Details

Time bar (total: 8.7s)

analyze289.0ms (3.3%)

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)

sample68.0ms (0.8%)

Algorithm
intervals
Results
18.0ms195×body128valid
11.0ms30×body1024valid
10.0ms256×pre128true
5.0ms19×body512valid
4.0msbody2048valid
2.0msbody256valid
Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify221.0ms (2.5%)

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

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
15.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
15.7b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
Compiler

Compiled 55 to 39 computations (29.1% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
2.2b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series82.0ms (0.9%)

Counts
2 → 48
Calls

2 calls:

61.0ms
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
20.0ms
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite14.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
25×times-frac_binary64
18×distribute-lft-out_binary64
14×add-cube-cbrt_binary64
Counts
2 → 64
Calls

2 calls:

9.0ms
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0ms
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify149.0ms (1.7%)

Algorithm
egg-herbie
Rules
960×times-frac_binary64
218×+-commutative_binary64
206×fma-def_binary64
194×fma-neg_binary64
193×associate-+r+_binary64
Counts
112 → 142
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03133790
19623664
234863620
349843620

prune262.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1357142
Fresh000
Picked101
Done000
Total1367143
Error
0.1b
Counts
143 → 7
Alt Table
StatusErrorProgram
15.8b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
45.6b
(/.f64 (+.f64 beta 1) alpha)
25.0b
(fma.f64 (*.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) -4)) (-.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
46.5b
(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
15.7b
(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
43.4b
(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
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 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))))))))))
Compiler

Compiled 4581 to 2821 computations (38.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.1b
(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
2.2b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
3.1b
(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

series397.0ms (4.6%)

Counts
2 → 48
Calls

2 calls:

309.0ms
(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
87.0ms
(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
log-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
exp-prod_binary64
Counts
2 → 31
Calls

2 calls:

3.0ms
(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
2.0ms
(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify219.0ms (2.5%)

Algorithm
egg-herbie
Rules
594×times-frac_binary64
585×associate-/r*_binary64
539×fma-def_binary64
383×associate-/l*_binary64
182×+-commutative_binary64
Counts
79 → 117
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05566288
118866047
252296047

prune562.0ms (6.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2563259
Fresh156
Picked101
Done000
Total2588266
Error
0.1b
Counts
266 → 8
Alt Table
StatusErrorProgram
15.8b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
45.6b
(/.f64 (+.f64 beta 1) alpha)
25.0b
(fma.f64 (*.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) -4)) (-.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
46.5b
(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
15.8b
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
15.8b
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
16.4b
(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -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 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))))))))))
Compiler

Compiled 12793 to 8801 computations (31.2% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.2b
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
2.2b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
3.1b
(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

series330.0ms (3.8%)

Counts
1 → 24
Calls

1 calls:

330.0ms
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
pow-unpow_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
pow1_binary64
Counts
1 → 24
Calls

1 calls:

5.0ms
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

simplify156.0ms (1.8%)

Algorithm
egg-herbie
Rules
298×times-frac_binary64
294×sub-neg_binary64
271×associate-/r*_binary64
239×associate-/l*_binary64
232×fma-def_binary64
Counts
48 → 75
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02943718
110163263
243943176
350483176

prune841.0ms (9.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2772279
Fresh167
Picked011
Done000
Total2789287
Error
0.1b
Counts
287 → 9
Alt Table
StatusErrorProgram
16.4b
(pow.f64 (E.f64) (*.f64 (*.f64 (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))))
15.8b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
45.6b
(/.f64 (+.f64 beta 1) alpha)
25.0b
(fma.f64 (*.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) -4)) (-.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
46.5b
(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
16.8b
(*.f64 (pow.f64 (*.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (pow.f64 (cbrt.f64 (E.f64)) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))
15.8b
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
15.8b
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -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 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))))))))))
Compiler

Compiled 15709 to 10785 computations (31.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha))))
0.2b
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
3.1b
(log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2))
4.9b
(fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

series481.0ms (5.5%)

Counts
4 → 96
Calls

4 calls:

307.0ms
(log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2))
74.0ms
(fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)
64.0ms
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
35.0ms
(*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha))))

rewrite42.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
21×associate-*r*_binary64
17×times-frac_binary64
17×add-cube-cbrt_binary64
Counts
4 → 93
Calls

4 calls:

23.0ms
(*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha))))
3.0ms
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
1.0ms
(log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2))
1.0ms
(fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

simplify321.0ms (3.7%)

Algorithm
egg-herbie
Rules
646×fma-def_binary64
622×times-frac_binary64
219×+-commutative_binary64
180×*-commutative_binary64
165×associate-+r+_binary64
Counts
189 → 226
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07019793
123359363
249729363
349699363

prune627.0ms (7.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2260226
Fresh077
Picked011
Done011
Total2269235
Error
0.1b
Counts
235 → 9
Alt Table
StatusErrorProgram
16.4b
(pow.f64 (E.f64) (*.f64 (*.f64 (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))))
15.8b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
45.6b
(/.f64 (+.f64 beta 1) alpha)
25.0b
(fma.f64 (*.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) (+.f64 beta alpha) -4)) (-.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
46.5b
(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
16.8b
(*.f64 (pow.f64 (*.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (pow.f64 (cbrt.f64 (E.f64)) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))
15.8b
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
15.8b
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -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 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))))))))))
Compiler

Compiled 11449 to 8191 computations (28.5% saved)

regimes1.1s (12.6%)

Accuracy

Total 0.0b remaining (53.8%)

Threshold costs 0.0b (53.8%)

Counts
81 → 2
Compiler

Compiled 8639 to 6355 computations (26.4% saved)

bsearch6.0ms (0.1%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02678
13778
24878
36178
46778
56978
66778

end2.0ms (0%)

Compiler

Compiled 55 to 30 computations (45.5% saved)

sample2.4s (27.7%)

Algorithm
intervals
Results
524.0ms5991×body128valid
400.0ms1022×body1024valid
272.0ms8000×pre128true
157.0ms580×body512valid
59.0ms329×body256valid
42.0ms78×body2048valid
Compiler

Compiled 374 to 241 computations (35.6% saved)

Profiling

Loading profile data...