Details

Time bar (total: 8.8s)

analyze618.0ms (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
34.7%55.4%9.9%9
36.1%51.1%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)

sample2.4s (27.3%)

Results
644.0ms5390×body128valid
518.0ms1128×body2048valid
366.0ms738×body1024valid
234.0ms411×body4096valid
124.0ms1077×body128invalid
117.0ms395×body512valid
45.0ms194×body256valid
Compiler

Compiled 50 to 32 computations (36% saved)

simplify86.0ms (1%)

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
33.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
33.0b
(/.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)
0.4b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.7b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
23.3b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series174.0ms (2%)

Counts
4 → 96
Calls

4 calls:

73.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
54.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
39.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
8.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

rewrite28.0ms (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:

8.0ms
(/.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))

simplify298.0ms (3.4%)

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
02725492
16834712
224844515
345214514
449154514
549904514
650004514
749994514
849324514

prune226.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New22512237
Fresh000
Picked101
Done000
Total22612238
Error
5.6b
Counts
238 → 12
Alt Table
StatusErrorProgram
33.0b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
35.6b
(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
46.2b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
29.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
46.1b
(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)) (sqrt.f64 a))
29.8b
(*.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))
45.6b
(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (*.f64 a (+.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 (*.f64 b_2 b_2) (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))))
56.5b
(/.f64 (-.f64 b_2 b_2) a)
42.1b
(/.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)
34.2b
(/.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (neg.f64 b_2)) a)
46.1b
(fma.f64 -1/2 (/.f64 c b_2) (*.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
42.0b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 6043 to 1748 computations (71.1% saved)

localize10.0ms (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)))
1.0b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series806.0ms (9.2%)

Counts
4 → 36
Calls

4 calls:

397.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
252.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
138.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
19.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite34.0ms (0.4%)

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:

7.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
4.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
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)))

simplify190.0ms (2.2%)

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 → 300
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03157449
17196508
226046286
347446282
450146282

prune198.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2937300
Fresh8311
Picked011
Done000
Total30111312
Error
0.2b
Counts
312 → 11
Alt Table
StatusErrorProgram
46.2b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
29.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
29.8b
(/.f64 1 (*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
30.2b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
41.8b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
42.0b
(*.f64 -1/2 (/.f64 c b_2))
29.8b
(/.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))))
43.7b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
44.4b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
29.7b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
34.2b
(/.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (neg.f64 b_2)) a)
Compiler

Compiled 8517 to 2451 computations (71.2% 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)
0.2b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
1.0b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series306.0ms (3.5%)

Counts
2 → 26
Calls

2 calls:

198.0ms
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
108.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
18×prod-diff_binary64
13×associate-*l*_binary64
Counts
2 → 79
Calls

2 calls:

8.0ms
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
0.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify92.0ms (1%)

Algorithm
egg-herbie
Rules
676×fma-def_binary64
341×neg-mul-1_binary64
288×fma-neg_binary64
226×cancel-sign-sub-inv_binary64
201×distribute-rgt-in_binary64
Counts
105 → 153
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02382794
15622517
219412327
344732325
449952325

prune142.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2272229
Fresh099
Picked101
Done101
Total22911240
Error
0.2b
Counts
240 → 11
Alt Table
StatusErrorProgram
46.2b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
29.8b
(/.f64 1 (*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
30.2b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
41.8b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
43.7b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2))
34.2b
(/.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (neg.f64 b_2)) a)
42.0b
(*.f64 -1/2 (/.f64 c b_2))
29.8b
(/.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))))
43.7b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
44.4b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
44.3b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))
Compiler

Compiled 6354 to 2208 computations (65.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
0.2b
(/.f64 1 (*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
1.0b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series554.0ms (6.3%)

Counts
2 → 24
Calls

2 calls:

351.0ms
(*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
202.0ms
(/.f64 1 (*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
46×add-exp-log_binary64
27×add-sqr-sqrt_binary64
21×associate-*r*_binary64
21×*-un-lft-identity_binary64
20×times-frac_binary64
Counts
2 → 88
Calls

2 calls:

8.0ms
(*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
7.0ms
(/.f64 1 (*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))

simplify91.0ms (1%)

Algorithm
egg-herbie
Rules
755×fma-def_binary64
704×associate-/r*_binary64
288×associate-*l/_binary64
263×fma-neg_binary64
254×associate-*r/_binary64
Counts
112 → 162
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02002979
15192512
217602476
345572474
450752474

prune139.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2371238
Fresh01010
Picked011
Done000
Total23712249
Error
0.2b
Counts
249 → 12
Alt Table
StatusErrorProgram
46.2b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
29.8b
(/.f64 1 (*.f64 a (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))))
30.2b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
41.8b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
43.7b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2))
34.2b
(/.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (neg.f64 b_2)) a)
42.0b
(*.f64 -1/2 (/.f64 c b_2))
29.8b
(/.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))))
43.7b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
44.4b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
44.4b
(/.f64 1 (*.f64 a (/.f64 1 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))))
44.3b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))
Compiler

Compiled 6413 to 2391 computations (62.7% saved)

regimes2.1s (24.2%)

Accuracy

Total 9.9b remaining (99.2%)

Threshold costs 0b (0%)

Counts
187 → 3
Compiler

Compiled 15308 to 9262 computations (39.5% saved)

bsearch57.0ms (0.6%)

Steps
ItersRangePoint
7
1.722475599156956e-41
3.78407367449035e-40
5.587248024540979e-41
4
-3.6546654010417935e+111
-2.0203226596413257e+111
-3.591573910838058e+111
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
02554
13554
25054
36054
46754
56954
66954

end146.0ms (1.7%)

Compiler

Compiled 297 to 184 computations (38% saved)

Profiling

Loading profile data...