Details

Time bar (total: 5.9s)

analyze294.0ms (5%)

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)

sample66.0ms (1.1%)

Algorithm
intervals
Results
18.0ms195×body128valid
11.0ms30×body1024valid
9.0ms256×pre128true
5.0ms19×body512valid
2.0msbody256valid
1.0msbody2048valid
Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify223.0ms (3.8%)

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)

localize15.0ms (0.3%)

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)

series113.0ms (1.9%)

Counts
2 → 48
Calls

2 calls:

75.0ms
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
38.0ms
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite32.0ms (0.5%)

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:

20.0ms
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
1.0ms
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify168.0ms (2.8%)

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

prune263.0ms (4.4%)

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
45.6b
(/.f64 (+.f64 beta 1) alpha)
15.8b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
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)
15.7b
(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.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)))))
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)

localize19.0ms (0.3%)

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))

series394.0ms (6.6%)

Counts
2 → 48
Calls

2 calls:

321.0ms
(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
73.0ms
(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite7.0ms (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))

simplify214.0ms (3.6%)

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

prune660.0ms (11.1%)

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
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
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)
45.6b
(/.f64 (+.f64 beta 1) alpha)
15.8b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.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)))
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)

localize13.0ms (0.2%)

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))

series197.0ms (3.3%)

Counts
1 → 24
Calls

1 calls:

197.0ms
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite3.0ms (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:

2.0ms
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

simplify87.0ms (1.5%)

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

prune434.0ms (7.3%)

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
15.8b
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
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)
45.6b
(/.f64 (+.f64 beta 1) alpha)
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)))
15.8b
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
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))))
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)))))
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)

localize11.0ms (0.2%)

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)

series261.0ms (4.4%)

Counts
4 → 96
Calls

4 calls:

158.0ms
(log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2))
43.0ms
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
37.0ms
(fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)
22.0ms
(*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha))))

rewrite21.0ms (0.4%)

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:

12.0ms
(*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha))))
2.0ms
(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))
0.0ms
(fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

simplify197.0ms (3.3%)

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

prune402.0ms (6.8%)

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
15.8b
(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
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)
45.6b
(/.f64 (+.f64 beta 1) alpha)
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)))
15.8b
(exp.f64 (log.f64 (fma.f64 (*.f64 (-.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
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))))
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)))))
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)

regimes544.0ms (9.2%)

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)

bsearch3.0ms (0.1%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03276
14776
26176
37676
48376
58576
68376

end1.0ms (0%)

Compiler

Compiled 54 to 31 computations (42.6% saved)

sample1.3s (21.6%)

Algorithm
intervals
Results
305.0ms5991×body128valid
185.0ms1022×body1024valid
159.0ms8000×pre128true
77.0ms580×body512valid
28.0ms329×body256valid
16.0ms78×body2048valid
Compiler

Compiled 373 to 242 computations (35.1% saved)

Profiling

Loading profile data...