Details

Time bar (total: 7.7s)

analyze1.9s (24.9%)

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
1.6%98.1%0.3%13
2.3%97.4%0.3%14
Compiler

Compiled 24 to 18 computations (25% saved)

sample1.9s (24.7%)

Symmetry

(sort y z t)

(sort a b)

Results
1.2s8256×body128valid
444.0ms3140×body128invalid
Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify70.0ms (0.9%)

Algorithm
egg-herbie
Rules
712×fma-neg_binary64
641×fma-def_binary64
213×cancel-sign-sub-inv_binary64
172×distribute-rgt-neg-in_binary64
157×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01825
13923
211521
330821
455221
590221
6120121
7143321
8167221
9178721
10179121
11179121
12179121
13167421

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
3.2b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))
3.2b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
Compiler

Compiled 126 to 90 computations (28.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))
0.2b
(*.f64 (*.f64 y 9) z)
0.2b
(*.f64 (*.f64 a 27) b)
7.3b
(*.f64 (*.f64 (*.f64 y 9) z) t)

series34.0ms (0.4%)

Counts
4 → 132
Calls

4 calls:

13.0ms
(-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))
12.0ms
(*.f64 (*.f64 (*.f64 y 9) z) t)
4.0ms
(*.f64 (*.f64 a 27) b)
4.0ms
(*.f64 (*.f64 y 9) z)

rewrite20.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
23×pow1_binary64
12×cbrt-unprod_binary64
12×prod-exp_binary64
Counts
4 → 79
Calls

4 calls:

5.0ms
(*.f64 (*.f64 (*.f64 y 9) z) t)
5.0ms
(-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))
4.0ms
(*.f64 (*.f64 y 9) z)
3.0ms
(*.f64 (*.f64 a 27) b)

simplify100.0ms (1.3%)

Algorithm
egg-herbie
Rules
543×distribute-rgt-neg-in_binary64
369×fma-def_binary64
365×associate-*l*_binary64
300×fma-neg_binary64
292×cancel-sign-sub-inv_binary64
Counts
211 → 127
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01542455
13722243
216212227
331172227
448412227
548942227

prune164.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1189127
Fresh011
Picked101
Done000
Total11910129
Error
0.0b
Counts
129 → 10
Alt Table
StatusErrorProgram
3.2b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 a (*.f64 27 b)))
3.2b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
3.2b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))
3.2b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
8.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 y 9) z))) t)) (*.f64 (*.f64 a 27) b))
8.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 9 (*.f64 y z)) (sqrt.f64 t)) (sqrt.f64 t))) (*.f64 (*.f64 a 27) b))
21.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 y 9) z) t)) (sqrt.f64 (*.f64 (*.f64 (*.f64 y 9) z) t)))) (*.f64 (*.f64 a 27) b))
3.4b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))))) (*.f64 (*.f64 a 27) b))
36.9b
(+.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))) (sqrt.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)))) (*.f64 (*.f64 a 27) b))
3.2b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y (*.f64 t z)) -9)) (*.f64 (*.f64 a 27) b))
Compiler

Compiled 3411 to 2147 computations (37.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))
0.2b
(*.f64 (*.f64 y 9) z)
0.2b
(*.f64 a (*.f64 27 b))
7.3b
(*.f64 (*.f64 (*.f64 y 9) z) t)

series4.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

4.0ms
(*.f64 a (*.f64 27 b))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
associate-*l*_binary64
cbrt-unprod_binary64
Counts
1 → 20
Calls

1 calls:

3.0ms
(*.f64 a (*.f64 27 b))

simplify71.0ms (0.9%)

Algorithm
egg-herbie
Rules
525×associate-/r/_binary64
451×associate-*l*_binary64
384×associate-/l*_binary64
370×*-commutative_binary64
301×associate-*r*_binary64
Counts
44 → 30
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
042378
190342
2302342
3821342
41011342
51137342
62002342
74806342
84922342

prune170.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1261127
Fresh189
Picked101
Done000
Total1289137
Error
0.0b
Counts
137 → 9
Alt Table
StatusErrorProgram
3.1b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y (*.f64 t z)) -9)) (*.f64 a (*.f64 27 b)))
3.4b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z))))) (cbrt.f64 (*.f64 9 (*.f64 y (*.f64 t z)))))) (*.f64 (*.f64 a 27) b))
3.2b
(fma.f64 y (*.f64 (*.f64 z t) -9) (fma.f64 x 2 (*.f64 (*.f64 a 27) b)))
3.2b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
8.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (expm1.f64 (log1p.f64 (*.f64 (*.f64 y 9) z))) t)) (*.f64 (*.f64 a 27) b))
3.2b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
8.0b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 9 (*.f64 y z)) (sqrt.f64 t)) (sqrt.f64 t))) (*.f64 (*.f64 a 27) b))
21.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 y 9) z) t)) (sqrt.f64 (*.f64 (*.f64 (*.f64 y 9) z) t)))) (*.f64 (*.f64 a 27) b))
36.9b
(+.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))) (sqrt.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)))) (*.f64 (*.f64 a 27) b))
Compiler

Compiled 3365 to 2112 computations (37.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x 2 (*.f64 (*.f64 y (*.f64 t z)) -9))
0.2b
(*.f64 a (*.f64 27 b))
0.3b
(*.f64 (*.f64 y (*.f64 t z)) -9)
8.1b
(*.f64 y (*.f64 t z))

series35.0ms (0.4%)

Counts
3 → 84
Calls

3 calls:

16.0ms
(fma.f64 x 2 (*.f64 (*.f64 y (*.f64 t z)) -9))
10.0ms
(*.f64 y (*.f64 t z))
9.0ms
(*.f64 (*.f64 y (*.f64 t z)) -9)

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
17×pow1_binary64
cbrt-unprod_binary64
prod-exp_binary64
Counts
3 → 53
Calls

3 calls:

5.0ms
(*.f64 (*.f64 y (*.f64 t z)) -9)
3.0ms
(*.f64 y (*.f64 t z))
0.0ms
(fma.f64 x 2 (*.f64 (*.f64 y (*.f64 t z)) -9))

simplify86.0ms (1.1%)

Algorithm
egg-herbie
Rules
946×fma-def_binary64
367×*-commutative_binary64
287×unsub-neg_binary64
286×distribute-rgt-neg-out_binary64
235×sqr-pow_binary64
Counts
137 → 71
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0861712
11821566
26621566
312581566
424271566
544271566
651451566

prune120.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New974101
Fresh628
Picked101
Done000
Total1046110
Error
0.0b
Counts
110 → 6
Alt Table
StatusErrorProgram
3.2b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
3.2b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y (*.f64 t z)) -9)) (*.f64 27 (*.f64 a b)))
4.4b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 (*.f64 y t) z) -9)) (*.f64 a (*.f64 27 b)))
15.0b
(+.f64 (fma.f64 x 2 (expm1.f64 (log1p.f64 (*.f64 (*.f64 y (*.f64 t z)) -9)))) (*.f64 a (*.f64 27 b)))
21.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 y 9) z) t)) (sqrt.f64 (*.f64 (*.f64 (*.f64 y 9) z) t)))) (*.f64 (*.f64 a 27) b))
3.1b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))) (*.f64 a (*.f64 27 b)))
Compiler

Compiled 2469 to 1360 computations (44.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 a (*.f64 27 b))
0.3b
(*.f64 (*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))
0.3b
(*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)))
8.1b
(*.f64 y (*.f64 t z))

series331.0ms (4.3%)

Counts
2 → 72
Calls

2 calls:

190.0ms
(*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)))
140.0ms
(*.f64 (*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))

rewrite27.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
52×add-exp-log_binary64
52×pow1_binary64
37×cbrt-unprod_binary64
37×prod-exp_binary64
37×pow-prod-down_binary64
Counts
2 → 68
Calls

2 calls:

13.0ms
(*.f64 (*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))
8.0ms
(*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)))

simplify108.0ms (1.4%)

Algorithm
egg-herbie
Rules
644×*-commutative_binary64
446×fma-def_binary64
358×sqr-pow_binary64
331×associate-*l*_binary64
315×unswap-sqr_binary64
Counts
140 → 81
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01072223
12321859
210921859
320181857
430951852
548721852
650641852

prune138.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1292131
Fresh145
Picked101
Done000
Total1316137
Error
0.0b
Counts
137 → 6
Alt Table
StatusErrorProgram
3.2b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 y (*.f64 9 z)) t)) (*.f64 (*.f64 a 27) b))
3.2b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y (*.f64 t z)) -9)) (*.f64 27 (*.f64 a b)))
4.4b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 (*.f64 y t) z) -9)) (*.f64 a (*.f64 27 b)))
3.2b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 (*.f64 (*.f64 y (*.f64 t z)) (cbrt.f64 -9)) (cbrt.f64 -9)) (cbrt.f64 -9))) (*.f64 a (*.f64 27 b)))
3.1b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y (*.f64 t (*.f64 (pow.f64 (cbrt.f64 -9) 2) z))) (cbrt.f64 -9))) (*.f64 a (*.f64 27 b)))
21.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 y 9) z) t)) (sqrt.f64 (*.f64 (*.f64 (*.f64 y 9) z) t)))) (*.f64 (*.f64 a 27) b))
Compiler

Compiled 3950 to 2539 computations (35.7% saved)

regimes1.6s (20.8%)

Accuracy

Total 0.6b remaining (95.6%)

Threshold costs 0.6b (95.6%)

Counts
59 → 2
Compiler

Compiled 24716 to 17924 computations (27.5% saved)

bsearch2.0ms (0%)

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02860
14460
26060
37660
48660
59160
69260
79160

end727.0ms (9.4%)

Compiler

Compiled 439 to 316 computations (28% saved)

Profiling

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