Details

Time bar (total: 13.1s)

analyze1.6s (12.5%)

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)

sample85.0ms (0.7%)

Algorithm
intervals
Results
26.0ms45×body2048valid
20.0ms169×body128valid
8.0ms19×body1024valid
5.0msbody4096valid
3.0msbody512valid
2.0ms22×body128nan
1.0msbody256valid
1.0msbody128invalid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify100.0ms (0.8%)

Algorithm
egg-herbie
Rules
518×div-sub_binary64
428×fma-neg_binary64
246×associate-/l*_binary64
205×fma-def_binary64
183×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01120
12720
25420
311520
417920
529120
641720
752820
860220
985420
10180220
11104320
12102720
13103520
14104320
15104320
16110120
17113720
18113920
19115120
20104620

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
35.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
35.9b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
Compiler

Compiled 48 to 30 computations (37.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.3b
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
25.8b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite80.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt_binary64
80×*-un-lft-identity_binary64
61×prod-diff_binary64
60×add-cube-cbrt_binary64
41×sqrt-prod_binary64
Counts
4 → 176
Calls

4 calls:

22.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
16.0ms
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
6.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
6.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series455.0ms (3.5%)

Counts
4 → 96
Calls

4 calls:

247.0ms
(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) a)
92.0ms
(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))
72.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
43.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

simplify590.0ms (4.5%)

Algorithm
egg-herbie
Rules
819×fma-neg_binary64
295×cancel-sign-sub-inv_binary64
181×unswap-sqr_binary64
169×sub-neg_binary64
135×associate-*r*_binary64
Counts
272 → 521
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03178791
17796792
226825750
345845750
449745750

prune361.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New50912521
Fresh000
Picked101
Done000
Total51012522
Error
7.2b
Counts
522 → 12
Alt Table
StatusErrorProgram
44.1b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
43.9b
(/.f64 (*.f64 -2 b_2) a)
34.3b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
56.5b
(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
40.8b
(*.f64 -1/2 (/.f64 c b_2))
36.7b
(/.f64 (-.f64 (neg.f64 b_2) (*.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)))))) a)
38.8b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
34.8b
(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
50.8b
(/.f64 (-.f64 (*.f64 (neg.f64 b_2) (neg.f64 b_2)) (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) (*.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
48.3b
(/.f64 (fma.f64 (/.f64 (*.f64 c a) b_2) -1/2 (*.f64 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b_2 3)) -1/8)) a)
36.0b
(*.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
38.9b
(/.f64 (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)
Compiler

Compiled 9117 to 2052 computations (77.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
0.1b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
0.9b
(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
16.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite92.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
172×*-un-lft-identity_binary64
162×times-frac_binary64
139×add-sqr-sqrt_binary64
104×add-cube-cbrt_binary64
34×distribute-lft-out--_binary64
Counts
4 → 244
Calls

4 calls:

20.0ms
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
13.0ms
(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
11.0ms
(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
3.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.4s (11%)

Counts
4 → 42
Calls

4 calls:

615.0ms
(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
451.0ms
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
351.0ms
(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
27.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify504.0ms (3.9%)

Algorithm
egg-herbie
Rules
715×fma-def_binary64
401×fma-neg_binary64
316×cancel-sign-sub-inv_binary64
186×sub-neg_binary64
154×distribute-frac-neg_binary64
Counts
286 → 505
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03499712
17948164
227057612
347987608
449067608

prune344.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New4996505
Fresh7411
Picked101
Done000
Total50710517
Error
0.1b
Counts
517 → 10
Alt Table
StatusErrorProgram
34.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))))
40.8b
(*.f64 -1/2 (/.f64 c b_2))
34.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2))))
43.9b
(/.f64 (*.f64 -2 b_2) a)
47.0b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
40.7b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
38.8b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
34.2b
(*.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))
48.3b
(/.f64 (fma.f64 (/.f64 (*.f64 c a) b_2) -1/2 (*.f64 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b_2 3)) -1/8)) a)
45.9b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
Compiler

Compiled 10499 to 2706 computations (74.2% saved)

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
0.9b
(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
16.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
18×times-frac_binary64
12×add-cube-cbrt_binary64
distribute-lft-out--_binary64
Counts
1 → 44
Calls

1 calls:

15.0ms
(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)

series440.0ms (3.4%)

Counts
1 → 14
Calls

1 calls:

439.0ms
(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)

simplify170.0ms (1.3%)

Algorithm
egg-herbie
Rules
758×times-frac_binary64
487×div-sub_binary64
449×fma-neg_binary64
361×associate-/l*_binary64
320×associate-/r*_binary64
Counts
58 → 85
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01421895
13771768
210831747
345081745
457401745

prune196.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2352237
Fresh099
Picked011
Done000
Total23512247
Error
0.0b
Counts
247 → 12
Alt Table
StatusErrorProgram
34.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))))
40.8b
(*.f64 -1/2 (/.f64 c b_2))
34.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2))))
43.9b
(/.f64 (*.f64 -2 b_2) a)
47.0b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
40.7b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
38.8b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
34.2b
(*.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))
48.3b
(/.f64 (fma.f64 (/.f64 (*.f64 c a) b_2) -1/2 (*.f64 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b_2 3)) -1/8)) a)
47.0b
(*.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a))
45.9b
(*.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a))
45.9b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
Compiler

Compiled 5807 to 1693 computations (70.8% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))))
0.9b
(-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2))
16.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))
16.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite62.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
98×sqrt-prod_binary64
85×add-sqr-sqrt_binary64
41×*-un-lft-identity_binary64
37×add-cube-cbrt_binary64
32×sqrt-pow1_binary64
Counts
2 → 155
Calls

2 calls:

23.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))))
10.0ms
(-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2))

series290.0ms (2.2%)

Counts
2 → 14
Calls

2 calls:

262.0ms
(-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2))
28.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))))

simplify290.0ms (2.2%)

Algorithm
egg-herbie
Rules
501×associate-/l*_binary64
493×associate-/r*_binary64
382×fma-def_binary64
371×fma-neg_binary64
165×cancel-sign-sub-inv_binary64
Counts
169 → 324
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02294053
14393002
214372569
347002553
449242537
549112537

prune265.0ms (2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New4560456
Fresh01010
Picked011
Done011
Total45612468
Error
0.0b
Counts
468 → 12
Alt Table
StatusErrorProgram
34.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (fabs.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))))
40.8b
(*.f64 -1/2 (/.f64 c b_2))
34.4b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2))))
43.9b
(/.f64 (*.f64 -2 b_2) a)
47.0b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
40.7b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
38.8b
(/.f64 (/.f64 (*.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
34.2b
(*.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a))
48.3b
(/.f64 (fma.f64 (/.f64 (*.f64 c a) b_2) -1/2 (*.f64 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b_2 3)) -1/8)) a)
47.0b
(*.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a))
45.9b
(*.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a))
45.9b
(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
Compiler

Compiled 8796 to 2092 computations (76.2% saved)

regimes2.6s (19.8%)

Accuracy

Total 10.2b remaining (97.6%)

Threshold costs 0b (0%)

Compiler

Compiled 7717 to 4809 computations (37.7% saved)

bsearch94.0ms (0.7%)

Steps
ItersRangePoint
7
5.362061886227093e+73
1.1850802691350075e+75
2.4564051867231585e+74
7
-7.680582332002418e-57
-4.541047086951128e-59
-7.176929411205444e-59
Compiler

Compiled 4 to 3 computations (25% saved)

simplify10.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02653
14053
25553
37053
47953
58353
68453
78453

end3.0ms (0%)

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample2.9s (21.9%)

Algorithm
intervals
Results
619.0ms1116×body2048valid
575.0ms5265×body128valid
311.0ms708×body1024valid
251.0ms376×body4096valid
117.0ms366×body512valid
90.0ms805×body128nan
38.0ms169×body256valid
26.0ms244×body128invalid
Compiler

Compiled 274 to 180 computations (34.3% saved)

Profiling

Loading profile data...