Details

Time bar (total: 7.0s)

analyze2.0ms (0%)

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)

sample290.0ms (4.2%)

Algorithm
intervals
Results
10.0ms203×body128valid
4.0ms256×pre128true
4.0ms28×body1024valid
2.0ms15×body512valid
1.0msbody2048valid
0.0msbody256valid
Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify205.0ms (2.9%)

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
13.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
13.1b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
1.1b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series51.0ms (0.7%)

Counts
2 → 48
Calls

2 calls:

32.0ms
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
18.0ms
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite13.0ms (0.2%)

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:

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

simplify117.0ms (1.7%)

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

prune123.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1375142
Fresh000
Picked101
Done000
Total1385143
Error
0.0b
Counts
143 → 5
Alt Table
StatusErrorProgram
13.1b
(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
49.6b
(-.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)))))
13.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
13.1b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
51.1b
(-.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 4585 to 2823 computations (38.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0b
(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))
0.2b
(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
1.1b
(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

series91.0ms (1.3%)

Counts
3 → 72
Calls

3 calls:

40.0ms
(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
32.0ms
(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
18.0ms
(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
log1p-expm1-u_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
3 → 32
Calls

3 calls:

0.0ms
(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
0.0ms
(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
0.0ms
(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))

simplify84.0ms (1.2%)

Algorithm
egg-herbie
Rules
309×times-frac_binary64
309×fma-def_binary64
276×associate-+l+_binary64
250×associate-/r*_binary64
233×associate-/l*_binary64
Counts
104 → 142
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04324807
113734631
250064631

prune219.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2380238
Fresh044
Picked011
Done000
Total2385243
Error
0.0b
Counts
243 → 5
Alt Table
StatusErrorProgram
13.1b
(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
49.6b
(-.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)))))
13.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
13.1b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
51.1b
(-.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 8565 to 5667 computations (33.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0b
(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
1.1b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
1.1b
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

series72.0ms (1%)

Counts
2 → 48
Calls

2 calls:

40.0ms
(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
32.0ms
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
exp-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
log-prod_binary64
Counts
2 → 32
Calls

2 calls:

3.0ms
(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
1.0ms
(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify96.0ms (1.4%)

Algorithm
egg-herbie
Rules
363×sub-neg_binary64
288×times-frac_binary64
253×fma-def_binary64
251×+-commutative_binary64
247×associate-+r+_binary64
Counts
80 → 113
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03704045
111053894
245793852
351693852

prune326.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2541255
Fresh033
Picked101
Done011
Total2555260
Error
0.0b
Counts
260 → 5
Alt Table
StatusErrorProgram
13.1b
(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
49.6b
(-.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)))))
13.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
13.6b
(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))))
51.1b
(-.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 9615 to 6391 computations (33.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
0.5b
(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
0.9b
(log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
1.1b
(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series1.1s (16%)

Counts
3 → 72
Calls

3 calls:

447.0ms
(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
445.0ms
(log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
221.0ms
(cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
19×cbrt-prod_binary64
13×*-un-lft-identity_binary64
13×add-cube-cbrt_binary64
11×pow1_binary64
Counts
3 → 71
Calls

3 calls:

5.0ms
(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
2.0ms
(log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
1.0ms
(cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify354.0ms (5.1%)

Algorithm
egg-herbie
Rules
381×*-commutative_binary64
332×+-commutative_binary64
294×fma-def_binary64
280×associate-+r+_binary64
168×associate-*r/_binary64
Counts
143 → 179
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0114627367
1423926174
2497026174

prune1.3s (18.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New4372439
Fresh123
Picked101
Done011
Total4395444
Error
0.0b
Counts
444 → 5
Alt Table
StatusErrorProgram
13.1b
(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
49.6b
(-.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)))))
13.6b
(*.f64 (cbrt.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))))
13.6b
(*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (*.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (log.f64 (exp.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))))
51.1b
(-.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 57191 to 41100 computations (28.1% saved)

regimes1.3s (18.6%)

Accuracy

Total 0.3b remaining (91.2%)

Threshold costs 0.3b (91.2%)

Counts
174 → 2
Compiler

Compiled 24050 to 17091 computations (28.9% saved)

bsearch12.0ms (0.2%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03380
14380
25680
37180
47880
58080
67880

end1.0ms (0%)

Compiler

Compiled 56 to 32 computations (42.9% saved)

sample1.2s (16.9%)

Algorithm
intervals
Results
257.0ms5945×body128valid
170.0ms1034×body1024valid
160.0ms8000×pre128true
69.0ms602×body512valid
40.0ms325×body256valid
18.0ms94×body2048valid
Compiler

Compiled 316 to 201 computations (36.4% saved)

Profiling

Loading profile data...