Details

Time bar (total: 14.4s)

analyze1.5s (10.7%)

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)

sample79.0ms (0.5%)

Algorithm
intervals
Results
19.0ms174×body128valid
14.0ms26×body2048valid
9.0ms22×body1024valid
8.0ms12×body4096valid
5.0ms16×body512valid
2.0ms22×body128nan
1.0msbody256valid
0.0msbody128invalid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify126.0ms (0.9%)

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

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
34.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
34.2b
(/.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)

localize17.0ms (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)
1.0b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.3b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
22.3b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite59.0ms (0.4%)

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:

17.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
14.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
8.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
6.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

series378.0ms (2.6%)

Counts
4 → 96
Calls

4 calls:

152.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
99.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
82.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
44.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

simplify592.0ms (4.1%)

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 → 398
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02725492
16834712
224844515
345214514
449154514
549904514
650004514
749994514
849324514

prune292.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New38612398
Fresh000
Picked101
Done000
Total38712399
Error
6.0b
Counts
399 → 12
Alt Table
StatusErrorProgram
37.3b
(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
31.9b
(*.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))
33.6b
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
43.0b
(/.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (*.f64 b_2 b_2)) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
48.4b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (sqrt.f64 a)))
57.2b
(/.f64 (-.f64 b_2 b_2) a)
45.0b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
46.0b
(fma.f64 -1/2 (/.f64 c b_2) (*.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
41.4b
(*.f64 -1/2 (/.f64 c b_2))
31.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
44.8b
(/.f64 (*.f64 -2 b_2) a)
44.1b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
Compiler

Compiled 5922 to 1716 computations (71% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
0.2b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
0.4b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.8b
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite66.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
138×times-frac_binary64
116×add-sqr-sqrt_binary64
115×*-un-lft-identity_binary64
81×add-cube-cbrt_binary64
26×associate-/r*_binary64
Counts
4 → 197
Calls

4 calls:

15.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
9.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
8.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
3.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.8s (12.2%)

Counts
4 → 36
Calls

4 calls:

787.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
494.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
454.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
29.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify410.0ms (2.8%)

Algorithm
egg-herbie
Rules
726×fma-def_binary64
384×cancel-sign-sub-inv_binary64
289×fma-neg_binary64
216×div-sub_binary64
164×distribute-neg-frac_binary64
Counts
233 → 406
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03157449
17196508
226046286
347446282
450146282

prune316.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New4033406
Fresh4711
Picked011
Done000
Total40711418
Error
0.1b
Counts
418 → 11
Alt Table
StatusErrorProgram
44.6b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
33.6b
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
43.0b
(/.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (*.f64 b_2 b_2)) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
48.4b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (sqrt.f64 a)))
41.0b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
31.9b
(*.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))
45.0b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
41.4b
(*.f64 -1/2 (/.f64 c b_2))
31.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
44.1b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
46.4b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
Compiler

Compiled 8527 to 2445 computations (71.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
0.4b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.8b
(sqrt.f64 (neg.f64 (*.f64 c a)))
12.8b
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify23.0ms (0.2%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
100

prune172.0ms (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2751276
Fresh099
Picked011
Done011
Total27512287
Error
0.1b
Counts
287 → 12
Alt Table
StatusErrorProgram
49.3b
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (*.f64 (+.f64 (sqrt.f64 b_2) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) (-.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (sqrt.f64 b_2)))) a))
31.9b
(*.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))
44.6b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
33.6b
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
43.0b
(/.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (*.f64 b_2 b_2)) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
48.4b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (sqrt.f64 a)))
41.0b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
45.0b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
41.4b
(*.f64 -1/2 (/.f64 c b_2))
31.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
44.1b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
46.4b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
Compiler

Compiled 5799 to 1397 computations (75.9% saved)

localize18.0ms (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 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a)
2.7b
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
12.8b
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite114.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
271×times-frac_binary64
221×add-sqr-sqrt_binary64
217×*-un-lft-identity_binary64
209×add-cube-cbrt_binary64
169×prod-diff_binary64
Counts
3 → 258
Calls

3 calls:

29.0ms
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
4.0ms
(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a)
1.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

series827.0ms (5.7%)

Counts
3 → 40
Calls

3 calls:

362.0ms
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
278.0ms
(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a)
187.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify618.0ms (4.3%)

Algorithm
egg-herbie
Rules
523×fma-neg_binary64
265×associate-/l/_binary64
201×sub-neg_binary64
180×distribute-neg-frac_binary64
163×distribute-rgt-neg-in_binary64
Counts
298 → 530
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
043015919
1103810195
225828433
347258428
448258428

prune436.0ms (3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New6135618
Fresh369
Picked101
Done022
Total61713630
Error
0.1b
Counts
630 → 13
Alt Table
StatusErrorProgram
35.4b
(fma.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) (/.f64 1 a) (neg.f64 (/.f64 b_2 a)))
48.4b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (sqrt.f64 a)))
45.0b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
44.6b
(-.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) a) (/.f64 b_2 a))
41.4b
(*.f64 -1/2 (/.f64 c b_2))
33.8b
(-.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) a) (/.f64 b_2 a))
35.5b
(+.f64 (fma.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) (/.f64 1 a) (neg.f64 (*.f64 (cbrt.f64 (/.f64 b_2 a)) (*.f64 (cbrt.f64 (/.f64 b_2 a)) (cbrt.f64 (/.f64 b_2 a)))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 b_2 a))) (*.f64 (cbrt.f64 (/.f64 b_2 a)) (cbrt.f64 (/.f64 b_2 a))) (*.f64 (cbrt.f64 (/.f64 b_2 a)) (*.f64 (cbrt.f64 (/.f64 b_2 a)) (cbrt.f64 (/.f64 b_2 a))))))
44.6b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
43.0b
(/.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (*.f64 b_2 b_2)) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
41.0b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
31.9b
(*.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))
47.2b
(-.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) a) (/.f64 b_2 a))
31.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
Compiler

Compiled 15141 to 2948 computations (80.5% saved)

regimes3.4s (23.5%)

Accuracy

Total 10.3b remaining (99%)

Threshold costs 0b (0%)

Compiler

Compiled 14464 to 8302 computations (42.6% saved)

bsearch113.0ms (0.8%)

Steps
ItersRangePoint
7
8.919908615144367e-71
3.075875476014322e-69
3.021168818743586e-70
9
-5.7949350621940804e+159
-3.6908192290380517e+151
-4.3543135764255064e+153
Compiler

Compiled 4 to 3 computations (25% saved)

simplify13.0ms (0.1%)

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
03263
14763
25963
36663
46963
56863

end2.0ms (0%)

Compiler

Compiled 46 to 30 computations (34.8% saved)

sample3.0s (20.8%)

Algorithm
intervals
Results
614.0ms1132×body2048valid
591.0ms5180×body128valid
321.0ms712×body1024valid
265.0ms385×body4096valid
137.0ms421×body512valid
94.0ms839×body128nan
40.0ms170×body256valid
26.0ms238×body128invalid
Compiler

Compiled 355 to 195 computations (45.1% saved)

Profiling

Loading profile data...