Details

Time bar (total: 9.4s)

analyze2.1s (22.6%)

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)

sample2.8s (29.9%)

Symmetry

(sort x y)

(sort t a)

Results
1.7s8256×body128valid
920.0ms5017×body128invalid
Compiler

Compiled 80 to 56 computations (30% saved)

simplify65.0ms (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

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
14.7b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
19.2b
(/.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)

localize11.0ms (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))
0.3b
(fma.f64 x (*.f64 9 y) b)
2.0b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
12.0b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)

series153.0ms (1.6%)

Counts
4 → 240
Calls

4 calls:

85.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
38.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
21.0ms
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
9.0ms
(fma.f64 x (*.f64 9 y) b)

rewrite81.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
334×prod-diff_binary64
302×log1p-udef_binary64
166×add-sqr-sqrt_binary64
155×add-log-exp_binary64
155×log1p-expm1-u_binary64
Counts
4 → 112
Calls

4 calls:

78.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
78.0ms
(fma.f64 x (*.f64 9 y) b)
78.0ms
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
78.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01658
133058
2397458
3510458
000
100

simplify466.0ms (4.9%)

Algorithm
egg-herbie
Rules
834×associate-/r/_binary64
656×div-sub_binary64
485×distribute-lft-neg-in_binary64
456×unsub-neg_binary64
438×fma-neg_binary64
Counts
352 → 146
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0434761
11134427
22724179
37153981
413843981
524583981
634733486
739333486
839233486
940583486
1041273486
1141433486
1248653486
1349283486

prune308.0ms (3.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New13313146
Fresh011
Picked101
Done000
Total13414148
Error
6.6b
Counts
148 → 14
Alt Table
StatusErrorProgram
38.2b
(pow.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) 2)
35.7b
(/.f64 (+.f64 (*.f64 9 (/.f64 (*.f64 y x) z)) (/.f64 b z)) c)
14.8b
(/.f64 (fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z))) c)
15.5b
(*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) 2))
15.4b
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) 2) (*.f64 (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (/.f64 1 c)))
45.1b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
40.7b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c) 3))
40.9b
(/.f64 (fma.f64 t (*.f64 a -4) (*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 x (*.f64 9 y) b) (sqrt.f64 z)))) c)
41.5b
(*.f64 (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (*.f64 (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (/.f64 1 c)))
19.2b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
47.2b
(/.f64 b (*.f64 c z))
14.8b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
38.6b
(*.f64 -4 (/.f64 (*.f64 a t) c))
11.5b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
Compiler

Compiled 3621 to 2162 computations (40.3% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
4.3b
(/.f64 b (*.f64 c z))
5.0b
(/.f64 (*.f64 a t) c)
9.4b
(/.f64 (*.f64 y x) (*.f64 c z))

series192.0ms (2%)

Counts
4 → 0
Calls

4 calls:

71.0ms
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
60.0ms
(/.f64 (*.f64 y x) (*.f64 c z))
34.0ms
(/.f64 b (*.f64 c z))
27.0ms
(/.f64 (*.f64 a t) c)

rewrite132.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
174×times-frac_binary64
174×add-sqr-sqrt_binary64
163×egg-rr
162×add-log-exp_binary64
162×log1p-expm1-u_binary64
Counts
4 → 163
Calls

4 calls:

126.0ms
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
126.0ms
(/.f64 b (*.f64 c z))
126.0ms
(/.f64 (*.f64 a t) c)
126.0ms
(/.f64 (*.f64 y x) (*.f64 c z))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01637
134437
2491937
3512837
000
100

simplify19.0ms (0.2%)

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
100

prune304.0ms (3.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1567163
Fresh7613
Picked101
Done000
Total16413177
Error
0.3b
Counts
177 → 13
Alt Table
StatusErrorProgram
12.0b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y z) (/.f64 x c)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
38.2b
(pow.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) 2)
35.7b
(/.f64 (+.f64 (*.f64 9 (/.f64 (*.f64 y x) z)) (/.f64 b z)) c)
10.9b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 (/.f64 a c) t)))
47.2b
(/.f64 b (*.f64 c z))
12.5b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
14.8b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
9.1b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y (*.f64 c z)) x))) (*.f64 4 (/.f64 (*.f64 a t) c)))
11.7b
(-.f64 (+.f64 (*.f64 b (/.f64 1 (*.f64 c z))) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
33.9b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 (sqrt.f64 (*.f64 a t)) (*.f64 (sqrt.f64 (*.f64 a t)) (/.f64 1 c)))))
10.1b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 (/.f64 a 1) (/.f64 t c))))
40.9b
(/.f64 (fma.f64 t (*.f64 a -4) (*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 x (*.f64 9 y) b) (sqrt.f64 z)))) c)
19.2b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
Compiler

Compiled 5188 to 1984 computations (61.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.8b
(*.f64 (/.f64 y (*.f64 c z)) x)
4.3b
(/.f64 b (*.f64 c z))
4.8b
(/.f64 y (*.f64 c z))
5.0b
(/.f64 (*.f64 a t) c)

series49.0ms (0.5%)

Counts
2 → 48
Calls

2 calls:

31.0ms
(*.f64 (/.f64 y (*.f64 c z)) x)
18.0ms
(/.f64 y (*.f64 c z))

rewrite59.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
867×log1p-expm1-u_binary64
867×expm1-log1p-u_binary64
86×add-sqr-sqrt_binary64
79×add-log-exp_binary64
78×add-cube-cbrt_binary64
Counts
2 → 69
Calls

2 calls:

58.0ms
(*.f64 (/.f64 y (*.f64 c z)) x)
58.0ms
(/.f64 y (*.f64 c z))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
116617
2222917
3542717
000
100

simplify23.0ms (0.2%)

Algorithm
egg-herbie
Rules
14×associate-/l*_binary64
associate-*r/_binary64
associate-/r/_binary64
*-commutative_binary64
associate-/r*_binary64
Counts
117 → 69
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08480
117480
238480
363480
469480
568480
668480

prune182.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1482150
Fresh21012
Picked101
Done000
Total15112163
Error
0.0b
Counts
163 → 12
Alt Table
StatusErrorProgram
12.0b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y z) (/.f64 x c)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
38.2b
(pow.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) 2)
35.7b
(/.f64 (+.f64 (*.f64 9 (/.f64 (*.f64 y x) z)) (/.f64 b z)) c)
11.9b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (*.f64 (/.f64 1 c) (/.f64 y z)) x))) (*.f64 4 (/.f64 (*.f64 a t) c)))
12.5b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
14.8b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
11.7b
(-.f64 (+.f64 (*.f64 b (/.f64 1 (*.f64 c z))) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
33.9b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 (sqrt.f64 (*.f64 a t)) (*.f64 (sqrt.f64 (*.f64 a t)) (/.f64 1 c)))))
10.1b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 (/.f64 a 1) (/.f64 t c))))
40.9b
(/.f64 (fma.f64 t (*.f64 a -4) (*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 x (*.f64 9 y) b) (sqrt.f64 z)))) c)
8.6b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y (*.f64 c z)) x))) (*.f64 4 (*.f64 (/.f64 a c) t)))
19.2b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
Compiler

Compiled 4815 to 1899 computations (60.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.8b
(*.f64 (/.f64 y (*.f64 c z)) x)
4.3b
(/.f64 b (*.f64 c z))
4.8b
(/.f64 y (*.f64 c z))
6.0b
(*.f64 (/.f64 a c) t)

series16.0ms (0.2%)

Counts
1 → 36
Calls

1 calls:

16.0ms
(*.f64 (/.f64 a c) t)

rewrite43.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
629×log1p-expm1-u_binary64
629×expm1-log1p-u_binary64
349×log-prod_binary64
119×expm1-udef_binary64
119×log1p-udef_binary64
Counts
1 → 28
Calls

1 calls:

42.0ms
(*.f64 (/.f64 a c) t)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11257
216307
351147
000
100

simplify15.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-/l*_binary64
associate-/r/_binary64
Counts
64 → 28
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06252
19252
213252
316252
417252
517252

prune155.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1351136
Fresh11011
Picked011
Done000
Total13612148
Error
0.0b
Counts
148 → 12
Alt Table
StatusErrorProgram
12.0b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y z) (/.f64 x c)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
38.2b
(pow.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) 2)
35.7b
(/.f64 (+.f64 (*.f64 9 (/.f64 (*.f64 y x) z)) (/.f64 b z)) c)
11.9b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (*.f64 (/.f64 1 c) (/.f64 y z)) x))) (*.f64 4 (/.f64 (*.f64 a t) c)))
12.5b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
14.8b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
11.7b
(-.f64 (+.f64 (*.f64 b (/.f64 1 (*.f64 c z))) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))
10.1b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (*.f64 (/.f64 a 1) (/.f64 t c))))
40.9b
(/.f64 (fma.f64 t (*.f64 a -4) (*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 x (*.f64 9 y) b) (sqrt.f64 z)))) c)
8.6b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y (*.f64 c z)) x))) (*.f64 4 (*.f64 (/.f64 a c) t)))
7.8b
(-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (*.f64 (/.f64 y (*.f64 c z)) x))) (*.f64 4 (/.f64 a (/.f64 c t))))
19.2b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
Compiler

Compiled 4038 to 1522 computations (62.3% saved)

regimes1.6s (16.9%)

Accuracy

Total 4.8b remaining (99.1%)

Threshold costs 0b (0%)

Counts
67 → 4
Compiler

Compiled 19150 to 13080 computations (31.7% saved)

bsearch4.0ms (0%)

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify11.0ms (0.1%)

Algorithm
egg-herbie
Rules
25×*-commutative_binary64
17×+-commutative_binary64
14×sub-neg_binary64
12×distribute-rgt-neg-in_binary64
11×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
051218
181218
2109218
3138218
4157218
5166218
6168218
7167218

end535.0ms (5.7%)

Compiler

Compiled 1263 to 738 computations (41.6% saved)

Profiling

Loading profile data...