Details

Time bar (total: 12.1s)

analyze586.0ms (4.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.1%0.1%6
18.7%76.5%4.8%7
28.1%66.3%5.6%8
35.1%55%9.9%9
36.3%50.9%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample715.0ms (5.9%)

Algorithm
intervals
Results
289.0ms178×body128valid
7.0ms25×body2048valid
5.0ms25×body1024valid
3.0msbody4096valid
2.0ms11×body512valid
2.0ms30×body128nan
1.0msbody256valid
1.0msbody128invalid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify85.0ms (0.7%)

Algorithm
egg-herbie
Rules
808×fma-neg_binary64
379×associate-/l*_binary64
361×div-sub_binary64
341×fma-def_binary64
224×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01120
12318
23918
36918
410718
517818
627918
738218
854718
958718
1085518
11124718
12111718
13103518
14104318
15105118
16107718
17109318
18112918
19113118
20114318
21105018

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
30.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
30.5b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
Compiler

Compiled 58 to 30 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
0.7b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
0.8b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
19.4b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series269.0ms (2.2%)

Counts
4 → 96
Calls

4 calls:

125.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
74.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
61.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
9.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

rewrite66.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt_binary64
41×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
20×sqrt-prod_binary64
19×prod-diff_binary64
Counts
4 → 120
Calls

4 calls:

44.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
8.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
3.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
3.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

simplify269.0ms (2.2%)

Algorithm
egg-herbie
Rules
682×fma-neg_binary64
364×cancel-sign-sub-inv_binary64
248×distribute-rgt-neg-in_binary64
220×distribute-lft-neg-in_binary64
172×distribute-rgt-in_binary64
Counts
216 → 237
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02725568
16834769
224844515
345214514
449154514
549904514
650004514
749994514
849324514

prune161.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New22710237
Fresh000
Picked101
Done000
Total22810238
Error
4.8b
Counts
238 → 10
Alt Table
StatusErrorProgram
45.4b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
32.2b
(/.f64 (+.f64 (fma.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 c a)))) (neg.f64 b_2)) 0) a)
27.8b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
43.7b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)))
43.5b
(exp.f64 (log.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
43.9b
(/.f64 (*.f64 -2 b_2) a)
28.0b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
30.7b
(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))
30.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
43.1b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 5919 to 1696 computations (71.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
0.1b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
0.2b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
13.1b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series631.0ms (5.2%)

Counts
4 → 38
Calls

4 calls:

348.0ms
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
153.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
111.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
19.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64
33×*-un-lft-identity_binary64
23×add-cube-cbrt_binary64
15×times-frac_binary64
prod-diff_binary64
Counts
4 → 98
Calls

4 calls:

5.0ms
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
4.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
2.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))
0.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify218.0ms (1.8%)

Algorithm
egg-herbie
Rules
713×fma-def_binary64
405×fma-neg_binary64
351×cancel-sign-sub-inv_binary64
265×div-sub_binary64
202×associate-/l/_binary64
Counts
136 → 175
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02483637
15953108
219742972
345712968
450932968

prune124.0ms (1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1714175
Fresh459
Picked011
Done000
Total17510185
Error
0.0b
Counts
185 → 10
Alt Table
StatusErrorProgram
27.8b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
43.7b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)))
43.9b
(/.f64 (*.f64 -2 b_2) a)
45.4b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
28.0b
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
43.6b
(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
46.6b
(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
28.0b
(/.f64 (-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2) a)
30.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
43.1b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 4481 to 1405 computations (68.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
0.2b
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
0.2b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
13.1b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.0s (8.4%)

Counts
2 → 16
Calls

2 calls:

692.0ms
(/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
321.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))

rewrite110.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
480×times-frac_binary64
340×*-un-lft-identity_binary64
340×add-sqr-sqrt_binary64
310×sqrt-prod_binary64
216×add-cube-cbrt_binary64
Counts
2 → 348
Calls

2 calls:

13.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
5.0ms
(/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

simplify513.0ms (4.2%)

Algorithm
egg-herbie
Rules
348×associate-/r/_binary64
334×associate-/l/_binary64
315×fma-neg_binary64
258×fma-def_binary64
228×associate-*l/_binary64
Counts
364 → 387
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041523735
191821479
2298219917
3412219412
4505819412

prune266.0ms (2.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New5381539
Fresh088
Picked011
Done011
Total53811549
Error
0.0b
Counts
549 → 11
Alt Table
StatusErrorProgram
27.8b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
43.7b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)))
43.9b
(/.f64 (*.f64 -2 b_2) a)
45.4b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
28.0b
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
43.6b
(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
46.6b
(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
28.0b
(/.f64 (-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2) a)
30.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
43.1b
(*.f64 -1/2 (/.f64 c b_2))
28.1b
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) 1) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))))
Compiler

Compiled 23333 to 3095 computations (86.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2) a)
0.2b
(*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
0.2b
(-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)
14.4b
(cbrt.f64 (neg.f64 (*.f64 c a)))

series2.5s (20.4%)

Counts
4 → 120
Calls

4 calls:

857.0ms
(/.f64 (-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2) a)
733.0ms
(-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)
479.0ms
(*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
408.0ms
(cbrt.f64 (neg.f64 (*.f64 c a)))

rewrite34.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt_binary64
39×*-un-lft-identity_binary64
31×cbrt-prod_binary64
29×add-cube-cbrt_binary64
19×sqrt-prod_binary64
Counts
4 → 143
Calls

4 calls:

10.0ms
(*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
5.0ms
(/.f64 (-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2) a)
3.0ms
(-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)
1.0ms
(cbrt.f64 (neg.f64 (*.f64 c a)))

simplify275.0ms (2.3%)

Algorithm
egg-herbie
Rules
402×fma-neg_binary64
362×cancel-sign-sub-inv_binary64
280×unswap-sqr_binary64
252×associate-*l*_binary64
246×associate-*r*_binary64
Counts
263 → 290
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
042810513
110359246
230527746
345516013
448555968
549485968

prune270.0ms (2.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New3230323
Fresh088
Picked011
Done022
Total32311334
Error
0.0b
Counts
334 → 11
Alt Table
StatusErrorProgram
27.8b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
43.7b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)))
43.9b
(/.f64 (*.f64 -2 b_2) a)
45.4b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
28.0b
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
43.6b
(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
46.6b
(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
28.0b
(/.f64 (-.f64 (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2) a)
30.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
43.1b
(*.f64 -1/2 (/.f64 c b_2))
28.1b
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) 1) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))))
Compiler

Compiled 10265 to 3438 computations (66.5% saved)

regimes1.8s (14.8%)

Accuracy

Total 9.9b remaining (98%)

Threshold costs 0b (0%)

Counts
131 → 3
Compiler

Compiled 11380 to 6262 computations (45% saved)

bsearch60.0ms (0.5%)

Steps
ItersRangePoint
8
8.917626247832984e-69
2.964083076904332e-64
2.500953026669186e-66
9
-9.669433575652751e+86
-1.6719072592032416e+78
-9.527912883871295e+86
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (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
02547
13847
24847
35547
45947
56047
65947

end1.0ms (0%)

Compiler

Compiled 35 to 23 computations (34.3% saved)

sample2.1s (17.4%)

Algorithm
intervals
Results
317.0ms5230×body128valid
308.0ms1124×body2048valid
155.0ms721×body1024valid
153.0ms413×body4096valid
52.0ms321×body512valid
41.0ms749×body128nan
20.0ms191×body256valid
17.0ms251×body128invalid
Compiler

Compiled 258 to 152 computations (41.1% saved)

Profiling

Loading profile data...