Details

Time bar (total: 9.7s)

analyze1.2s (12.7%)

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)

sample46.0ms (0.5%)

Algorithm
intervals
Results
12.0ms167×body128valid
10.0ms36×body2048valid
7.0ms36×body1024valid
3.0ms10×body4096valid
2.0ms31×body128nan
1.0msbody512valid
1.0ms10×body128invalid
0.0msbody256valid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify86.0ms (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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
31.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
31.8b
(/.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)

localize9.0ms (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)
0.2b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
0.9b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
18.8b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series182.0ms (1.9%)

Counts
4 → 96
Calls

4 calls:

76.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
52.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
42.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
11.0ms
(-.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:

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

simplify387.0ms (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

prune146.0ms (1.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New22413237
Fresh000
Picked011
Done000
Total22414238
Error
4.9b
Counts
238 → 14
Alt Table
StatusErrorProgram
57.1b
(log.f64 (exp.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
48.0b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
41.8b
(/.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)
42.8b
(fma.f64 -1/2 (/.f64 c b_2) (*.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
31.6b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) a)
30.0b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 a)))
32.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 a)))
43.3b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
47.6b
(/.f64 (*.f64 -2 b_2) a)
29.5b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
45.6b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
56.1b
(/.f64 (-.f64 b_2 b_2) a)
31.8b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
39.7b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 6078 to 1771 computations (70.9% saved)

localize9.0ms (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)))
0.6b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
11.5b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series889.0ms (9.2%)

Counts
4 → 36
Calls

4 calls:

486.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
225.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
159.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
19.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite36.0ms (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)
2.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify189.0ms (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

prune208.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2946300
Fresh8412
Picked101
Done011
Total30311314
Error
0.1b
Counts
314 → 11
Alt Table
StatusErrorProgram
46.2b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
29.5b
(/.f64 1 (pow.f64 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) 1))
44.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
29.6b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
39.3b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
41.8b
(/.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)
30.0b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 a)))
47.6b
(/.f64 (*.f64 -2 b_2) a)
42.0b
(/.f64 1 (fma.f64 (/.f64 (*.f64 a (neg.f64 (*.f64 c a))) (pow.f64 b_2 3)) -1/8 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c))))))
31.8b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
39.7b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 8532 to 2469 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 (pow.f64 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) 1))
0.6b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
11.5b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series242.0ms (2.5%)

Counts
1 → 12
Calls

1 calls:

242.0ms
(/.f64 1 (pow.f64 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) 1))

rewrite32.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
135×times-frac_binary64
91×*-un-lft-identity_binary64
91×add-sqr-sqrt_binary64
84×unpow-prod-down_binary64
67×add-cube-cbrt_binary64
Counts
1 → 130
Calls

1 calls:

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

simplify139.0ms (1.4%)

Algorithm
egg-herbie
Rules
570×associate-/r*_binary64
493×associate-/l*_binary64
451×fma-def_binary64
247×associate-*l/_binary64
230×associate-/r/_binary64
Counts
142 → 184
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02235095
14704654
213914362
348934360
451714360

prune201.0ms (2.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New3290329
Fresh099
Picked011
Done011
Total32911340
Error
0.1b
Counts
340 → 11
Alt Table
StatusErrorProgram
46.2b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
29.5b
(/.f64 1 (pow.f64 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) 1))
44.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
29.6b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
39.3b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
41.8b
(/.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)
30.0b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (cbrt.f64 a)))
47.6b
(/.f64 (*.f64 -2 b_2) a)
42.0b
(/.f64 1 (fma.f64 (/.f64 (*.f64 a (neg.f64 (*.f64 c a))) (pow.f64 b_2 3)) -1/8 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c))))))
31.8b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
39.7b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 10029 to 3418 computations (65.9% saved)

localize10.0ms (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 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
0.6b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
11.5b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series599.0ms (6.2%)

Counts
2 → 24
Calls

2 calls:

382.0ms
(/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
217.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

rewrite95.0ms (1%)

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))

simplify417.0ms (4.3%)

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

prune297.0ms (3.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New4894493
Fresh268
Picked011
Done022
Total49113504
Error
0.0b
Counts
504 → 13
Alt Table
StatusErrorProgram
46.3b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
46.2b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
29.5b
(/.f64 1 (pow.f64 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) 1))
44.4b
(/.f64 (/.f64 1 a) (fma.f64 (/.f64 (neg.f64 (*.f64 c a)) (pow.f64 b_2 3)) -1/8 (fma.f64 2 (/.f64 b_2 (neg.f64 (*.f64 c a))) (/.f64 1/2 b_2))))
44.8b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
29.6b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
47.6b
(/.f64 (*.f64 -2 b_2) a)
44.8b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
30.0b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) (/.f64 1 (cbrt.f64 a))))
42.0b
(/.f64 1 (fma.f64 (/.f64 (*.f64 a (neg.f64 (*.f64 c a))) (pow.f64 b_2 3)) -1/8 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c))))))
41.8b
(/.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)
31.8b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
39.7b
(*.f64 -1/2 (/.f64 c b_2))
Compiler

Compiled 16375 to 6157 computations (62.4% saved)

regimes2.6s (26.7%)

Accuracy

Total 10.1b remaining (98.8%)

Threshold costs 0b (0%)

Counts
188 → 3
Compiler

Compiled 17992 to 11034 computations (38.7% saved)

bsearch40.0ms (0.4%)

Steps
ItersRangePoint
7
9.640412780087636e-60
6.232097247659063e-58
1.0494614885250299e-59
1
-1.0988306668534237e+138
-1.014844118199704e+135
-3.340673506078001e+136
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
02551
13551
24851
35651
46151
56251
66251

end1.0ms (0%)

Compiler

Compiled 38 to 23 computations (39.5% saved)

sample1.6s (16.1%)

Algorithm
intervals
Results
340.0ms1159×body2048valid
314.0ms5159×body128valid
166.0ms740×body1024valid
137.0ms394×body4096valid
57.0ms365×body512valid
39.0ms743×body128nan
19.0ms183×body256valid
13.0ms236×body128invalid
Compiler

Compiled 305 to 205 computations (32.8% saved)

Profiling

Loading profile data...