Details

Time bar (total: 10.0s)

analyze2.1s (21%)

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)

sample2.2s (22.6%)

Symmetry

(sort x y)

(sort t a)

Results
1.4s8256×body128valid
797.0ms4891×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
7.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
20.6b
(/.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
0.1b
(fma.f64 x (*.f64 9 y) b)
0.3b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
2.5b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
9.6b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)

series210.0ms (2.1%)

Counts
4 → 240
Calls

4 calls:

143.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
40.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
20.0ms
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
7.0ms
(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:

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)

simplify227.0ms (2.3%)

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

prune182.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New15813171
Fresh011
Picked101
Done000
Total15914173
Error
6.3b
Counts
173 → 14
Alt Table
StatusErrorProgram
41.7b
(*.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (/.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
31.8b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) (*.f64 c z))
12.7b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
40.2b
(*.f64 (/.f64 1 (sqrt.f64 c)) (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)))
38.7b
(/.f64 (*.f64 -4 (*.f64 a t)) c)
13.2b
(*.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)))
12.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)) c)
12.5b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
41.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (/.f64 (fma.f64 x (*.f64 9 y) b) (sqrt.f64 z)) (sqrt.f64 z))) c)
13.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)))
32.9b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
42.2b
(/.f64 b (*.f64 c z))
48.5b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
20.6b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
Compiler

Compiled 4588 to 2510 computations (45.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 9 (*.f64 y x))
0.3b
(fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z))
2.5b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)
9.6b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)) c)

series183.0ms (1.8%)

Counts
4 → 192
Calls

4 calls:

118.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)) c)
39.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z))
21.0ms
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)
5.0ms
(*.f64 9 (*.f64 y x))

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
21×add-cube-cbrt_binary64
18×times-frac_binary64
13×add-cbrt-cube_binary64
Counts
4 → 90
Calls

4 calls:

6.0ms
(*.f64 9 (*.f64 y x))
5.0ms
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)
2.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)) c)
0.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z))

simplify209.0ms (2.1%)

Algorithm
egg-herbie
Rules
683×div-sub_binary64
616×associate-*l*_binary64
479×fma-neg_binary64
464×associate-*r*_binary64
416×cancel-sign-sub-inv_binary64
Counts
282 → 173
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01866423
14065877
210985622
333345055
446085055
560005055

prune170.0ms (1.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1730173
Fresh01313
Picked011
Done000
Total17314187
Error
6.3b
Counts
187 → 14
Alt Table
StatusErrorProgram
41.7b
(*.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (/.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
31.8b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) (*.f64 c z))
12.7b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
40.2b
(*.f64 (/.f64 1 (sqrt.f64 c)) (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)))
38.7b
(/.f64 (*.f64 -4 (*.f64 a t)) c)
13.2b
(*.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)))
12.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)) c)
12.5b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
41.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (/.f64 (fma.f64 x (*.f64 9 y) b) (sqrt.f64 z)) (sqrt.f64 z))) c)
13.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)))
32.9b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
42.2b
(/.f64 b (*.f64 c z))
48.5b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
20.6b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
Compiler

Compiled 4808 to 2571 computations (46.5% saved)

localize14.0ms (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))
2.5b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
9.7b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

series87.0ms (0.9%)

Counts
1 → 84
Calls

1 calls:

87.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

rewrite8.0ms (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:

5.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

simplify90.0ms (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

prune194.0ms (1.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1783181
Fresh21012
Picked101
Done011
Total18114195
Error
6.3b
Counts
195 → 14
Alt Table
StatusErrorProgram
41.7b
(*.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (/.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
31.8b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) (*.f64 c z))
12.3b
(*.f64 (fma.f64 t (*.f64 a -4) (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z))) (/.f64 1 c))
42.2b
(/.f64 b (*.f64 c z))
12.6b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (*.f64 y x) b)))) (/.f64 1 c))
48.5b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
12.7b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
40.2b
(*.f64 (/.f64 1 (sqrt.f64 c)) (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)))
38.7b
(/.f64 (*.f64 -4 (*.f64 a t)) c)
41.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (/.f64 (fma.f64 x (*.f64 9 y) b) (sqrt.f64 z)) (sqrt.f64 z))) c)
13.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)))
20.6b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
13.3b
(*.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)))
12.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)) c)
Compiler

Compiled 4968 to 2892 computations (41.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 t (*.f64 a -4) (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)))
0.6b
(fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z))
3.0b
(/.f64 (*.f64 y x) z)
9.7b
(*.f64 (fma.f64 t (*.f64 a -4) (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z))) (/.f64 1 c))

series186.0ms (1.9%)

Counts
4 → 204
Calls

4 calls:

103.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z))) (/.f64 1 c))
44.0ms
(fma.f64 t (*.f64 a -4) (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)))
24.0ms
(fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z))
14.0ms
(/.f64 (*.f64 y x) z)

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
18×add-exp-log_binary64
15×*-un-lft-identity_binary64
14×times-frac_binary64
14×add-cube-cbrt_binary64
Counts
4 → 81
Calls

4 calls:

7.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z))) (/.f64 1 c))
3.0ms
(/.f64 (*.f64 y x) z)
0.0ms
(fma.f64 t (*.f64 a -4) (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)))
0.0ms
(fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z))

simplify183.0ms (1.8%)

Algorithm
egg-herbie
Rules
495×associate-/l*_binary64
372×associate-*l*_binary64
336×times-frac_binary64
288×associate-*r*_binary64
260×fma-neg_binary64
Counts
285 → 148
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01586353
13455649
210305533
341325533
447735533
550025533

prune148.0ms (1.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1453148
Fresh11112
Picked101
Done011
Total14715162
Error
4.6b
Counts
162 → 15
Alt Table
StatusErrorProgram
13.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)))
12.1b
(*.f64 (fma.f64 t (*.f64 a -4) (fma.f64 9 (*.f64 y (/.f64 x z)) (/.f64 b z))) (/.f64 1 c))
41.7b
(*.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (/.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
31.8b
(/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) (*.f64 c z))
12.6b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 1 (/.f64 z (fma.f64 9 (*.f64 y x) b)))) (/.f64 1 c))
48.5b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
12.7b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
40.2b
(*.f64 (/.f64 1 (sqrt.f64 c)) (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)))
38.7b
(/.f64 (*.f64 -4 (*.f64 a t)) c)
12.0b
(*.f64 (fma.f64 t (*.f64 a -4) (fma.f64 9 (/.f64 y (/.f64 z x)) (/.f64 b z))) (/.f64 1 c))
12.1b
(*.f64 (fma.f64 t (*.f64 a -4) (fma.f64 9 (*.f64 (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z))) (/.f64 b z))) (/.f64 1 c))
42.2b
(/.f64 b (*.f64 c z))
20.6b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
13.3b
(*.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)))
12.4b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (+.f64 (*.f64 9 (*.f64 y x)) b) z)) c)
Compiler

Compiled 4055 to 1877 computations (53.7% saved)

regimes2.8s (28%)

Accuracy

Total 2.5b remaining (38.2%)

Threshold costs 0b (0%)

Counts
141 → 4
Compiler

Compiled 43428 to 29350 computations (32.4% saved)

bsearch7.0ms (0.1%)

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Rules
22×*-commutative_binary64
13×+-commutative_binary64
11×sub-neg_binary64
10×distribute-rgt-neg-in_binary64
distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053212
179212
2100212
3121212
4140212
5148212
6150212
7148212

end587.0ms (5.9%)

Compiler

Compiled 1308 to 787 computations (39.8% saved)

Profiling

Loading profile data...