Details

Time bar (total: 4.3s)

analyze2.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
28.1%28.1%43.8%2
56.2%0%43.8%3
Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.8s (42.1%)

Results
854.0ms6173×body128valid
398.0ms1041×body1024valid
177.0ms617×body512valid
67.0ms325×body256valid
43.0ms100×body2048valid
Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify205.0ms (4.7%)

Algorithm
egg-herbie
Rules
890×sub-neg_binary64
434×cancel-sign-sub-inv_binary64
422×associate-/l*_binary64
388×distribute-rgt-neg-in_binary64
379×neg-mul-1_binary64
Counts
1 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01119
12319
23919
36419
410819
521517
635317
760317
8114117
9248417
10319517
11398117
12423517
13439917
14450317
15453117
16453317
17476817
18470817
19493017
20482617

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
15.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
15.5b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
2.7b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series39.0ms (0.9%)

Counts
2 → 48
Calls

2 calls:

25.0ms
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
14.0ms
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite63.0ms (1.5%)

Algorithm
batch-egg-rewrite
Rules
472×fma-def_binary64
257×fma-neg_binary64
236×expm1-udef_binary64
236×log1p-udef_binary64
132×add-sqr-sqrt_binary64
Counts
2 → 76
Calls

2 calls:

61.0ms
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
61.0ms
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01130
126130
2356330
3490830
000
100

simplify65.0ms (1.5%)

Algorithm
egg-herbie
Rules
935×times-frac_binary64
498×cancel-sign-sub-inv_binary64
367×sub-neg_binary64
205×+-commutative_binary64
189×associate-+r+_binary64
Counts
124 → 130
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02212358
17492323
229132279
352522279

prune123.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1264130
Fresh000
Picked101
Done000
Total1274131
Error
0.1b
Counts
131 → 4
Alt Table
StatusErrorProgram
15.5b
(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
47.8b
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
48.9b
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
46.0b
(/.f64 (+.f64 beta 1) alpha)
Compiler

Compiled 4173 to 2664 computations (36.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta))
0.1b
(pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1)
2.7b
(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)

series87.0ms (2%)

Counts
3 → 72
Calls

3 calls:

45.0ms
(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
29.0ms
(pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1)
13.0ms
(/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta))

rewrite71.0ms (1.6%)

Algorithm
batch-egg-rewrite
Rules
647×prod-diff_binary64
144×add-sqr-sqrt_binary64
140×log1p-expm1-u_binary64
140×expm1-log1p-u_binary64
136×add-log-exp_binary64
Counts
3 → 108
Calls

3 calls:

68.0ms
(/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta))
68.0ms
(pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1)
68.0ms
(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01349
129543
2367343
3489243
000
100

simplify88.0ms (2%)

Algorithm
egg-herbie
Rules
514×fma-def_binary64
430×associate-+l+_binary64
329×times-frac_binary64
287×associate-/r*_binary64
193×associate-/l*_binary64
Counts
180 → 191
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04224212
114834134
252804134

prune223.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1910191
Fresh033
Picked011
Done000
Total1914195
Error
0.1b
Counts
195 → 4
Alt Table
StatusErrorProgram
15.5b
(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
47.8b
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
48.9b
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
46.0b
(/.f64 (+.f64 beta 1) alpha)
Compiler

Compiled 7212 to 4805 computations (33.4% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 beta 1) alpha)

series6.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

6.0ms
(/.f64 (+.f64 beta 1) alpha)

rewrite43.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
645×log1p-expm1-u_binary64
645×expm1-log1p-u_binary64
298×log-prod_binary64
112×log1p-udef_binary64
111×expm1-udef_binary64
Counts
1 → 37
Calls

1 calls:

42.0ms
(/.f64 (+.f64 beta 1) alpha)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11287
216217
352987
000
100

simplify8.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
1-exp_binary64
Counts
49 → 40
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07102
110102
29102

prune29.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New40040
Fresh022
Picked011
Done011
Total40444
Error
0.1b
Counts
44 → 4
Alt Table
StatusErrorProgram
15.5b
(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
47.8b
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
48.9b
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
46.0b
(/.f64 (+.f64 beta 1) alpha)
Compiler

Compiled 743 to 499 computations (32.8% saved)

localize26.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
6.9b
(/.f64 beta (pow.f64 alpha 3))
7.0b
(/.f64 beta (*.f64 alpha alpha))
9.8b
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
18.2b
(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))

series130.0ms (3%)

Counts
4 → 72
Calls

4 calls:

41.0ms
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
35.0ms
(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
27.0ms
(/.f64 beta (pow.f64 alpha 3))
27.0ms
(/.f64 beta (*.f64 alpha alpha))

rewrite63.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
332×log1p-expm1-u_binary64
332×expm1-log1p-u_binary64
315×add-cbrt-cube_binary64
314×add-log-exp_binary64
313×add-exp-log_binary64
Counts
4 → 88
Calls

4 calls:

59.0ms
(/.f64 beta (pow.f64 alpha 3))
59.0ms
(/.f64 beta (*.f64 alpha alpha))
59.0ms
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
59.0ms
(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030105
1709101
25227101
000
100

simplify89.0ms (2.1%)

Algorithm
egg-herbie
Rules
745×times-frac_binary64
481×fma-neg_binary64
473×associate-+l+_binary64
428×fma-def_binary64
409×associate--l+_binary64
Counts
160 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0631749
11971724
26981602
332961602
449481602
549721602

prune159.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1092111
Fresh011
Picked101
Done022
Total1105115
Error
0.1b
Counts
115 → 5
Alt Table
StatusErrorProgram
15.5b
(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
57.5b
(/.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 5))))) 3) (pow.f64 (fma.f64 2 (pow.f64 alpha -2) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2))) 3)) (+.f64 (pow.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 5))))) 2) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 alpha -2) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2))) 2) (*.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 5))))) (fma.f64 2 (pow.f64 alpha -2) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2)))))))
48.9b
(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 5 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
46.0b
(/.f64 (+.f64 beta 1) alpha)
48.2b
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 5)))))) 2) (cbrt.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 5)))))) (neg.f64 (fma.f64 2 (pow.f64 alpha -2) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2)))))
Compiler

Compiled 7290 to 4074 computations (44.1% saved)

regimes725.0ms (16.8%)

Accuracy

Total 0.1b remaining (46.5%)

Threshold costs 0.1b (46.5%)

Counts
85 → 2
Compiler

Compiled 20550 to 13351 computations (35% saved)

bsearch7.0ms (0.2%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03686
14886
25786
36386
46686
56586

end226.0ms (5.2%)

Compiler

Compiled 509 to 328 computations (35.6% saved)

Profiling

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