
19.4b
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
19.4b
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 3617 to 1139 computations (68.5% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps)))
0.1b
(*.f64 (sin.f64 x) (cos.f64 eps))
2.7b
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))

series40.0ms (0.6%)

Counts
3 → 56
Calls

18 calls:

5.0ms
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
eps
-inf
3.0ms
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
eps
inf
3.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps)))
x
-inf
3.0ms
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
x
inf
3.0ms
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
x
-inf

rewrite60.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
530×log-prod_binary64
346×fma-def_binary64
207×expm1-udef_binary64
207×log1p-udef_binary64
204×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01045
121425
2294025
Stop Event
node limit
Counts
3 → 152

simplify44.0ms (0.6%)

Algorithm
egg-herbie
Rules
400×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
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0861114
12741092
28681018
333411013
Stop Event
node limit
Counts
208 → 199

prune137.0ms (1.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1909199
Fresh358
Picked011
Done000
Total19315208
Error
0.0b
Counts
208 → 15
Alt Table
StatusErrorProgram
0.5b
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
19.8b
(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)))
20.0b
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (log.f64 (pow.f64 (exp.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 -1 (cos.f64 eps))))
32.3b
(fma.f64 (cos.f64 x) (-.f64 eps (*.f64 1/6 (pow.f64 eps 3))) (*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps -1/2))))
32.5b
(fma.f64 (*.f64 (cos.f64 x) (sqrt.f64 (sin.f64 eps))) (sqrt.f64 (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
0.5b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
13.2b
(fma.f64 (*.f64 (cos.f64 x) (cbrt.f64 (pow.f64 (sin.f64 eps) 2))) (cbrt.f64 (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
19.8b
(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)))
30.0b
(fma.f64 (sqrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (sqrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
19.4b
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) (sin.f64 x))
32.3b
(-.f64 (*.f64 eps (cos.f64 x)) (+.f64 (*.f64 1/6 (*.f64 (pow.f64 eps 3) (cos.f64 x))) (*.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x)))))
40.5b
(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)))
1.6b
(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)))
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)))
Compiler

Compiled 4122 to 1393 computations (66.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series60.0ms (0.8%)

Counts
3 → 64
Calls

18 calls:

24.0ms
(-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))
eps
-inf
3.0ms
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
eps
-inf
3.0ms
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
eps
inf
3.0ms
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
x
-inf
3.0ms
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
x
inf

rewrite74.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
664×fma-def_binary64
388×fma-neg_binary64
237×expm1-udef_binary64
237×log1p-udef_binary64
135×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01142
124730
2362530
Stop Event
node limit
Counts
3 → 208

simplify43.0ms (0.6%)

Algorithm
egg-herbie
Rules
727×fma-def_binary64
471×cancel-sign-sub-inv_binary64
370×associate-*r*_binary64
344×associate-*l*_binary64
238×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01211266
13861222
212861092
Stop Event
node limit
Counts
272 → 257

prune366.0ms (5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2839292
Fresh10313
Picked101
Done101
Total29512307
Error
0.0b
Counts
307 → 12
Alt Table
StatusErrorProgram
0.8b
(fma.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 2) (pow.f64 (sin.f64 x) 2)) (/.f64 1 (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 x))) (*.f64 (cos.f64 x) (sin.f64 eps)))
19.4b
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 -1 (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))))
40.5b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (cos.f64 eps)) (neg.f64 (sin.f64 x))))
20.0b
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (log.f64 (pow.f64 (exp.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 -1 (cos.f64 eps))))
32.3b
(fma.f64 (cos.f64 x) (-.f64 eps (*.f64 1/6 (pow.f64 eps 3))) (*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps -1/2))))
32.5b
(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 (sin.f64 x) (-.f64 (cos.f64 eps) 1) (*.f64 (cos.f64 x) (sin.f64 eps)))
17.7b
(+.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) 3)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
30.0b
(fma.f64 (sqrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (sqrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) 1)))
29.2b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 -1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x))))
0.8b
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (*.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 eps)) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) 1)))
Compiler

Compiled 6871 to 2373 computations (65.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 -1 (cos.f64 eps))))
0.2b
(*.f64 (sin.f64 x) (+.f64 -1 (cos.f64 eps)))
2.5b
(+.f64 -1 (cos.f64 eps))

series29.0ms (0.4%)

Counts
3 → 60
Calls

15 calls:

3.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 -1 (cos.f64 eps))))
x
inf
3.0ms
(*.f64 (sin.f64 x) (+.f64 -1 (cos.f64 eps)))
eps
0
3.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 -1 (cos.f64 eps))))
x
-inf
3.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 -1 (cos.f64 eps))))
eps
-inf
3.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 -1 (cos.f64 eps))))
eps
inf

rewrite56.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
468×prod-diff_binary64
207×expm1-udef_binary64
207×log1p-udef_binary64
195×fma-def_binary64
173×log-pow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01136
122736
2292836
Stop Event
node limit
Counts
3 → 112

simplify49.0ms (0.7%)

Algorithm
egg-herbie
Rules
638×fma-def_binary64
575×sub-neg_binary64
424×cancel-sign-sub-inv_binary64
273×associate-*l*_binary64
256×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01061102
13271032
21070986
34773986
Stop Event
node limit
Counts
172 → 157

prune178.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1561157
Fresh2911
Picked101
Done000
Total15910169
Error
0.0b
Counts
169 → 10
Alt Table
StatusErrorProgram
0.8b
(fma.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 2) (pow.f64 (sin.f64 x) 2)) (/.f64 1 (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 x))) (*.f64 (cos.f64 x) (sin.f64 eps)))
19.4b
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 -1 (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))))
40.5b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (cos.f64 eps)) (neg.f64 (sin.f64 x))))
32.5b
(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 (sin.f64 x) (-.f64 (cos.f64 eps) 1) (*.f64 (cos.f64 x) (sin.f64 eps)))
0.4b
(fma.f64 (sin.f64 eps) (cos.f64 x) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (sin.f64 x)) (-.f64 -1 (cos.f64 eps))))
17.7b
(+.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) 3)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
30.0b
(fma.f64 (sqrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (sqrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) 1)))
29.2b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 -1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x))))
0.8b
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (*.f64 (cbrt.f64 (cos.f64 x)) (sin.f64 eps)) (*.f64 (sin.f64 x) (-.f64 (cos.f64 eps) 1)))
Compiler

Compiled 3167 to 1341 computations (57.7% saved)

regimes825.0ms (11.3%)

Accuracy

Total 0.3b remaining (78.6%)

Threshold costs 0.3b (78.6%)

Counts
260 → 1
Compiler

Compiled 13886 to 9208 computations (33.7% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01427
11727
22127
32327
42427
Stop Event
saturated

end154.0ms (2.1%)

Stop Event
fuel
Compiler

Compiled 234 to 151 computations (35.5% saved)

Profiling

Loading profile data...