Details

Time bar (total: 23.0s)

analyze1.8s (7.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
0%28.1%71.9%4
0%28.1%71.9%5
0.9%27.2%71.9%6
4.8%23.2%71.9%7
5.3%22.8%71.9%8
6.3%21.8%71.9%9
7.9%20.2%71.9%10
8.7%19.4%71.9%11
9.7%18.4%71.9%12
10.8%17.3%71.9%13
11.5%16.6%71.9%14
Compiler

Compiled 43 to 28 computations (34.9% saved)

sample1.9s (8.2%)

Results
1.1s6667×body128valid
373.0ms696×body1024valid
216.0ms543×body512valid
82.0ms285×body256valid
44.0ms65×body2048valid
Compiler

Compiled 75 to 48 computations (36% saved)

simplify50.0ms (0.2%)

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
18.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
23.9b
(/.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)
18.6b
(/.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)

localize11.0ms (0%)

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))))
11.5b
(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)
18.3b
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series1.3s (5.8%)

Counts
3 → 108
Calls

3 calls:

986.0ms
(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)
322.0ms
(/.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))))

rewrite20.0ms (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)))))
5.0ms
(*.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)

simplify227.0ms (1%)

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

prune522.0ms (2.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2032205
Fresh101
Picked101
Done000
Total2052207
Error
0.0b
Counts
207 → 2
Alt Table
StatusErrorProgram
50.7b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
11.5b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 24501 to 15834 computations (35.4% saved)

localize63.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.0b
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
0.1b
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
11.5b
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

series1.0s (4.4%)

Counts
4 → 144
Calls

4 calls:

555.0ms
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
338.0ms
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
84.0ms
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
38.0ms
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))

rewrite42.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
82×*-un-lft-identity_binary64
75×add-sqr-sqrt_binary64
65×times-frac_binary64
40×add-cube-cbrt_binary64
32×add-exp-log_binary64
Counts
4 → 162
Calls

4 calls:

16.0ms
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
7.0ms
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
2.0ms
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
0.0ms
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify282.0ms (1.2%)

Algorithm
egg-herbie
Rules
579×fma-def_binary64
560×associate-+r+_binary64
386×associate-*r/_binary64
174×associate-/l*_binary64
155×associate-/r*_binary64
Counts
306 → 370
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0171726289
1548426289

prune673.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3691370
Fresh011
Picked011
Done000
Total3693372
Error
0.0b
Counts
372 → 3
Alt Table
StatusErrorProgram
50.7b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
11.4b
(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
11.5b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 34359 to 21590 computations (37.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
0.1b
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
2.0b
(+.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)
2.7b
(*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))

series837.0ms (3.6%)

Counts
2 → 72
Calls

2 calls:

517.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)
319.0ms
(*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))

rewrite37.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
34×add-exp-log_binary64
20×add-cbrt-cube_binary64
17×prod-exp_binary64
frac-times_binary64
cbrt-unprod_binary64
Counts
2 → 56
Calls

2 calls:

16.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)
14.0ms
(*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))

simplify267.0ms (1.2%)

Algorithm
egg-herbie
Rules
405×+-commutative_binary64
355×associate-+r+_binary64
354×fma-def_binary64
331×*-commutative_binary64
217×associate-*r/_binary64
Counts
128 → 178
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0113918961
1446618780
2499218780

prune836.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3941395
Fresh011
Picked101
Done011
Total3953398
Error
0.0b
Counts
398 → 3
Alt Table
StatusErrorProgram
22.1b
(/.f64 (/.f64 (-.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) (*.f64 1 1)) (-.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)) 2)
50.7b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
11.5b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 41926 to 26804 computations (36.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
2.7b
(*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))
3.5b
(-.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)
5.4b
(-.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) (*.f64 1 1))

series7.8s (33.7%)

Counts
2 → 72
Calls

2 calls:

7.2s
(-.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) (*.f64 1 1))
529.0ms
(-.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)

rewrite64.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
35×add-exp-log_binary64
17×prod-exp_binary64
10×expm1-def_binary64
div-exp_binary64
add-log-exp_binary64
Counts
2 → 47
Calls

2 calls:

43.0ms
(-.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) (*.f64 1 1))
16.0ms
(-.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)

simplify404.0ms (1.8%)

Algorithm
egg-herbie
Rules
1021×fma-def_binary64
503×times-frac_binary64
11×cube-mult_binary64
11×unpow3_binary64
unpow2_binary64
Counts
119 → 165
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0310941544
1499241544

prune3.7s (16.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New9141915
Fresh011
Picked101
Done011
Total9153918
Error
0.0b
Counts
918 → 3
Alt Table
StatusErrorProgram
22.1b
(/.f64 (/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) 3) 1) (fma.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) (+.f64 1 (*.f64 (*.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) 1)))) (-.f64 (*.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)) 2)
50.7b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
11.5b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 184120 to 113323 computations (38.5% saved)

regimes1.0s (4.4%)

Accuracy

Total 1.6b remaining (87.9%)

Threshold costs 0b (0%)

Counts
92 → 2
Compiler

Compiled 22987 to 14603 computations (36.5% 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
03199
14499
24799
34999
45099
54999

end144.0ms (0.6%)

Compiler

Compiled 435 to 238 computations (45.3% saved)

Profiling

Loading profile data...