Details

Time bar (total: 31.7s)

analyze191.0ms (0.6%)

Algorithm
1×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
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%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)

sample48.0ms (0.1%)

Algorithm
1×intervals
Results
17.0ms210×body128valid
6.0ms18×body1024valid
6.0ms256×pre128true
4.0ms17×body512valid
1.0ms4×body2048valid
1.0ms7×body256valid
Compiler

Compiled 78 to 51 computations (34.6% saved)

simplify44.0ms (0.1%)

Algorithm
1×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
18.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
23.4b
(/.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)
▶18.8b
(/.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%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 2 i (+.f64 alpha beta))
✓0.0b
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓12.8b
(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)
✓17.3b
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series904.0ms (2.9%)

Counts
4 → 144
Calls

4 calls:

557.0ms
(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)
316.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
24.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
6.0ms
(fma.f64 2 i (+.f64 alpha beta))

rewrite22.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
14×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
8×add-cube-cbrt_binary64
Counts
4 → 77
Calls

4 calls:

13.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
4.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.0ms
(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)

simplify235.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
562×+-commutative_binary64
490×fma-def_binary64
488×associate-+r+_binary64
392×*-commutative_binary64
294×associate-*r/_binary64
Counts
221 → 227
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0140520324
1545620324

prune599.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2454249
Fresh101
Picked101
Done000
Total2474251
Error
0.1b
Counts
251 → 4
Alt Table
StatusErrorProgram
▶12.7b
(/.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)
18.8b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 beta (fma.f64 2 alpha (fma.f64 4 (*.f64 i beta) (fma.f64 4 (*.f64 alpha i) (+.f64 (*.f64 alpha alpha) (+.f64 (*.f64 beta beta) (fma.f64 4 i (fma.f64 2 (*.f64 alpha beta) (*.f64 4 (*.f64 i i))))))))))) 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)
49.1b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
Compiler

Compiled 25945 to 16566 computations (36.1% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 2 i (+.f64 alpha beta))
✓0.1b
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓12.8b
(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)

series912.0ms (2.9%)

Counts
3 → 108
Calls

3 calls:

524.0ms
(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)
336.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
51.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))

rewrite41.0ms (0.1%)

Algorithm
1×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:

10.0ms
(/.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)

simplify257.0ms (0.8%)

Algorithm
1×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 → 297
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0159125853
1504625853

prune625.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3401341
Fresh033
Picked101
Done000
Total3414345
Error
0.1b
Counts
345 → 4
Alt Table
StatusErrorProgram
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)
▶12.7b
(/.f64 (log.f64 (exp.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)
49.1b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
18.8b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 beta (fma.f64 2 alpha (fma.f64 4 (*.f64 i beta) (fma.f64 4 (*.f64 alpha i) (+.f64 (*.f64 alpha alpha) (+.f64 (*.f64 beta beta) (fma.f64 4 i (fma.f64 2 (*.f64 alpha beta) (*.f64 4 (*.f64 i i))))))))))) 1) 2)
Compiler

Compiled 31505 to 19357 computations (38.6% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓3.9b
(log.f64 (exp.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)))
12.8b
(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)

series514.0ms (1.6%)

Counts
1 → 36
Calls

1 calls:

514.0ms
(log.f64 (exp.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)))

rewrite3.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
4×log-prod_binary64
4×log-pow_binary64
3×*-un-lft-identity_binary64
3×add-sqr-sqrt_binary64
3×exp-prod_binary64
Counts
1 → 18
Calls

1 calls:

2.0ms
(log.f64 (exp.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)))

simplify142.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
894×fma-def_binary64
441×associate-*l/_binary64
266×+-commutative_binary64
241×*-commutative_binary64
229×associate-+r+_binary64
Counts
54 → 77
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07959427
130519078
253699078

prune928.0ms (2.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3722374
Fresh123
Picked011
Done000
Total3735378
Error
0.1b
Counts
378 → 5
Alt Table
StatusErrorProgram
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)
✓12.7b
(/.f64 (log.f64 (exp.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)
49.1b
(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)
▶13.0b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (log.f64 (exp.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)))) (cbrt.f64 (log.f64 (exp.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))))) (cbrt.f64 (log.f64 (exp.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)
18.8b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 beta (fma.f64 2 alpha (fma.f64 4 (*.f64 i beta) (fma.f64 4 (*.f64 alpha i) (+.f64 (*.f64 alpha alpha) (+.f64 (*.f64 beta beta) (fma.f64 4 i (fma.f64 2 (*.f64 alpha beta) (*.f64 4 (*.f64 i i))))))))))) 1) 2)
Compiler

Compiled 42449 to 26912 computations (36.6% saved)

localize20.0ms (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))))
✓0.2b
(cbrt.f64 (log.f64 (exp.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))))
3.9b
(log.f64 (exp.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)))
12.8b
(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)

series4.9s (15.4%)

Counts
1 → 36
Calls

1 calls:

4.9s
(cbrt.f64 (log.f64 (exp.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))))

rewrite3.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
7×cbrt-prod_binary64
4×log-pow_binary64
3×*-un-lft-identity_binary64
3×add-sqr-sqrt_binary64
3×exp-prod_binary64
Counts
1 → 17
Calls

1 calls:

1.0ms
(cbrt.f64 (log.f64 (exp.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))))

simplify397.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
606×fma-def_binary64
425×associate-/r*_binary64
418×associate-/l*_binary64
407×times-frac_binary64
75×sqr-pow_binary64
Counts
53 → 83
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0233041163
1527341163

prune15.3s (48.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New112111122
Fresh033
Picked101
Done011
Total112251127
Error
0.1b
Counts
1127 → 5
Alt Table
StatusErrorProgram
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)
✓12.7b
(/.f64 (log.f64 (exp.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)
49.1b
(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)
13.5b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (log.f64 (exp.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)))) (cbrt.f64 (log.f64 (exp.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))))) (cbrt.f64 (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (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))))) (log.f64 (cbrt.f64 (exp.f64 (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)
18.8b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 beta (fma.f64 2 alpha (fma.f64 4 (*.f64 i beta) (fma.f64 4 (*.f64 alpha i) (+.f64 (*.f64 alpha alpha) (+.f64 (*.f64 beta beta) (fma.f64 4 i (fma.f64 2 (*.f64 alpha beta) (*.f64 4 (*.f64 i i))))))))))) 1) 2)
Compiler

Compiled 344724 to 229387 computations (33.5% saved)

regimes3.8s (12%)

Accuracy

Total 1.3b remaining (89.8%)

Threshold costs 0b (0%)

Counts
227 → 2
Compiler

Compiled 53531 to 33458 computations (37.5% saved)

bsearch13.0ms (0%)

Compiler

Compiled 28 to 16 computations (42.9% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
034103
147103
251103
353103
454103
553103

end1.0ms (0%)

Compiler

Compiled 72 to 43 computations (40.3% saved)

sample1.7s (5.5%)

Algorithm
1×intervals
Results
498.0ms6480×body128valid
282.0ms684×body1024valid
207.0ms8000×pre128true
123.0ms485×body512valid
49.0ms312×body256valid
14.0ms39×body2048valid
Compiler

Compiled 400 to 239 computations (40.3% saved)

Profiling

Loading profile data...