Details

Time bar (total: 17.1s)

analyze118.0ms (0.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
7%21.1%71.9%3
17.5%10.5%71.9%4
21.1%7%71.9%5
22.8%5.3%71.9%6
23.2%4.8%71.9%7
23.7%4.4%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 43 to 28 computations (34.9% saved)

sample2.3s (13.5%)

Results
1.4s6694×body128valid
419.0ms557×body512valid
312.0ms671×body1024valid
74.0ms279×body256valid
31.0ms55×body2048valid
Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify45.0ms (0.3%)

Algorithm
egg-herbie
Rules
847×times-frac_binary64
817×distribute-rgt-in_binary64
748×distribute-lft-in_binary64
537×div-sub_binary64
535×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01643
13439
211037
343537
4167237
5249437
6335837
7539237

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
18.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
22.8b
(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
19.0b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 180 to 106 computations (41.1% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
11.2b
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
17.8b
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series889.0ms (5.2%)

Counts
3 → 108
Calls

3 calls:

556.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
308.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
25.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

rewrite19.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
add-cube-cbrt_binary64
Counts
3 → 67
Calls

3 calls:

8.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
6.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify200.0ms (1.2%)

Algorithm
egg-herbie
Rules
561×+-commutative_binary64
490×fma-def_binary64
487×associate-+r+_binary64
392×*-commutative_binary64
294×associate-*r/_binary64
Counts
175 → 205
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0140019973
1545019973

prune685.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2023205
Fresh011
Picked101
Done000
Total2034207
Error
0.0b
Counts
207 → 4
Alt Table
StatusErrorProgram
50.6b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
11.1b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
22.8b
(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
52.6b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
Compiler

Compiled 24695 to 15944 computations (35.4% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.3b
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
11.2b
(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series966.0ms (5.7%)

Counts
3 → 108
Calls

3 calls:

585.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)
327.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
53.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))

rewrite43.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
166×times-frac_binary64
156×*-un-lft-identity_binary64
116×add-sqr-sqrt_binary64
78×add-cube-cbrt_binary64
24×associate-/l*_binary64
Counts
3 → 169
Calls

3 calls:

11.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
5.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
0.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

simplify262.0ms (1.5%)

Algorithm
egg-herbie
Rules
490×fma-def_binary64
477×associate-+r+_binary64
326×associate-*r/_binary64
177×associate-/l*_binary64
171×associate-/r*_binary64
Counts
277 → 298
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0159125853
1504625853

prune679.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2962298
Fresh123
Picked101
Done000
Total2984302
Error
0.0b
Counts
302 → 4
Alt Table
StatusErrorProgram
11.1b
(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
50.6b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
52.6b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
11.1b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
Compiler

Compiled 30279 to 18745 computations (38.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.3b
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
2.0b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
2.8b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

series848.0ms (5%)

Counts
2 → 72
Calls

2 calls:

520.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
328.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

rewrite69.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
139×times-frac_binary64
123×*-un-lft-identity_binary64
92×add-sqr-sqrt_binary64
82×associate-*r*_binary64
59×add-cube-cbrt_binary64
Counts
2 → 125
Calls

2 calls:

25.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
16.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify293.0ms (1.7%)

Algorithm
egg-herbie
Rules
404×+-commutative_binary64
361×*-commutative_binary64
354×fma-def_binary64
349×associate-+r+_binary64
271×associate-*r/_binary64
Counts
197 → 265
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0123621338
1472821233
2501321233

prune1.2s (7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New5052507
Fresh033
Picked101
Done000
Total5065511
Error
0.0b
Counts
511 → 5
Alt Table
StatusErrorProgram
11.1b
(/.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))) 2)
50.6b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
27.9b
(/.f64 (/.f64 (fma.f64 (pow.f64 (+.f64 beta alpha) 2) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) -1) (fma.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))) -1)) 2)
52.6b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
11.1b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
Compiler

Compiled 48820 to 29876 computations (38.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))))
0.3b
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha)))
2.0b
(*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
2.8b
(log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))

series4.4s (25.8%)

Counts
4 → 144
Calls

4 calls:

2.5s
(log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))
1.5s
(exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))))
381.0ms
(*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
70.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha)))

rewrite62.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
154×times-frac_binary64
144×*-un-lft-identity_binary64
113×add-sqr-sqrt_binary64
82×associate-*r*_binary64
72×add-cube-cbrt_binary64
Counts
4 → 176
Calls

4 calls:

24.0ms
(*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
5.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha)))
1.0ms
(exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))))
0.0ms
(log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))

simplify609.0ms (3.6%)

Algorithm
egg-herbie
Rules
1155×fma-def_binary64
457×times-frac_binary64
14×cube-mult_binary64
14×unpow3_binary64
13×unpow2_binary64
Counts
320 → 345
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0325568432
1523468432

prune2.0s (11.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3450345
Fresh044
Picked011
Done000
Total3455350
Error
0.0b
Counts
350 → 5
Alt Table
StatusErrorProgram
11.1b
(/.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))))) 2)
50.6b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
27.9b
(/.f64 (/.f64 (fma.f64 (pow.f64 (+.f64 beta alpha) 2) (*.f64 (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) -1) (fma.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))) -1)) 2)
52.6b
(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (*.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
11.1b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
Compiler

Compiled 90497 to 61843 computations (31.7% saved)

regimes1.2s (6.7%)

Accuracy

Total 1.4b remaining (92.8%)

Threshold costs 0b (0%)

Counts
109 → 2
Compiler

Compiled 21880 to 15248 computations (30.3% saved)

bsearch5.0ms (0%)

Compiler

Compiled 28 to 16 computations (42.9% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03299
14299
24799
34999
45099
55099

end173.0ms (1%)

Compiler

Compiled 359 to 207 computations (42.3% saved)

Profiling

Loading profile data...