Details

Time bar (total: 10.3s)

analyze2.2s (20.9%)

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)

sample2.4s (23.7%)

Symmetry

(sort x y)

(sort t a)

Results
1.5s8256×body128valid
841.0ms4839×body128invalid
Compiler

Compiled 80 to 56 computations (30% saved)

simplify60.0ms (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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
9.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
16.7b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
22.0b
(/.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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x (*.f64 9 y) b)
0.5b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
3.6b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
11.8b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)

series185.0ms (1.8%)

Counts
4 → 240
Calls

4 calls:

87.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
70.0ms
(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)

rewrite17.0ms (0.2%)

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)

simplify190.0ms (1.8%)

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

prune175.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New15813171
Fresh011
Picked101
Done000
Total15914173
Error
8.8b
Counts
173 → 14
Alt Table
StatusErrorProgram
43.6b
(/.f64 b (*.f64 c z))
41.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
27.6b
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
41.2b
(/.f64 (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (/.f64 c (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))))
42.7b
(*.f64 -4 (/.f64 (*.f64 a t) c))
17.5b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) (/.f64 c (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))))
33.7b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
16.8b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
17.5b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))
47.2b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
17.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (cbrt.f64 c)))
16.7b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
37.7b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)))
22.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
Compiler

Compiled 4672 to 2558 computations (45.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x (*.f64 9 y) b)
0.5b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
3.6b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
11.8b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

series121.0ms (1.2%)

Counts
1 → 84
Calls

1 calls:

121.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

rewrite11.0ms (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))

simplify88.0ms (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

prune177.0ms (1.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1792181
Fresh21113
Picked011
Done000
Total18114195
Error
8.8b
Counts
195 → 14
Alt Table
StatusErrorProgram
43.6b
(/.f64 b (*.f64 c z))
16.9b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (/.f64 (fma.f64 9 (*.f64 y x) b) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))) (/.f64 1 c))
41.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
47.2b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
17.2b
(*.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 1 (cbrt.f64 c)))
27.6b
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
41.2b
(/.f64 (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (/.f64 c (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))))
42.7b
(*.f64 -4 (/.f64 (*.f64 a t) c))
17.5b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) (/.f64 c (cbrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))))
33.7b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
16.8b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))
16.7b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
37.7b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)))
22.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
Compiler

Compiled 4971 to 2883 computations (42% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x (*.f64 9 y) b)
0.5b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
3.6b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
11.8b
(/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))

series315.0ms (3.1%)

Counts
1 → 84
Calls

1 calls:

315.0ms
(/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))

rewrite4.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
times-frac_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
associate-/r*_binary64
Counts
1 → 29
Calls

1 calls:

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

simplify137.0ms (1.3%)

Algorithm
egg-herbie
Rules
781×times-frac_binary64
445×associate-/r*_binary64
410×associate-/l*_binary64
293×fma-def_binary64
163×*-commutative_binary64
Counts
113 → 99
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04719399
114839151
251199151

prune274.0ms (2.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1957202
Fresh4812
Picked101
Done011
Total20016216
Error
8.8b
Counts
216 → 16
Alt Table
StatusErrorProgram
43.6b
(/.f64 b (*.f64 c z))
41.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
39.0b
(/.f64 1 (*.f64 (sqrt.f64 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) (sqrt.f64 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))))
49.5b
(/.f64 1 (*.f64 1/9 (/.f64 c (/.f64 (*.f64 y x) z))))
47.2b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
17.2b
(*.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 1 (cbrt.f64 c)))
32.3b
(/.f64 1 (-.f64 (/.f64 c (-.f64 (/.f64 b z) (*.f64 4 (*.f64 a t)))) (*.f64 9 (/.f64 (*.f64 c (*.f64 y x)) (*.f64 z (pow.f64 (-.f64 (/.f64 b z) (*.f64 4 (*.f64 a t))) 2))))))
27.6b
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
41.2b
(/.f64 (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))) (/.f64 c (sqrt.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))))
16.8b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z)))))
22.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
42.8b
(/.f64 1 (*.f64 -1/4 (/.f64 c (*.f64 a t))))
36.8b
(/.f64 1 (fma.f64 4 (/.f64 (*.f64 c (*.f64 a t)) (pow.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) 2)) (/.f64 c (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)))))
47.2b
(/.f64 1 (*.f64 1/9 (/.f64 (*.f64 c z) (*.f64 y x))))
16.7b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
33.7b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
Compiler

Compiled 9941 to 5585 computations (43.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x (*.f64 9 y) b)
0.5b
(fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z)))
3.8b
(*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z))
11.8b
(/.f64 c (fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z))))

series365.0ms (3.5%)

Counts
3 → 204
Calls

3 calls:

301.0ms
(/.f64 c (fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z))))
41.0ms
(fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z)))
22.0ms
(*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
20×times-frac_binary64
19×add-cube-cbrt_binary64
14×add-exp-log_binary64
Counts
3 → 77
Calls

3 calls:

6.0ms
(*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z))
2.0ms
(/.f64 c (fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z))))
0.0ms
(fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z)))

simplify184.0ms (1.8%)

Algorithm
egg-herbie
Rules
786×times-frac_binary64
454×associate-/r*_binary64
423×associate-/l*_binary64
297×fma-def_binary64
177×*-commutative_binary64
Counts
281 → 207
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
052812281
1159211895
2533711895

prune258.0ms (2.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New2271228
Fresh11314
Picked011
Done011
Total22816244
Error
8.8b
Counts
244 → 16
Alt Table
StatusErrorProgram
43.6b
(/.f64 b (*.f64 c z))
41.9b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
39.0b
(/.f64 1 (*.f64 (sqrt.f64 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)))) (sqrt.f64 (/.f64 c (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))))))
49.5b
(/.f64 1 (*.f64 1/9 (/.f64 c (/.f64 (*.f64 y x) z))))
47.2b
(*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))
17.2b
(*.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 1 (cbrt.f64 c)))
32.3b
(/.f64 1 (-.f64 (/.f64 c (-.f64 (/.f64 b z) (*.f64 4 (*.f64 a t)))) (*.f64 9 (/.f64 (*.f64 c (*.f64 y x)) (*.f64 z (pow.f64 (-.f64 (/.f64 b z) (*.f64 4 (*.f64 a t))) 2))))))
41.3b
(/.f64 1 (/.f64 c (cbrt.f64 (pow.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) 3))))
47.2b
(/.f64 1 (*.f64 1/9 (/.f64 (*.f64 c z) (*.f64 y x))))
16.8b
(/.f64 1 (/.f64 c (fma.f64 t (*.f64 a -4) (*.f64 (fma.f64 x (*.f64 9 y) b) (/.f64 1 z)))))
22.0b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
42.8b
(/.f64 1 (*.f64 -1/4 (/.f64 c (*.f64 a t))))
36.8b
(/.f64 1 (fma.f64 4 (/.f64 (*.f64 c (*.f64 a t)) (pow.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) 2)) (/.f64 c (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)))))
27.6b
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
16.7b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
33.7b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
Compiler

Compiled 10523 to 6072 computations (42.3% saved)

regimes2.6s (25.2%)

Accuracy

Total 2.6b remaining (30.7%)

Threshold costs 0b (0%)

Counts
135 → 4
Compiler

Compiled 38012 to 26432 computations (30.5% saved)

bsearch6.0ms (0.1%)

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify11.0ms (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
048209
174209
295209
3116209
4135209
5143209
6145209
7143209

end453.0ms (4.4%)

Remove

(sort t a)

Compiler

Compiled 1593 to 981 computations (38.4% saved)

Profiling

Loading profile data...