Details

Time bar (total: 11.5s)

analyze564.0ms (4.9%)

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)

sample372.0ms (3.2%)

Algorithm
intervals
Results
10.0ms178×body128valid
7.0ms25×body2048valid
6.0ms25×body1024valid
3.0msbody4096valid
2.0ms11×body512valid
2.0ms30×body128nan
1.0msbody256valid
0.0msbody128invalid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify281.0ms (2.4%)

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)))

series298.0ms (2.6%)

Counts
4 → 96
Calls

4 calls:

118.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
98.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
73.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
9.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

rewrite29.0ms (0.3%)

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:

9.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
6.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
3.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
3.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

simplify275.0ms (2.4%)

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

prune160.0ms (1.4%)

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
27.8b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
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)
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)
30.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 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 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
43.1b
(*.f64 -1/2 (/.f64 c b_2))
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))))
Compiler

Compiled 5919 to 1696 computations (71.3% saved)

localize7.0ms (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)))

series588.0ms (5.1%)

Counts
4 → 38
Calls

4 calls:

314.0ms
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
146.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
109.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
18.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite16.0ms (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:

6.0ms
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
1.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))
0.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify108.0ms (0.9%)

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

prune215.0ms (1.9%)

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
43.9b
(/.f64 (*.f64 -2 b_2) a)
30.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
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)
27.8b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_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))
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)))
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)
43.1b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 4481 to 1405 computations (68.6% saved)

localize11.0ms (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)))

series985.0ms (8.5%)

Counts
2 → 16
Calls

2 calls:

738.0ms
(/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
247.0ms
(/.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))))

rewrite109.0ms (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))))
6.0ms
(/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

simplify487.0ms (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

prune286.0ms (2.5%)

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
43.9b
(/.f64 (*.f64 -2 b_2) a)
30.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
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)
27.8b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
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)))))
45.4b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
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)))
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)
43.1b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 23333 to 3095 computations (86.7% saved)

localize10.0ms (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 (21.4%)

Counts
4 → 120
Calls

4 calls:

850.0ms
(/.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)
719.0ms
(-.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)
490.0ms
(*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
410.0ms
(cbrt.f64 (neg.f64 (*.f64 c a)))

rewrite31.0ms (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:

9.0ms
(*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
6.0ms
(/.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)))

simplify253.0ms (2.2%)

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

prune220.0ms (1.9%)

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
43.9b
(/.f64 (*.f64 -2 b_2) a)
30.6b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
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)
27.8b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
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)))))
45.4b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
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)))
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)
43.1b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 10265 to 3438 computations (66.5% saved)

regimes2.2s (18.9%)

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)

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
02858
14558
25758
36858
47658
58058
68158
77958

end1.0ms (0%)

Compiler

Compiled 42 to 25 computations (40.5% saved)

sample1.5s (12.9%)

Algorithm
intervals
Results
331.0ms5230×body128valid
296.0ms1124×body2048valid
154.0ms721×body1024valid
142.0ms413×body4096valid
53.0ms321×body512valid
39.0ms749×body128nan
20.0ms191×body256valid
14.0ms251×body128invalid
Compiler

Compiled 265 to 154 computations (41.9% saved)

Profiling

Loading profile data...