Details

Time bar (total: 13.2s)

analyze596.0ms (4.5%)

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)

sample686.0ms (5.2%)

Algorithm
intervals
Results
255.0ms172×body128valid
10.0ms35×body2048valid
5.0ms23×body1024valid
3.0ms10×body4096valid
2.0ms12×body512valid
2.0ms28×body128nan
0.0msbody256valid
0.0msbody128invalid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify84.0ms (0.6%)

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
34.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
34.9b
(/.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)
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.0b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
24.5b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series279.0ms (2.1%)

Counts
4 → 96
Calls

4 calls:

104.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
84.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
75.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
16.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

rewrite80.0ms (0.6%)

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:

58.0ms
(-.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))

simplify260.0ms (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
02725492
16834712
224844515
345214514
449154514
549904514
650004514
749994514
849324514

prune164.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New22413237
Fresh000
Picked101
Done000
Total22513238
Error
6.5b
Counts
238 → 13
Alt Table
StatusErrorProgram
45.4b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
45.2b
(/.f64 (*.f64 -2 b_2) a)
35.5b
(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
40.7b
(*.f64 -1/2 (/.f64 c b_2))
41.8b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.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)))) a)
47.0b
(/.f64 (*.f64 -1/2 (/.f64 (*.f64 c a) b_2)) a)
49.2b
(/.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 a (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
37.0b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) a)
34.9b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
35.0b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
35.9b
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
51.5b
(/.f64 (fma.f64 (/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b_2 5)) -1/16 (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)
46.5b
(/.f64 (-.f64 (fma.f64 1/2 (/.f64 (*.f64 b_2 b_2) (sqrt.f64 (neg.f64 (*.f64 c a)))) (sqrt.f64 (neg.f64 (*.f64 c a)))) b_2) a)
Compiler

Compiled 6103 to 1790 computations (70.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
0.6b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.0b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
24.5b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series74.0ms (0.6%)

Counts
1 → 20
Calls

1 calls:

74.0ms
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
13×associate-*r*_binary64
12×*-un-lft-identity_binary64
11×times-frac_binary64
10×add-exp-log_binary64
Counts
1 → 45
Calls

1 calls:

11.0ms
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

simplify87.0ms (0.7%)

Algorithm
egg-herbie
Rules
461×times-frac_binary64
381×associate-*l*_binary64
320×associate-/l*_binary64
257×associate-/r*_binary64
248×fma-neg_binary64
Counts
65 → 91
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01421800
13721651
212041581
347351581
449851581
549511581

prune236.0ms (1.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2412243
Fresh3912
Picked011
Done000
Total24412256
Error
6.5b
Counts
256 → 12
Alt Table
StatusErrorProgram
45.4b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
45.2b
(/.f64 (*.f64 -2 b_2) a)
41.8b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.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)))) a)
47.0b
(/.f64 (*.f64 -1/2 (/.f64 (*.f64 c a) b_2)) a)
49.2b
(/.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 a (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
37.0b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) a)
34.9b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
35.0b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
35.9b
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
40.7b
(*.f64 -1/2 (/.f64 c b_2))
45.5b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
51.5b
(*.f64 (fma.f64 (/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b_2 5)) -1/16 (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))) (/.f64 1 a))
Compiler

Compiled 6473 to 2278 computations (64.8% saved)

localize11.0ms (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))
0.1b
(/.f64 1 (/.f64 a (-.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)))

series935.0ms (7.1%)

Counts
4 → 36
Calls

4 calls:

490.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
284.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
144.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
17.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite40.0ms (0.3%)

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)))
5.0ms
(/.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)
2.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify217.0ms (1.6%)

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

prune215.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2955300
Fresh5510
Picked011
Done011
Total30012312
Error
0.1b
Counts
312 → 12
Alt Table
StatusErrorProgram
35.0b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
44.3b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
49.2b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
45.2b
(/.f64 (*.f64 -2 b_2) a)
41.8b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.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)))) a)
40.2b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
35.1b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
49.9b
(fma.f64 1/16 (/.f64 (pow.f64 (neg.f64 (*.f64 c a)) 3) (*.f64 a (pow.f64 b_2 5))) (fma.f64 (*.f64 (neg.f64 c) (/.f64 (neg.f64 (*.f64 c a)) (pow.f64 b_2 3))) -1/8 (*.f64 1/2 (/.f64 (neg.f64 c) b_2))))
34.9b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
35.9b
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
40.7b
(*.f64 -1/2 (/.f64 c b_2))
45.5b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
Compiler

Compiled 8602 to 2488 computations (71.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (-.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)
0.2b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
13.1b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series614.0ms (4.6%)

Counts
2 → 24
Calls

2 calls:

394.0ms
(/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
219.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

rewrite94.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
696×times-frac_binary64
384×*-un-lft-identity_binary64
384×add-sqr-sqrt_binary64
292×add-cube-cbrt_binary64
46×distribute-lft-out--_binary64
Counts
2 → 384
Calls

2 calls:

13.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
4.0ms
(/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

simplify330.0ms (2.5%)

Algorithm
egg-herbie
Rules
643×associate-/l*_binary64
372×fma-def_binary64
363×associate-/l/_binary64
273×associate-/r/_binary64
225×distribute-rgt-in_binary64
Counts
408 → 417
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
028016372
173715023
2223414657
3503114657

prune311.0ms (2.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New4921493
Fresh099
Picked101
Done022
Total49312505
Error
0.1b
Counts
505 → 12
Alt Table
StatusErrorProgram
35.0b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
44.3b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
49.2b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
45.2b
(/.f64 (*.f64 -2 b_2) a)
35.9b
(-.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) a) (/.f64 b_2 a))
44.3b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
41.8b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.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)))) a)
40.2b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
49.9b
(fma.f64 1/16 (/.f64 (pow.f64 (neg.f64 (*.f64 c a)) 3) (*.f64 a (pow.f64 b_2 5))) (fma.f64 (*.f64 (neg.f64 c) (/.f64 (neg.f64 (*.f64 c a)) (pow.f64 b_2 3))) -1/8 (*.f64 1/2 (/.f64 (neg.f64 c) b_2))))
34.9b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
40.7b
(*.f64 -1/2 (/.f64 c b_2))
45.5b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
Compiler

Compiled 16376 to 6136 computations (62.5% saved)

regimes6.0s (45.6%)

Accuracy

Total 10.2b remaining (98.9%)

Threshold costs 0b (0%)

Counts
239 → 3
Compiler

Compiled 25628 to 13438 computations (47.6% saved)

bsearch68.0ms (0.5%)

Steps
ItersRangePoint
8
3.1989822348130844e-77
1.0427440384171165e-73
4.903807995826219e-77
6
-7.651076310541402e+93
-1.1871159469048892e+93
-7.563214498963372e+93
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
03263
14863
26063
36763
47063
56963

end1.0ms (0%)

Compiler

Compiled 46 to 30 computations (34.8% saved)

sample1.8s (13.4%)

Algorithm
intervals
Results
389.0ms1159×body2048valid
314.0ms5149×body128valid
178.0ms718×body1024valid
150.0ms408×body4096valid
69.0ms379×body512valid
65.0ms248×body128invalid
45.0ms756×body128nan
21.0ms187×body256valid
Compiler

Compiled 314 to 191 computations (39.2% saved)

Profiling

Loading profile data...