Details

Time bar (total: 24.8s)

analyze360.0ms (1.5%)

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 42 to 27 computations (35.7% saved)

sample86.0ms (0.3%)

Algorithm
1×intervals
Results
32.0ms213×body128valid
11.0ms256×pre128true
11.0ms18×body1024valid
7.0ms15×body512valid
2.0ms8×body256valid
1.0ms2×body2048valid
Compiler

Compiled 77 to 50 computations (35.1% saved)

simplify61.0ms (0.2%)

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

prune10.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
19.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶19.4b
(/.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)
24.2b
(/.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)
Compiler

Compiled 180 to 106 computations (41.1% saved)

localize24.0ms (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))))
✓10.7b
(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)
✓18.5b
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

rewrite34.0ms (0.1%)

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

3 calls:

16.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
9.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
1.0ms
(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)

series1.5s (6.2%)

Counts
3 → 108
Calls

3 calls:

882.0ms
(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)
592.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
59.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

simplify373.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
561×+-commutative_binary64
490×fma-def_binary64
487×associate-+r+_binary64
392×*-commutative_binary64
294×associate-*r/_binary64
Counts
175 → 301
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0140019973
1545019973

prune1.5s (5.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2965301
Fresh101
Picked101
Done000
Total2985303
Error
0.1b
Counts
303 → 5
Alt Table
StatusErrorProgram
19.5b
(/.f64 (exp.f64 (log.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)
▶10.7b
(/.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)
10.7b
(/.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)
53.5b
(/.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)
51.5b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
Compiler

Compiled 24715 to 15962 computations (35.4% saved)

localize24.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓0.0b
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓10.7b
(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)

rewrite54.0ms (0.2%)

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:

16.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
8.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
1.0ms
(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)

series1.6s (6.5%)

Counts
3 → 108
Calls

3 calls:

948.0ms
(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)
582.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
84.0ms
(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))

simplify577.0ms (2.3%)

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 → 433
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0159125853
1504625853

prune1.4s (5.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New4330433
Fresh044
Picked011
Done000
Total4335438
Error
0.1b
Counts
438 → 5
Alt Table
StatusErrorProgram
19.5b
(/.f64 (exp.f64 (log.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)
✓10.7b
(/.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)
▶10.7b
(/.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)
53.5b
(/.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)
51.5b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
Compiler

Compiled 30273 to 18749 computations (38.1% saved)

localize27.0ms (0.1%)

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)))))
✓10.7b
(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)

rewrite79.0ms (0.3%)

Algorithm
1×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:

33.0ms
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
13.0ms
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
6.0ms
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
1.0ms
(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)

series2.0s (8%)

Counts
4 → 144
Calls

4 calls:

985.0ms
(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)
613.0ms
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
204.0ms
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
174.0ms
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))

simplify668.0ms (2.7%)

Algorithm
1×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 → 520
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0171726289
1548426289

prune2.1s (8.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New5191520
Fresh033
Picked101
Done011
Total5205525
Error
0.1b
Counts
525 → 5
Alt Table
StatusErrorProgram
✓10.7b
(/.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)
▶11.1b
(/.f64 (*.f64 (*.f64 (cbrt.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)) (cbrt.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))) (cbrt.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)
19.5b
(/.f64 (exp.f64 (log.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)
53.5b
(/.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)
51.5b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
Compiler

Compiled 34649 to 21750 computations (37.2% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(cbrt.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))
10.7b
(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)
10.7b
(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)
10.7b
(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)

rewrite3.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
3×cbrt-prod_binary64
2×*-un-lft-identity_binary64
2×add-sqr-sqrt_binary64
2×add-cube-cbrt_binary64
1×add-cbrt-cube_binary64
Counts
1 → 13
Calls

1 calls:

1.0ms
(cbrt.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))

series6.3s (25.2%)

Counts
1 → 36
Calls

1 calls:

6.3s
(cbrt.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))

simplify464.0ms (1.9%)

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
49 → 85
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0231540947
1526340947

prune3.2s (12.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New6861687
Fresh033
Picked101
Done011
Total6875692
Error
0.1b
Counts
692 → 5
Alt Table
StatusErrorProgram
19.5b
(/.f64 (exp.f64 (log.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)
✓10.7b
(/.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)
11.2b
(/.f64 (*.f64 (*.f64 (cbrt.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)) (cbrt.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))) (cbrt.f64 (exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))))) 2)
53.5b
(/.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)
51.5b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
Compiler

Compiled 102587 to 70290 computations (31.5% saved)

regimes762.0ms (3.1%)

Accuracy

Total 1.1b remaining (90.5%)

Threshold costs 0b (0%)

Compiler

Compiled 16081 to 10472 computations (34.9% saved)

bsearch4.0ms (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
03096
14296
24696
34896
44996
54896

end1.0ms (0%)

Compiler

Compiled 69 to 40 computations (42% saved)

sample1.7s (6.7%)

Algorithm
1×intervals
Results
547.0ms6493×body128valid
213.0ms671×body1024valid
203.0ms8000×pre128true
125.0ms489×body512valid
53.0ms295×body256valid
26.0ms52×body2048valid
Compiler

Compiled 344 to 203 computations (41% saved)

Profiling

Loading profile data...