Details

Time bar (total: 10.2s)

analyze2.0s (19.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
0%99.7%0.3%13
0%99.7%0.3%14
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample2.3s (22.1%)

Symmetry

(sort x y)

(sort t a)

Results
1.4s8256×body128valid
804.0ms4831×body128invalid
Compiler

Compiled 80 to 56 computations (30% saved)

simplify57.0ms (0.6%)

Algorithm
egg-herbie
Rules
828×fma-def_binary64
568×div-sub_binary64
502×associate-/r/_binary64
476×distribute-neg-frac_binary64
465×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01928
14228
211624
335224
488023
5204121
6415421
7436521
8494121

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
13.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
21.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
Compiler

Compiled 137 to 92 computations (32.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
0.1b
(fma.f64 x (*.f64 9 y) b)
2.4b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
10.5b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)

series132.0ms (1.3%)

Counts
4 → 240
Calls

4 calls:

74.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
34.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
18.0ms
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
6.0ms
(fma.f64 x (*.f64 9 y) b)

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
18×times-frac_binary64
add-cbrt-cube_binary64
Counts
4 → 78
Calls

4 calls:

3.0ms
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
2.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
0.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
0.0ms
(fma.f64 x (*.f64 9 y) b)

simplify175.0ms (1.7%)

Algorithm
egg-herbie
Rules
913×div-sub_binary64
630×fma-def_binary64
477×fma-neg_binary64
332×associate-/l/_binary64
274×distribute-rgt-in_binary64
Counts
318 → 171
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01516685
12966160
27255908
319955341
442785341
564635341

prune155.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New16011171
Fresh011
Picked101
Done000
Total16112173
Error
5.6b
Counts
173 → 12
Alt Table
StatusErrorProgram
14.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)))) (/.f64 (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
42.4b
(/.f64 b (*.f64 c z))
13.5b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
40.0b
(*.f64 -4 (/.f64 (*.f64 a t) c))
13.5b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
10.7b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
31.2b
(/.f64 (fma.f64 9 (*.f64 y x) b) (*.f64 z c))
36.8b
(/.f64 (*.f64 (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) c)
13.5b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))) c)
49.8b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
21.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
34.0b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
Compiler

Compiled 4470 to 2430 computations (45.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
5.8b
(/.f64 (*.f64 a t) c)
6.5b
(/.f64 b (*.f64 c z))
8.3b
(/.f64 (*.f64 y x) (*.f64 c z))

series85.0ms (0.8%)

Counts
4 → 0
Calls

4 calls:

32.0ms
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
26.0ms
(/.f64 (*.f64 y x) (*.f64 c z))
16.0ms
(/.f64 b (*.f64 c z))
11.0ms
(/.f64 (*.f64 a t) c)

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
44×add-cbrt-cube_binary64
44×add-exp-log_binary64
15×cbrt-unprod_binary64
15×prod-exp_binary64
12×add-sqr-sqrt_binary64
Counts
4 → 100
Calls

4 calls:

5.0ms
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
4.0ms
(/.f64 (*.f64 y x) (*.f64 c z))
3.0ms
(/.f64 (*.f64 a t) c)
3.0ms
(/.f64 b (*.f64 c z))

simplify86.0ms (0.8%)

Algorithm
egg-herbie
Rules
613×associate-/r/_binary64
459×associate-/l/_binary64
441×*-commutative_binary64
280×times-frac_binary64
243×sub-neg_binary64
Counts
100 → 127
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01691507
14011168
216991168
332461168
444521168
549421168
650111168

prune153.0ms (1.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1189127
Fresh5611
Picked101
Done000
Total12415139
Error
0.5b
Counts
139 → 15
Alt Table
StatusErrorProgram
31.2b
(/.f64 (fma.f64 9 (*.f64 y x) b) (*.f64 z c))
9.7b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 (*.f64 c z) x)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
37.1b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 (/.f64 a (sqrt.f64 c)) (/.f64 t (sqrt.f64 c)))))
42.4b
(/.f64 b (*.f64 c z))
12.3b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
14.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)))) (/.f64 (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
10.8b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 a (/.f64 t c))))
11.2b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (/.f64 (*.f64 y x) c) z))) (*.f64 4 (/.f64 (*.f64 a t) c)))
11.5b
(-.f64 (+.f64 (/.f64 (/.f64 b c) z) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
21.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
13.5b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
13.5b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
11.5b
(-.f64 (+.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 b) (cbrt.f64 b)) c) (/.f64 (cbrt.f64 b) z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
11.1b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 a (/.f64 c t))))
10.7b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 c (/.f64 x z))))) (*.f64 4 (/.f64 (*.f64 a t) c)))
Compiler

Compiled 4564 to 1715 computations (62.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.0b
(/.f64 (*.f64 c z) x)
4.6b
(/.f64 y (/.f64 (*.f64 c z) x))
5.8b
(/.f64 (*.f64 a t) c)
6.5b
(/.f64 b (*.f64 c z))

series43.0ms (0.4%)

Counts
2 → 48
Calls

2 calls:

29.0ms
(/.f64 y (/.f64 (*.f64 c z) x))
14.0ms
(/.f64 (*.f64 c z) x)

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
36×times-frac_binary64
20×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
16×add-cbrt-cube_binary64
Counts
2 → 73
Calls

2 calls:

4.0ms
(/.f64 y (/.f64 (*.f64 c z) x))
3.0ms
(/.f64 (*.f64 c z) x)

simplify81.0ms (0.8%)

Algorithm
egg-herbie
Rules
862×times-frac_binary64
653×associate-/l*_binary64
482×associate-/l/_binary64
478×associate-*l/_binary64
453×associate-/r/_binary64
Counts
121 → 103
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01281662
12901530
210591518
347881518
449951518

prune192.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1552157
Fresh31114
Picked101
Done000
Total15913172
Error
0.0b
Counts
172 → 13
Alt Table
StatusErrorProgram
14.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)))) (/.f64 (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
12.3b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
13.5b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
9.3b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 (*.f64 c z) x)))) (*.f64 4 (/.f64 a (/.f64 c t))))
11.5b
(-.f64 (+.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 b) (cbrt.f64 b)) c) (/.f64 (cbrt.f64 b) z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
36.2b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 (*.f64 c z) x)))) (*.f64 4 (/.f64 (*.f64 t (/.f64 a (sqrt.f64 c))) (sqrt.f64 c))))
10.8b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 a (/.f64 t c))))
11.2b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (/.f64 (*.f64 y x) c) z))) (*.f64 4 (/.f64 (*.f64 a t) c)))
31.2b
(/.f64 (fma.f64 9 (*.f64 y x) b) (*.f64 z c))
11.5b
(-.f64 (+.f64 (/.f64 (/.f64 b c) z) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
21.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
13.5b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
10.7b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 c (/.f64 x z))))) (*.f64 4 (/.f64 (*.f64 a t) c)))
Compiler

Compiled 5285 to 1934 computations (63.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.0b
(/.f64 (*.f64 c z) x)
4.6b
(/.f64 y (/.f64 (*.f64 c z) x))
6.5b
(/.f64 b (*.f64 c z))
6.5b
(/.f64 a (/.f64 c t))

series13.0ms (0.1%)

Counts
1 → 36
Calls

1 calls:

13.0ms
(/.f64 a (/.f64 c t))

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
75×times-frac_binary64
43×*-un-lft-identity_binary64
43×add-sqr-sqrt_binary64
43×add-cube-cbrt_binary64
13×associate-/r*_binary64
Counts
1 → 72
Calls

1 calls:

4.0ms
(/.f64 a (/.f64 c t))

simplify145.0ms (1.4%)

Algorithm
egg-herbie
Rules
1089×associate-/r/_binary64
835×fma-def_binary64
611×fma-neg_binary64
460×distribute-rgt-in_binary64
452×div-sub_binary64
Counts
108 → 114
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01491514
13101454
29241451
322121451
423561451
525441451
629551451
738951451
843791451
950311451

prune297.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2403243
Fresh21012
Picked101
Done000
Total24313256
Error
0b
Counts
256 → 13
Alt Table
StatusErrorProgram
14.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)))) (/.f64 (cbrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
12.3b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
31.2b
(/.f64 (fma.f64 9 (*.f64 y x) b) (*.f64 z c))
8.0b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 (*.f64 c z) x)))) (*.f64 4 (*.f64 (/.f64 a c) t)))
9.0b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 (*.f64 c z) x)))) (*.f64 4 (*.f64 a (/.f64 t c))))
9.6b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 (*.f64 c z) x)))) (*.f64 4 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 c t)) (cbrt.f64 (/.f64 c t)))) (/.f64 a (cbrt.f64 (/.f64 c t))))))
11.5b
(-.f64 (+.f64 (/.f64 (/.f64 b c) z) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
21.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
13.5b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
13.5b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
11.5b
(-.f64 (+.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 b) (cbrt.f64 b)) c) (/.f64 (cbrt.f64 b) z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
11.2b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (/.f64 (*.f64 y x) c) z))) (*.f64 4 (/.f64 (*.f64 a t) c)))
10.7b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 y (/.f64 c (/.f64 x z))))) (*.f64 4 (/.f64 (*.f64 a t) c)))
Compiler

Compiled 7710 to 2484 computations (67.8% saved)

regimes3.7s (36%)

Accuracy

Total 4.9b remaining (98.7%)

Threshold costs 0b (0%)

Counts
146 → 4
Compiler

Compiled 51130 to 32350 computations (36.7% saved)

bsearch13.0ms (0.1%)

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify12.0ms (0.1%)

Algorithm
egg-herbie
Rules
32×*-commutative_binary64
24×+-commutative_binary64
21×sub-neg_binary64
17×distribute-rgt-neg-in_binary64
17×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066249
1101249
2135249
3174249
4204249
5224249
6232249
7234249
8233249

end527.0ms (5.2%)

Compiler

Compiled 1442 to 813 computations (43.6% saved)

Profiling

Loading profile data...