Details

Time bar (total: 11.8s)

analyze1.6s (13.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
1.8%98%0.2%10
7.7%92.1%0.2%11
10.4%89.4%0.2%12
12.1%87.7%0.2%13
21.4%78.3%0.4%14
Compiler

Compiled 19 to 12 computations (36.8% saved)

sample2.0s (16.7%)

Results
1.1s6929×body128valid
215.0ms367×body1024valid
185.0ms1216×body128invalid
183.0ms517×body512valid
112.0ms374×body256valid
39.0ms69×body2048valid
Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify94.0ms (0.8%)

Algorithm
egg-herbie
Rules
836×unsub-neg_binary64
769×fma-def_binary64
696×div-sub_binary64
646×sub-neg_binary64
478×neg-mul-1_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01219
12119
25217
314417
442117
5109217
6265717
7390117
8440817
9480717
10488117

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
11.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
14.8b
(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
24.0b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
Compiler

Compiled 100 to 55 computations (45% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 t x) (-.f64 a z))
14.8b
(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series188.0ms (1.6%)

Counts
2 → 108
Calls

2 calls:

128.0ms
(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
59.0ms
(/.f64 (-.f64 t x) (-.f64 a z))

rewrite23.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity_binary64
38×add-sqr-sqrt_binary64
25×times-frac_binary64
14×add-cube-cbrt_binary64
12×distribute-lft-out--_binary64
Counts
2 → 64
Calls

2 calls:

14.0ms
(/.f64 (-.f64 t x) (-.f64 a z))
1.0ms
(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify131.0ms (1.1%)

Algorithm
egg-herbie
Rules
523×cancel-sign-sub-inv_binary64
479×sub-neg_binary64
353×associate-+r+_binary64
286×+-commutative_binary64
272×associate-+l+_binary64
Counts
172 → 136
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03566269
110456192
238516156
352336156

prune143.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New12511136
Fresh101
Picked101
Done000
Total12711138
Error
1.3b
Counts
138 → 11
Alt Table
StatusErrorProgram
14.8b
(fma.f64 (-.f64 y z) (*.f64 1 (/.f64 (-.f64 t x) (-.f64 a z))) x)
37.3b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (+.f64 t (/.f64 (*.f64 a t) z))) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 a x) z)))
15.6b
(fma.f64 (-.f64 y z) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))) x)
38.3b
(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
31.4b
(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
15.0b
(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
33.1b
(fma.f64 (-.f64 y z) (cbrt.f64 (pow.f64 (/.f64 (-.f64 t x) (-.f64 a z)) 3)) x)
39.6b
(-.f64 (+.f64 t (+.f64 (/.f64 (*.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 y (*.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 y x) z) (/.f64 (*.f64 a t) z))))) (+.f64 (/.f64 (*.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 a x) z) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 y (*.f64 a t)) (pow.f64 z 2))))))
36.0b
(fma.f64 (-.f64 y z) (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))) x)
20.2b
(-.f64 (+.f64 (/.f64 (*.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (*.f64 y x) (-.f64 a z)) (/.f64 (*.f64 t z) (-.f64 a z))))
37.9b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) t) (/.f64 (*.f64 y t) z))
Compiler

Compiled 5040 to 1636 computations (67.5% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 t x) (-.f64 a z))
14.8b
(fma.f64 (-.f64 y z) (*.f64 1 (/.f64 (-.f64 t x) (-.f64 a z))) x)

series64.0ms (0.5%)

Counts
1 → 60
Calls

1 calls:

63.0ms
(fma.f64 (-.f64 y z) (*.f64 1 (/.f64 (-.f64 t x) (-.f64 a z))) x)

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

2.0ms
(fma.f64 (-.f64 y z) (*.f64 1 (/.f64 (-.f64 t x) (-.f64 a z))) x)

simplify87.0ms (0.7%)

Algorithm
egg-herbie
Rules
987×times-frac_binary64
354×cancel-sign-sub-inv_binary64
331×sub-neg_binary64
320×associate-+r+_binary64
233×distribute-neg-in_binary64
Counts
70 → 69
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02273787
17013752
227783716
351153716

prune120.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1360136
Fresh01010
Picked011
Done000
Total13611147
Error
1.3b
Counts
147 → 11
Alt Table
StatusErrorProgram
14.8b
(fma.f64 (-.f64 y z) (*.f64 1 (/.f64 (-.f64 t x) (-.f64 a z))) x)
37.3b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (+.f64 t (/.f64 (*.f64 a t) z))) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 a x) z)))
15.6b
(fma.f64 (-.f64 y z) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))) x)
38.3b
(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
31.4b
(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
15.0b
(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
33.1b
(fma.f64 (-.f64 y z) (cbrt.f64 (pow.f64 (/.f64 (-.f64 t x) (-.f64 a z)) 3)) x)
39.6b
(-.f64 (+.f64 t (+.f64 (/.f64 (*.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 y (*.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 y x) z) (/.f64 (*.f64 a t) z))))) (+.f64 (/.f64 (*.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 a x) z) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 y (*.f64 a t)) (pow.f64 z 2))))))
36.0b
(fma.f64 (-.f64 y z) (*.f64 (/.f64 1 (sqrt.f64 (-.f64 a z))) (/.f64 (-.f64 t x) (sqrt.f64 (-.f64 a z)))) x)
20.2b
(-.f64 (+.f64 (/.f64 (*.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (*.f64 y x) (-.f64 a z)) (/.f64 (*.f64 t z) (-.f64 a z))))
37.9b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) t) (/.f64 (*.f64 y t) z))
Compiler

Compiled 5185 to 1805 computations (65.2% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 a z) (-.f64 t x))
0.4b
(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
14.7b
(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)

series124.0ms (1%)

Counts
3 → 156
Calls

3 calls:

65.0ms
(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
30.0ms
(/.f64 (-.f64 a z) (-.f64 t x))
28.0ms
(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))

rewrite40.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
218×times-frac_binary64
195×*-un-lft-identity_binary64
195×add-sqr-sqrt_binary64
91×add-cube-cbrt_binary64
52×distribute-lft-out--_binary64
Counts
3 → 214
Calls

3 calls:

9.0ms
(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
7.0ms
(/.f64 (-.f64 a z) (-.f64 t x))
0.0ms
(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)

simplify176.0ms (1.5%)

Algorithm
egg-herbie
Rules
388×associate-+r+_binary64
313×associate-+l+_binary64
283×times-frac_binary64
266×associate-/l*_binary64
227×associate--l+_binary64
Counts
370 → 317
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
048411287
1134710818
2499710818

prune256.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3152317
Fresh189
Picked011
Done101
Total31711328
Error
1.3b
Counts
328 → 11
Alt Table
StatusErrorProgram
15.6b
(fma.f64 (-.f64 y z) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))) x)
38.3b
(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
31.4b
(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
15.0b
(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
33.1b
(fma.f64 (-.f64 y z) (cbrt.f64 (pow.f64 (/.f64 (-.f64 t x) (-.f64 a z)) 3)) x)
39.6b
(-.f64 (+.f64 t (+.f64 (/.f64 (*.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 y (*.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 y x) z) (/.f64 (*.f64 a t) z))))) (+.f64 (/.f64 (*.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 a x) z) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 y (*.f64 a t)) (pow.f64 z 2))))))
37.3b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (+.f64 t (/.f64 (*.f64 a t) z))) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 a x) z)))
15.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)))
14.3b
(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
20.2b
(-.f64 (+.f64 (/.f64 (*.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (*.f64 y x) (-.f64 a z)) (/.f64 (*.f64 t z) (-.f64 a z))))
37.9b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) t) (/.f64 (*.f64 y t) z))
Compiler

Compiled 10174 to 3172 computations (68.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 a z) (-.f64 t x))
2.4b
(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
5.1b
(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

series167.0ms (1.4%)

Counts
2 → 120
Calls

2 calls:

99.0ms
(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
68.0ms
(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

rewrite138.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
585×times-frac_binary64
535×*-un-lft-identity_binary64
533×add-sqr-sqrt_binary64
187×add-cube-cbrt_binary64
173×distribute-lft-out--_binary64
Counts
2 → 386
Calls

2 calls:

48.0ms
(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
14.0ms
(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

simplify288.0ms (2.4%)

Algorithm
egg-herbie
Rules
844×times-frac_binary64
422×associate-/r/_binary64
239×associate-/l*_binary64
214×sub-neg_binary64
206×associate-/l/_binary64
Counts
506 → 437
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
063214909
1192114784
2484414700
3586214700

prune397.0ms (3.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New5007507
Fresh369
Picked101
Done011
Total50414518
Error
1.3b
Counts
518 → 14
Alt Table
StatusErrorProgram
15.0b
(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
39.2b
(fma.f64 (/.f64 (sqrt.f64 (-.f64 y z)) 1) (/.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (-.f64 a z) (-.f64 t x))) x)
33.1b
(fma.f64 (-.f64 y z) (cbrt.f64 (pow.f64 (/.f64 (-.f64 t x) (-.f64 a z)) 3)) x)
21.5b
(-.f64 (/.f64 y (/.f64 (-.f64 a z) (-.f64 t x))) (-.f64 (/.f64 (*.f64 (-.f64 t x) z) (-.f64 a z)) x))
37.3b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (+.f64 t (/.f64 (*.f64 a t) z))) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 a x) z)))
46.9b
(/.f64 (+.f64 (pow.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) 3) (pow.f64 x 3)) (fma.f64 x (-.f64 x (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)))) (*.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))))))
56.8b
(fma.f64 (/.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))) (+.f64 (sqrt.f64 t) (sqrt.f64 x)))) (/.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) (-.f64 (sqrt.f64 t) (sqrt.f64 x)))) x)
39.6b
(fma.f64 (sqrt.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))) (sqrt.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))) x)
31.4b
(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
39.6b
(-.f64 (+.f64 t (+.f64 (/.f64 (*.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 y (*.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 y x) z) (/.f64 (*.f64 a t) z))))) (+.f64 (/.f64 (*.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (*.f64 a x) z) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 y (*.f64 a t)) (pow.f64 z 2))))))
38.6b
(fma.f64 (/.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))) 1)) (/.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) (-.f64 t x))) x)
37.5b
(fma.f64 (/.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))) (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))))) (/.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 t x)))) x)
37.9b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) t) (/.f64 (*.f64 y t) z))
38.3b
(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
Compiler

Compiled 17170 to 3723 computations (78.3% saved)

regimes5.6s (47%)

Accuracy

Total 6.2b remaining (86.9%)

Threshold costs 0b (0%)

Counts
271 → 3
Compiler

Compiled 43698 to 23718 computations (45.7% saved)

bsearch13.0ms (0.1%)

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Rules
18×+-commutative_binary64
15×*-commutative_binary64
14×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048209
165209
280209
396209
4118209
5130209
6138209
7141209
8140209

end205.0ms (1.7%)

Compiler

Compiled 743 to 316 computations (57.5% saved)

Profiling

Loading profile data...