Details

Time bar (total: 6.2s)

analyze330.0ms (5.3%)

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
0%99.9%0.1%5
15.6%84.3%0.1%6
37.5%62.4%0.1%7
46.8%53.1%0.1%8
57.8%39.8%2.4%9
64.6%30.4%5%10
71.8%20.3%7.9%11
74.1%16.2%9.7%12
77.4%10.7%12%13
78.6%8.4%13%14
Compiler

Compiled 24 to 18 computations (25% saved)

sample1.4s (22.7%)

Results
1.3s8256×body128valid
62.0ms338×body128invalid
Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify37.0ms (0.6%)

Algorithm
egg-herbie
Rules
693×div-sub_binary64
599×times-frac_binary64
519×associate-/l*_binary64
357×associate-/l/_binary64
274×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01632
13729
29429
334529
4120728
5346828
6502028

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
13.4b
(*.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
0.3b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
Compiler

Compiled 127 to 87 computations (31.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
0.2b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.2b
(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
0.3b
(/.f64 (PI.f64) a)

series48.0ms (0.8%)

Counts
4 → 72
Calls

4 calls:

18.0ms
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
18.0ms
(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
9.0ms
(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
2.0ms
(/.f64 (PI.f64) a)

rewrite35.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt_binary64
59×*-un-lft-identity_binary64
55×times-frac_binary64
39×add-cube-cbrt_binary64
21×associate-*r*_binary64
Counts
4 → 143
Calls

4 calls:

17.0ms
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
4.0ms
(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
2.0ms
(/.f64 (PI.f64) a)
0.0ms
(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))

simplify218.0ms (3.5%)

Algorithm
egg-herbie
Rules
425×times-frac_binary64
380×associate-/l/_binary64
318×fma-neg_binary64
291×fma-def_binary64
232×distribute-rgt-in_binary64
Counts
215 → 237
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02655398
16764819
221334749
346294748
449894748
549984748
649724748

prune300.0ms (4.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2289237
Fresh101
Picked101
Done000
Total2309239
Error
0b
Counts
239 → 9
Alt Table
StatusErrorProgram
0.3b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
0.8b
(*.f64 (/.f64 1/2 (+.f64 b a)) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (cbrt.f64 (-.f64 b a)))))
0.4b
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
13.3b
(/.f64 (*.f64 1/2 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (-.f64 (*.f64 b b) (*.f64 a a)))
0.3b
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.8b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))) (cbrt.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))) (cbrt.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))))
24.1b
(*.f64 1/2 (/.f64 (PI.f64) (*.f64 a (*.f64 a b))))
0.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 b a))) (cbrt.f64 (/.f64 1/2 (+.f64 b a)))) (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
0.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (*.f64 (/.f64 (cbrt.f64 1/2) (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
Compiler

Compiled 7144 to 2751 computations (61.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
0.2b
(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
0.2b
(/.f64 (PI.f64) b)
0.3b
(/.f64 (PI.f64) a)

series41.0ms (0.7%)

Counts
3 → 48
Calls

3 calls:

20.0ms
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
18.0ms
(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
3.0ms
(/.f64 (PI.f64) b)

rewrite65.0ms (1%)

Algorithm
rewrite-expression-head
Rules
142×add-sqr-sqrt_binary64
133×times-frac_binary64
122×*-un-lft-identity_binary64
44×add-cube-cbrt_binary64
43×distribute-lft-out--_binary64
Counts
3 → 156
Calls

3 calls:

21.0ms
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
21.0ms
(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
4.0ms
(/.f64 (PI.f64) b)

simplify160.0ms (2.6%)

Algorithm
egg-herbie
Rules
663×times-frac_binary64
311×fma-def_binary64
299×fma-neg_binary64
273×distribute-rgt-in_binary64
248×distribute-lft-in_binary64
Counts
204 → 206
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03115679
17985327
222285259
349715259
451495259

prune262.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2352237
Fresh268
Picked011
Done000
Total2379246
Error
0b
Counts
246 → 9
Alt Table
StatusErrorProgram
0.3b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
0.8b
(*.f64 (/.f64 1/2 (+.f64 b a)) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (cbrt.f64 (-.f64 b a)))))
0.4b
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
13.3b
(/.f64 (*.f64 1/2 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (-.f64 (*.f64 b b) (*.f64 a a)))
0.3b
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
24.1b
(*.f64 1/2 (/.f64 (PI.f64) (*.f64 a (*.f64 a b))))
0.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 b a))) (cbrt.f64 (/.f64 1/2 (+.f64 b a)))) (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
0.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))) (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a)))) (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))))
0.3b
(/.f64 (*.f64 1/2 (/.f64 (PI.f64) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b))))) (+.f64 b a))
Compiler

Compiled 6867 to 1960 computations (71.5% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
0.2b
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.2b
(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
0.3b
(/.f64 (PI.f64) a)

series17.0ms (0.3%)

Counts
1 → 24
Calls

1 calls:

17.0ms
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

rewrite32.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt_binary64
31×times-frac_binary64
30×*-un-lft-identity_binary64
21×associate-*r*_binary64
18×associate-*l*_binary64
Counts
1 → 65
Calls

1 calls:

20.0ms
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

simplify107.0ms (1.7%)

Algorithm
egg-herbie
Rules
580×associate-/l*_binary64
373×times-frac_binary64
307×fma-neg_binary64
285×fma-def_binary64
257×associate-/l/_binary64
Counts
89 → 96
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01903185
15502861
218172795
347732795
449632795

prune262.0ms (4.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2121213
Fresh167
Picked011
Done011
Total2139222
Error
0b
Counts
222 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
13.3b
(/.f64 (*.f64 1/2 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (-.f64 (*.f64 b b) (*.f64 a a)))
0.3b
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
24.1b
(*.f64 1/2 (/.f64 (PI.f64) (*.f64 a (*.f64 a b))))
0.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 b a))) (cbrt.f64 (/.f64 1/2 (+.f64 b a)))) (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
0.3b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
0.8b
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (cbrt.f64 (-.f64 b a))))
0.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))) (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a)))) (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))))
0.3b
(/.f64 (*.f64 1/2 (/.f64 (PI.f64) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b))))) (+.f64 b a))
Compiler

Compiled 6361 to 2619 computations (58.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b
(/.f64 (*.f64 1/2 (/.f64 (PI.f64) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b))))) (+.f64 b a))
0.2b
(/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b)))
0.8b
(/.f64 (PI.f64) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b))))

series59.0ms (0.9%)

Counts
4 → 78
Calls

4 calls:

19.0ms
(/.f64 (*.f64 1/2 (/.f64 (PI.f64) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b))))) (+.f64 b a))
17.0ms
(/.f64 (PI.f64) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b))))
17.0ms
(/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b)))
5.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))

rewrite282.0ms (4.5%)

Algorithm
rewrite-expression-head
Rules
1523×times-frac_binary64
1325×add-sqr-sqrt_binary64
1113×*-un-lft-identity_binary64
485×add-cube-cbrt_binary64
339×difference-of-squares_binary64
Counts
4 → 824
Calls

4 calls:

46.0ms
(/.f64 (*.f64 1/2 (/.f64 (PI.f64) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b))))) (+.f64 b a))
27.0ms
(/.f64 (PI.f64) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b))))
19.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
18.0ms
(/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b)))

simplify639.0ms (10.3%)

Algorithm
egg-herbie
Rules
729×fma-def_binary64
413×associate-/r/_binary64
361×associate-/l/_binary64
321×associate-*l/_binary64
267×associate-/l*_binary64
Counts
902 → 915
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
058432403
1138528377
2483228347
3548928347

prune1.1s (16.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New9141915
Fresh156
Picked101
Done022
Total9168924
Error
0b
Counts
924 → 8
Alt Table
StatusErrorProgram
0.4b
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
13.3b
(/.f64 (*.f64 1/2 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (-.f64 (*.f64 b b) (*.f64 a a)))
0.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 b a))) (cbrt.f64 (/.f64 1/2 (+.f64 b a)))) (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
0.3b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
0.8b
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (cbrt.f64 (-.f64 b a))))
0.3b
(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))) (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a)))) (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))))
0.8b
(/.f64 (*.f64 1/2 (PI.f64)) (*.f64 (+.f64 b a) (/.f64 (-.f64 b a) (-.f64 (/.f64 1 a) (/.f64 1 b)))))
Compiler

Compiled 35792 to 19696 computations (45% saved)

regimes673.0ms (10.8%)

Accuracy

Total 0.2b remaining (74.1%)

Threshold costs 0.2b (74.1%)

Counts
210 → 1
Compiler

Compiled 15895 to 9981 computations (37.2% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01217
11817
21717

end119.0ms (1.9%)

Compiler

Compiled 254 to 149 computations (41.3% saved)

Profiling

Loading profile data...