Details

Time bar (total: 9.2s)

analyze468.0ms (5.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
50%50%0.1%5
50%50%0.1%6
50%37.5%12.6%7
50%37.5%12.6%8
50%31.2%18.8%9
50%31.2%18.8%10
50%28.1%22%11
50%28.1%22%12
50%26.5%23.5%13
50%26.5%23.5%14
Compiler

Compiled 15 to 12 computations (20% saved)

sample219.0ms (2.4%)

Algorithm
intervals
Results
68.0ms157×body1024valid
29.0ms63×body1024invalid
12.0ms50×body512valid
12.0ms18×body2048valid
6.0ms33×body512invalid
5.0ms23×body256valid
2.0ms23×body128invalid
1.0ms11×body256invalid
1.0msbody128valid
Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify86.0ms (0.9%)

Algorithm
egg-herbie
Rules
626×associate-/l*_binary64
509×div-sub_binary64
462×times-frac_binary64
386×sub-neg_binary64
367×associate-/r*_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01218
12218
24918
311118
420817
536217
669217
7151317
8372617
9428717
10485717
11474917

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
58.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
58.9b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
Compiler

Compiled 53 to 38 computations (28.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 re)
0.0b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
5.6b
(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

series22.0ms (0.2%)

Counts
3 → 40
Calls

3 calls:

18.0ms
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms
(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
2.0ms
(cos.f64 re)

rewrite62.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
234×prod-diff_binary64
139×*-un-lft-identity_binary64
139×add-sqr-sqrt_binary64
135×add-cube-cbrt_binary64
130×exp-sum_binary64
Counts
3 → 219
Calls

3 calls:

14.0ms
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
12.0ms
(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
1.0ms
(cos.f64 re)

simplify182.0ms (2%)

Algorithm
egg-herbie
Rules
886×fma-neg_binary64
429×exp-prod_binary64
383×cancel-sign-sub-inv_binary64
342×associate-*l*_binary64
337×associate-*r*_binary64
Counts
259 → 279
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
04016434
16385656
223034622
341864617
451624617

prune156.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2781279
Fresh000
Picked011
Done000
Total2782280
Error
0.1b
Counts
280 → 2
Alt Table
StatusErrorProgram
0.3b
(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
58.9b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
Compiler

Compiled 10495 to 4014 computations (61.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5)))
0.0b
(*.f64 (cos.f64 re) (pow.f64 im 3))
0.1b
(*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))
0.1b
(*.f64 (cos.f64 re) im)

series62.0ms (0.7%)

Counts
4 → 16
Calls

4 calls:

23.0ms
(*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5)))
19.0ms
(*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))
13.0ms
(*.f64 (cos.f64 re) (pow.f64 im 3))
7.0ms
(*.f64 (cos.f64 re) im)

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
31×add-exp-log_binary64
21×add-sqr-sqrt_binary64
18×add-cbrt-cube_binary64
18×prod-exp_binary64
17×associate-*r*_binary64
Counts
4 → 95
Calls

4 calls:

5.0ms
(*.f64 (cos.f64 re) (pow.f64 im 3))
5.0ms
(*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))
4.0ms
(*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5)))
3.0ms
(*.f64 (cos.f64 re) im)

simplify100.0ms (1.1%)

Algorithm
egg-herbie
Rules
827×fma-neg_binary64
476×fma-def_binary64
346×cancel-sign-sub-inv_binary64
313×associate-*r*_binary64
258×associate-*l*_binary64
Counts
111 → 164
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01961704
14731481
216871413
335691412
448701410
549241410

prune193.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1595164
Fresh000
Picked011
Done011
Total1597166
Error
0.0b
Counts
166 → 7
Alt Table
StatusErrorProgram
31.6b
(neg.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 re) im)) (sqrt.f64 (*.f64 (cos.f64 re) im))) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
1.6b
(neg.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 re) im)) (cbrt.f64 (*.f64 (cos.f64 re) im))) (cbrt.f64 (*.f64 (cos.f64 re) im))) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
0.3b
(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
58.9b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
1.7b
(neg.f64 (+.f64 (*.f64 (*.f64 (cos.f64 re) (pow.f64 (cbrt.f64 im) 2)) (cbrt.f64 im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
13.7b
(neg.f64 (+.f64 (*.f64 (sqrt.f64 (cos.f64 re)) (*.f64 (sqrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
0.8b
(neg.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
Compiler

Compiled 5221 to 3117 computations (40.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cbrt.f64 (cos.f64 re)) im)
0.1b
(*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (cbrt.f64 (cos.f64 re)) im))
0.2b
(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
0.3b
(cbrt.f64 (cos.f64 re))

series864.0ms (9.4%)

Counts
4 → 72
Calls

4 calls:

433.0ms
(*.f64 (cbrt.f64 (cos.f64 re)) im)
243.0ms
(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
179.0ms
(cbrt.f64 (cos.f64 re))
9.0ms
(*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (cbrt.f64 (cos.f64 re)) im))

rewrite25.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
25×pow1_binary64
23×cbrt-prod_binary64
20×add-exp-log_binary64
16×*-un-lft-identity_binary64
Counts
4 → 103
Calls

4 calls:

11.0ms
(*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (cbrt.f64 (cos.f64 re)) im))
5.0ms
(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
4.0ms
(*.f64 (cbrt.f64 (cos.f64 re)) im)
1.0ms
(cbrt.f64 (cos.f64 re))

simplify114.0ms (1.2%)

Algorithm
egg-herbie
Rules
439×fma-neg_binary64
382×*-commutative_binary64
372×cancel-sign-sub-inv_binary64
257×fma-def_binary64
231×associate-+l+_binary64
Counts
175 → 158
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01521804
13411606
211311555
322771535
446701409
548551409
648961409

prune262.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2004204
Fresh134
Picked101
Done022
Total2029211
Error
0.0b
Counts
211 → 9
Alt Table
StatusErrorProgram
58.9b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
0.9b
(neg.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 re)))) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
1.7b
(neg.f64 (+.f64 (*.f64 (*.f64 (cos.f64 re) (pow.f64 (cbrt.f64 im) 2)) (cbrt.f64 im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
0.6b
(neg.f64 (+.f64 (*.f64 (pow.f64 (pow.f64 (cos.f64 re) 2) 1/3) (*.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
13.7b
(neg.f64 (+.f64 (*.f64 (sqrt.f64 (cos.f64 re)) (*.f64 (sqrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
1.1b
(neg.f64 (+.f64 (*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) 5) (cbrt.f64 (cbrt.f64 (cos.f64 re)))) (*.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
31.6b
(neg.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 re) im)) (sqrt.f64 (*.f64 (cos.f64 re) im))) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
1.0b
(neg.f64 (+.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))) (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))))) (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))))) (*.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
0.3b
(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
Compiler

Compiled 8081 to 3924 computations (51.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(pow.f64 (pow.f64 (cos.f64 re) 2) 1/3)
0.1b
(*.f64 (pow.f64 (pow.f64 (cos.f64 re) 2) 1/3) (*.f64 (cbrt.f64 (cos.f64 re)) im))
0.2b
(pow.f64 (cos.f64 re) 2)
0.3b
(cbrt.f64 (cos.f64 re))

series252.0ms (2.7%)

Counts
3 → 32
Calls

3 calls:

237.0ms
(pow.f64 (pow.f64 (cos.f64 re) 2) 1/3)
8.0ms
(*.f64 (pow.f64 (pow.f64 (cos.f64 re) 2) 1/3) (*.f64 (cbrt.f64 (cos.f64 re)) im))
7.0ms
(pow.f64 (cos.f64 re) 2)

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
27×add-exp-log_binary64
25×unpow-prod-down_binary64
15×prod-exp_binary64
13×pow-exp_binary64
12×associate-*l*_binary64
Counts
3 → 84
Calls

3 calls:

7.0ms
(*.f64 (pow.f64 (pow.f64 (cos.f64 re) 2) 1/3) (*.f64 (cbrt.f64 (cos.f64 re)) im))
3.0ms
(pow.f64 (pow.f64 (cos.f64 re) 2) 1/3)
2.0ms
(pow.f64 (cos.f64 re) 2)

simplify83.0ms (0.9%)

Algorithm
egg-herbie
Rules
747×fma-neg_binary64
691×fma-def_binary64
363×*-commutative_binary64
216×unswap-sqr_binary64
205×associate-+l+_binary64
Counts
116 → 135
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01471654
13431348
210241202
321071194
445051192
549661192

prune292.0ms (3.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1571158
Fresh156
Picked011
Done022
Total1589167
Error
0.0b
Counts
167 → 9
Alt Table
StatusErrorProgram
58.9b
(*.f64 (*.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
0.9b
(neg.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 re)))) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
1.7b
(neg.f64 (+.f64 (*.f64 (*.f64 (cos.f64 re) (pow.f64 (cbrt.f64 im) 2)) (cbrt.f64 im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
0.6b
(neg.f64 (+.f64 (*.f64 (pow.f64 (pow.f64 (cos.f64 re) 2) 1/3) (*.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
13.7b
(neg.f64 (+.f64 (*.f64 (sqrt.f64 (cos.f64 re)) (*.f64 (sqrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
1.1b
(neg.f64 (+.f64 (*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) 5) (cbrt.f64 (cbrt.f64 (cos.f64 re)))) (*.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
31.6b
(neg.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 re) im)) (sqrt.f64 (*.f64 (cos.f64 re) im))) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
0.3b
(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
13.7b
(neg.f64 (+.f64 (*.f64 (pow.f64 (pow.f64 (cos.f64 re) 2) 1/3) (*.f64 (pow.f64 (cos.f64 re) 1/3) im)) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
Compiler

Compiled 6025 to 3683 computations (38.9% saved)

regimes573.0ms (6.2%)

Accuracy

Total 0.7b remaining (94.2%)

Threshold costs 0.7b (94.2%)

Counts
82 → 1
Compiler

Compiled 14776 to 9991 computations (32.4% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
01836
13236
25034
38034
410434
511634
612234
712434
812234

end1.0ms (0%)

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample5.1s (55.3%)

Algorithm
intervals
Results
2.4s4877×body1024valid
765.0ms1933×body1024invalid
514.0ms1672×body512valid
313.0ms419×body2048valid
196.0ms962×body512invalid
188.0ms653×body256valid
59.0ms449×body256invalid
57.0ms718×body128invalid
29.0ms379×body128valid
Compiler

Compiled 314 to 209 computations (33.4% saved)

Profiling

Loading profile data...