Details

Time bar (total: 9.3s)

analyze2.1s (22.3%)

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)

sample108.0ms (1.2%)

Algorithm
intervals
Symmetry

(sort x y)

(sort t a)

Results
19.0ms256×body128valid
11.0ms164×body128invalid
Compiler

Compiled 60 to 44 computations (26.7% saved)

simplify63.0ms (0.7%)

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
6.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
18.7b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
11.3b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
Compiler

Compiled 137 to 92 computations (32.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x (*.f64 9 y) b)
0.3b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
2.0b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
8.7b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)

series135.0ms (1.4%)

Counts
4 → 240
Calls

4 calls:

76.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
33.0ms
(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)
7.0ms
(fma.f64 x (*.f64 9 y) b)

rewrite8.0ms (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:

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

simplify180.0ms (1.9%)

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

prune169.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New15813171
Fresh011
Picked101
Done000
Total15914173
Error
6.1b
Counts
173 → 14
Alt Table
StatusErrorProgram
12.1b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (cbrt.f64 c)))
29.8b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
11.4b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
18.7b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
12.0b
(*.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))
42.3b
(/.f64 b (*.f64 c z))
11.3b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))) c)
38.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
39.8b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) c) 3))
29.5b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) (*.f64 c z))
38.6b
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) 3)) c)
11.7b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
25.2b
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
41.2b
(*.f64 -4 (/.f64 (*.f64 a t) c))
Compiler

Compiled 4552 to 2490 computations (45.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b))))
0.4b
(/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))
2.0b
(/.f64 z (fma.f64 x (*.f64 9 y) b))
8.7b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))) c)

series180.0ms (1.9%)

Counts
4 → 252
Calls

4 calls:

77.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))) c)
43.0ms
(fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b))))
42.0ms
(/.f64 z (fma.f64 x (*.f64 9 y) b))
18.0ms
(/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
93×times-frac_binary64
62×*-un-lft-identity_binary64
62×add-sqr-sqrt_binary64
62×add-cube-cbrt_binary64
19×associate-/r*_binary64
Counts
4 → 146
Calls

4 calls:

4.0ms
(/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))
2.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))) c)
2.0ms
(/.f64 z (fma.f64 x (*.f64 9 y) b))
0.0ms
(fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b))))

simplify205.0ms (2.2%)

Algorithm
egg-herbie
Rules
719×associate-/r*_binary64
387×associate-/r/_binary64
358×fma-neg_binary64
289×fma-def_binary64
247×associate-/l/_binary64
Counts
398 → 285
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02629758
15808908
218658615
347938615
450108615

prune284.0ms (3.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New2841285
Fresh11213
Picked011
Done000
Total28514299
Error
6.1b
Counts
299 → 14
Alt Table
StatusErrorProgram
12.1b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (cbrt.f64 c)))
29.8b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
11.4b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
18.7b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
12.0b
(*.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))
42.3b
(/.f64 b (*.f64 c z))
11.7b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
25.2b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z b))) c)
11.3b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))) c)
38.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
39.8b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) c) 3))
29.5b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) (*.f64 c z))
38.6b
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) 3)) c)
41.2b
(*.f64 -4 (/.f64 (*.f64 a t) c))
Compiler

Compiled 8350 to 4820 computations (42.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x (*.f64 9 y) b)
0.3b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
2.0b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
8.8b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

series81.0ms (0.9%)

Counts
1 → 84
Calls

1 calls:

81.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64
13×associate-*r*_binary64
11×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-exp-log_binary64
Counts
1 → 38
Calls

1 calls:

6.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

simplify87.0ms (0.9%)

Algorithm
egg-herbie
Rules
893×fma-def_binary64
740×distribute-rgt-in_binary64
236×associate-*l*_binary64
202×associate-*r*_binary64
162×fma-neg_binary64
Counts
122 → 78
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01003557
12313078
25992942
319012744
451822744

prune168.0ms (1.8%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1792181
Fresh01212
Picked011
Done011
Total17916195
Error
6.1b
Counts
195 → 16
Alt Table
StatusErrorProgram
12.1b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (cbrt.f64 c)))
29.8b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
11.4b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
25.2b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 b z)) (/.f64 1 c))
18.7b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
12.0b
(*.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))
42.3b
(/.f64 b (*.f64 c z))
11.7b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
25.2b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z b))) c)
11.3b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))) c)
38.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
39.8b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) c) 3))
12.2b
(*.f64 (*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 (/.f64 1 c)) (cbrt.f64 (/.f64 1 c)))) (cbrt.f64 (/.f64 1 c)))
29.5b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) (*.f64 c z))
38.6b
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) 3)) c)
41.2b
(*.f64 -4 (/.f64 (*.f64 a t) c))
Compiler

Compiled 4993 to 2912 computations (41.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
0.6b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
2.0b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
8.7b
(/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))

series367.0ms (3.9%)

Counts
2 → 168
Calls

2 calls:

284.0ms
(/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))
83.0ms
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
84×times-frac_binary64
52×*-un-lft-identity_binary64
52×add-sqr-sqrt_binary64
52×add-cube-cbrt_binary64
16×associate-/r*_binary64
Counts
2 → 107
Calls

2 calls:

4.0ms
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
2.0ms
(/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))

simplify193.0ms (2.1%)

Algorithm
egg-herbie
Rules
795×times-frac_binary64
466×associate-/r*_binary64
436×associate-/l*_binary64
295×fma-def_binary64
167×*-commutative_binary64
Counts
275 → 213
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
053214808
1161614085
2545514085

prune327.0ms (3.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New2896295
Fresh31013
Picked101
Done112
Total29417311
Error
6.1b
Counts
311 → 17
Alt Table
StatusErrorProgram
46.5b
(/.f64 1 (*.f64 1/9 (/.f64 c (/.f64 (*.f64 y x) z))))
11.3b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 x (*.f64 9 y) b)))) c)
39.1b
(/.f64 1 (*.f64 (sqrt.f64 c) (/.f64 (sqrt.f64 c) (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))))
29.8b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
12.1b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (cbrt.f64 c)))
18.7b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
11.7b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z)))))
25.2b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 b z)) (/.f64 1 c))
12.0b
(*.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))
42.3b
(/.f64 b (*.f64 c z))
43.4b
(/.f64 1 (/.f64 c (/.f64 b z)))
11.4b
(/.f64 (/.f64 1 c) (/.f64 1 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
38.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
29.5b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) (*.f64 c z))
38.6b
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) 3)) c)
25.2b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z b))) c)
41.2b
(/.f64 1 (*.f64 -1/4 (/.f64 c (*.f64 a t))))
Compiler

Compiled 12526 to 7087 computations (43.4% saved)

regimes2.3s (24.9%)

Accuracy

Total 1.4b remaining (17.9%)

Threshold costs 0b (0%)

Counts
111 → 5
Compiler

Compiled 32876 to 22720 computations (30.9% saved)

bsearch5.0ms (0.1%)

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify11.0ms (0.1%)

Algorithm
egg-herbie
Rules
14×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
distribute-rgt-neg-in_binary64
neg-sub0_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
039232
156206
275187
397185
4110185
5118185
6119185
7120185
8119185

end38.0ms (0.4%)

Remove

(sort x y)

Compiler

Compiled 917 to 560 computations (38.9% saved)

sample2.2s (23.7%)

Algorithm
intervals
Results
569.0ms8000×body128valid
412.0ms4730×body128invalid
Compiler

Compiled 565 to 386 computations (31.7% saved)

Profiling

Loading profile data...