Details

Time bar (total: 6.1s)

analyze1.3s (20.5%)

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
12.5%87.3%0.2%8
12.5%87.3%0.2%9
18.7%81.1%0.2%10
23.4%76.4%0.2%11
31.6%68.2%0.2%12
34.5%64.9%0.6%13
40.3%59.2%0.6%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample1.7s (27.2%)

Results
1.2s8256×body128valid
424.0ms3144×body128invalid
Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify214.0ms (3.5%)

Algorithm
egg-herbie
Rules
871×distribute-rgt-in_binary64
685×div-sub_binary64
652×distribute-lft-in_binary64
409×distribute-neg-frac_binary64
395×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01222
12522
25822
310922
422320
543716
687614
7209814
8232014
9245114
10304214
11322614
12332714
13491314

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
4.8b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
3.7b
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
Compiler

Compiled 95 to 62 computations (34.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 y (/.f64 t y))
0.4b
(/.f64 -1/3 z)
3.5b
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

series30.0ms (0.5%)

Counts
3 → 54
Calls

3 calls:

23.0ms
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
5.0ms
(-.f64 y (/.f64 t y))
1.0ms
(/.f64 -1/3 z)

rewrite19.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt_binary64
55×*-un-lft-identity_binary64
53×add-cube-cbrt_binary64
46×times-frac_binary64
39×prod-diff_binary64
Counts
3 → 110
Calls

3 calls:

9.0ms
(-.f64 y (/.f64 t y))
2.0ms
(/.f64 -1/3 z)
0.0ms
(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

simplify129.0ms (2.1%)

Algorithm
egg-herbie
Rules
421×associate-/l*_binary64
411×associate-*l/_binary64
388×associate-*r/_binary64
368×times-frac_binary64
350×fma-def_binary64
Counts
164 → 137
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02442830
15661960
212561654
344141654
448411654

prune125.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1307137
Fresh011
Picked101
Done000
Total1318139
Error
0.0b
Counts
139 → 8
Alt Table
StatusErrorProgram
4.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x))) (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
3.7b
(fma.f64 (/.f64 -1/3 z) (+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y))) x)
4.8b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
4.8b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
33.4b
(fma.f64 (/.f64 -1/3 z) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (neg.f64 (/.f64 t y))) x)
28.7b
(/.f64 (-.f64 (*.f64 1/3 (/.f64 t y)) (*.f64 1/3 y)) z)
4.2b
(fma.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (-.f64 y (/.f64 t y)) x)
3.8b
(fma.f64 (/.f64 1 (/.f64 z -1/3)) (-.f64 y (/.f64 t y)) x)
Compiler

Compiled 3595 to 1293 computations (64% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y)))
0.2b
(*.f64 (neg.f64 t) (/.f64 1 y))
0.4b
(/.f64 -1/3 z)
3.5b
(fma.f64 (/.f64 -1/3 z) (+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y))) x)

series37.0ms (0.6%)

Counts
3 → 96
Calls

3 calls:

23.0ms
(fma.f64 (/.f64 -1/3 z) (+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y))) x)
7.0ms
(+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y)))
6.0ms
(*.f64 (neg.f64 t) (/.f64 1 y))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
15×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
13×associate-*r*_binary64
12×add-exp-log_binary64
Counts
3 → 73
Calls

3 calls:

7.0ms
(*.f64 (neg.f64 t) (/.f64 1 y))
3.0ms
(+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y)))
0.0ms
(fma.f64 (/.f64 -1/3 z) (+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y))) x)

simplify114.0ms (1.8%)

Algorithm
egg-herbie
Rules
590×fma-neg_binary64
542×div-sub_binary64
352×unsub-neg_binary64
296×fma-def_binary64
255×distribute-rgt-neg-out_binary64
Counts
169 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01221874
13211655
29121575
326221575
438321575
549831575
650021575

prune158.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1620162
Fresh077
Picked011
Done000
Total1628170
Error
0.0b
Counts
170 → 8
Alt Table
StatusErrorProgram
4.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x))) (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
3.7b
(fma.f64 (/.f64 -1/3 z) (+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y))) x)
4.8b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
4.8b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
33.4b
(fma.f64 (/.f64 -1/3 z) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (neg.f64 (/.f64 t y))) x)
28.7b
(/.f64 (-.f64 (*.f64 1/3 (/.f64 t y)) (*.f64 1/3 y)) z)
4.2b
(fma.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (-.f64 y (/.f64 t y)) x)
3.8b
(fma.f64 (/.f64 1 (/.f64 z -1/3)) (-.f64 y (/.f64 t y)) x)
Compiler

Compiled 3157 to 1703 computations (46.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 y (/.f64 t y))
0.3b
(/.f64 1 (/.f64 z -1/3))
0.3b
(/.f64 z -1/3)
3.5b
(fma.f64 (/.f64 1 (/.f64 z -1/3)) (-.f64 y (/.f64 t y)) x)

series26.0ms (0.4%)

Counts
3 → 72
Calls

3 calls:

23.0ms
(fma.f64 (/.f64 1 (/.f64 z -1/3)) (-.f64 y (/.f64 t y)) x)
2.0ms
(/.f64 1 (/.f64 z -1/3))
2.0ms
(/.f64 z -1/3)

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
84×times-frac_binary64
53×*-un-lft-identity_binary64
53×add-sqr-sqrt_binary64
53×add-cube-cbrt_binary64
16×associate-/r*_binary64
Counts
3 → 117
Calls

3 calls:

4.0ms
(/.f64 1 (/.f64 z -1/3))
2.0ms
(/.f64 z -1/3)
0.0ms
(fma.f64 (/.f64 1 (/.f64 z -1/3)) (-.f64 y (/.f64 t y)) x)

simplify152.0ms (2.5%)

Algorithm
egg-herbie
Rules
401×fma-neg_binary64
311×associate-*l*_binary64
295×distribute-lft-neg-out_binary64
286×times-frac_binary64
282×distribute-rgt-neg-out_binary64
Counts
189 → 183
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01322426
12372044
25092009
311131943
428091943
548501943
649131943

prune222.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2620262
Fresh066
Picked011
Done011
Total2628270
Error
0.0b
Counts
270 → 8
Alt Table
StatusErrorProgram
4.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x))) (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
3.7b
(fma.f64 (/.f64 -1/3 z) (+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y))) x)
4.8b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
4.8b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
33.4b
(fma.f64 (/.f64 -1/3 z) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (neg.f64 (/.f64 t y))) x)
28.7b
(/.f64 (-.f64 (*.f64 1/3 (/.f64 t y)) (*.f64 1/3 y)) z)
4.2b
(fma.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (-.f64 y (/.f64 t y)) x)
3.8b
(fma.f64 (/.f64 1 (/.f64 z -1/3)) (-.f64 y (/.f64 t y)) x)
Compiler

Compiled 6210 to 2801 computations (54.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(cbrt.f64 z)
0.5b
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0b
(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))
3.5b
(fma.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (-.f64 y (/.f64 t y)) x)

series237.0ms (3.9%)

Counts
4 → 72
Calls

4 calls:

164.0ms
(fma.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (-.f64 y (/.f64 t y)) x)
43.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms
(cbrt.f64 z)
0.0ms
(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64
35×cbrt-prod_binary64
21×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
18×pow1_binary64
Counts
4 → 107
Calls

4 calls:

5.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
5.0ms
(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))
1.0ms
(cbrt.f64 z)
0.0ms
(fma.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (-.f64 y (/.f64 t y)) x)

simplify105.0ms (1.7%)

Algorithm
egg-herbie
Rules
757×fma-def_binary64
492×associate-/r*_binary64
366×unswap-sqr_binary64
318×distribute-rgt-in_binary64
290×associate-/l*_binary64
Counts
179 → 156
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01252440
12381880
27911739
325461651
446481651
550681651

prune164.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1920192
Fresh055
Picked011
Done022
Total1928200
Error
0.0b
Counts
200 → 8
Alt Table
StatusErrorProgram
4.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x))) (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)))
3.7b
(fma.f64 (/.f64 -1/3 z) (+.f64 y (*.f64 (neg.f64 t) (/.f64 1 y))) x)
4.8b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
4.8b
(-.f64 (+.f64 (*.f64 1/3 (/.f64 t (*.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
33.4b
(fma.f64 (/.f64 -1/3 z) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (neg.f64 (/.f64 t y))) x)
28.7b
(/.f64 (-.f64 (*.f64 1/3 (/.f64 t y)) (*.f64 1/3 y)) z)
4.2b
(fma.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (-.f64 y (/.f64 t y)) x)
3.8b
(fma.f64 (/.f64 1 (/.f64 z -1/3)) (-.f64 y (/.f64 t y)) x)
Compiler

Compiled 5378 to 2728 computations (49.3% saved)

regimes1.2s (19.6%)

Accuracy

Total 0.5b remaining (94.2%)

Threshold costs 0.5b (94.2%)

Counts
101 → 3
Compiler

Compiled 12214 to 7761 computations (36.5% saved)

bsearch54.0ms (0.9%)

Steps
ItersRangePoint
12
5.76938053489549e+48
1.4643971374639755e+88
1.4877270337603418e+50
2
-727469.8127402246
-151933.97422059634
-479840.16688788246
Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
03575
15873
27773
39473
410373
510673
610373

end129.0ms (2.1%)

Compiler

Compiled 279 to 180 computations (35.5% saved)

Profiling

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