Details

Time bar (total: 21.8s)

analyze1.3s (6.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.6%0.4%0
0%99.6%0.4%1
0%99.6%0.4%2
0%99.6%0.4%3
0%99.6%0.4%4
0%99.6%0.4%5
0%99.6%0.4%6
0%99.6%0.4%7
0%74.7%25.3%8
0%74.7%25.3%9
0%65.4%34.6%10
0%51.4%48.6%11
0%51.4%48.6%12
0%51.4%48.6%13
0%51.4%48.6%14
Compiler

Compiled 30 to 21 computations (30% saved)

sample4.0s (18.2%)

Symmetry

(sort z t a)

Results
2.2s11310×body128invalid
1.7s8254×body128valid
1.0msbody512valid
Compiler

Compiled 89 to 62 computations (30.3% saved)

simplify60.0ms (0.3%)

Algorithm
egg-herbie
Rules
1877×associate-+l+_binary64
859×associate-+r+_binary64
762×+-commutative_binary64
750×fma-def_binary64
*-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02130
14126
211326
349326
4158826
5215326
6225926
7225926
8225926
9225926
10402926
11428126
12428126
13450626
14450626
15470526
Stop Event
saturated
Counts
1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.1b
(+.f64 z (+.f64 t (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))
Compiler

Compiled 99 to 61 computations (38.4% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))
0.1b
(fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))
0.1b
(fma.f64 (+.f64 b -1/2) (log.f64 c) a)

series737.0ms (3.4%)

Counts
3 → 168
Calls

3 calls:

469.0ms
(fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))
157.0ms
(fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))
109.0ms
(fma.f64 (+.f64 b -1/2) (log.f64 c) a)

rewrite51.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
264×prod-diff_binary64
261×expm1-udef_binary64
261×log1p-udef_binary64
186×fma-def_binary64
146×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01444
128344
2342444
Stop Event
node limit
Counts
3 → 71
Calls

3 calls:

49.0ms
(fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))
49.0ms
(fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))
49.0ms
(fma.f64 (+.f64 b -1/2) (log.f64 c) a)

simplify86.0ms (0.4%)

Algorithm
egg-herbie
Rules
723×sub-neg_binary64
398×fma-neg_binary64
327×associate--r+_binary64
307×associate--l+_binary64
303×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0913345
12932748
27562556
324042458
443142458
Stop Event
node limit
Counts
239 → 107

prune104.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1043107
Fresh000
Picked011
Done000
Total1044108
Error
0.1b
Counts
108 → 4
Alt Table
StatusErrorProgram
51.8b
(+.f64 z (+.f64 t (cbrt.f64 (pow.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))) 3))))
21.0b
(+.f64 z (+.f64 t (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))
0.9b
(+.f64 z (+.f64 t (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 3)))
0.1b
(+.f64 z (+.f64 t (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))
Compiler

Compiled 2668 to 1247 computations (53.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))
0.1b
(fma.f64 (+.f64 b -1/2) (log.f64 c) a)
0.5b
(cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))
0.7b
(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 3)

series849.0ms (3.9%)

Counts
2 → 64
Calls

2 calls:

537.0ms
(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 3)
312.0ms
(cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))

rewrite52.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
290×expm1-udef_binary64
290×log1p-udef_binary64
264×prod-diff_binary64
163×add-sqr-sqrt_binary64
154×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01742
134342
2390242
Stop Event
node limit
Counts
2 → 50
Calls

2 calls:

51.0ms
(cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))
51.0ms
(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 3)

simplify96.0ms (0.4%)

Algorithm
egg-herbie
Rules
544×associate-*r*_binary64
382×fma-def_binary64
361×associate-*l*_binary64
204×associate-+r+_binary64
185×sqr-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04559600
116268535
Stop Event
node limit
Counts
114 → 132

prune253.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2062208
Fresh022
Picked011
Done011
Total2066212
Error
0.0b
Counts
212 → 6
Alt Table
StatusErrorProgram
21.0b
(+.f64 z (+.f64 t (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))
1.5b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) 3) (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))))
0.9b
(+.f64 z (+.f64 t (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 3)))
1.1b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))))
51.8b
(+.f64 z (+.f64 t (cbrt.f64 (pow.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))) 3))))
0.1b
(+.f64 z (+.f64 t (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))
Compiler

Compiled 13108 to 6045 computations (53.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2)
0.5b
(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)
0.5b
(cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))
0.5b
(cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))

series5.2s (23.9%)

Counts
3 → 176
Calls

3 calls:

2.8s
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2)
2.0s
(cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))
376.0ms
(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)

rewrite62.0ms (0.3%)

Algorithm
batch-egg-rewrite
Rules
319×log1p-udef_binary64
264×prod-diff_binary64
183×add-sqr-sqrt_binary64
174×log1p-expm1-u_binary64
174×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01976
138276
2436876
Stop Event
node limit
Counts
3 → 62
Calls

3 calls:

60.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2)
60.0ms
(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)
60.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))

simplify421.0ms (1.9%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05218446676653545
Stop Event
node limit
Counts
238 → 208

prune1.6s (7.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New4812483
Fresh033
Picked011
Done022
Total4818489
Error
0.0b
Counts
489 → 8
Alt Table
StatusErrorProgram
51.8b
(+.f64 z (+.f64 t (cbrt.f64 (pow.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))) 3))))
1.3b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) (*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))) 2) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))))) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))))
21.0b
(+.f64 z (+.f64 t (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))
1.5b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) 3) (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))))
0.9b
(+.f64 z (+.f64 t (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 3)))
1.1b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))))
42.7b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) (cbrt.f64 (pow.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))) 2))))))
0.1b
(+.f64 z (+.f64 t (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))
Compiler

Compiled 94295 to 56076 computations (40.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)
0.5b
(cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))
0.5b
(cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))
0.6b
(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))) 2)

series2.7s (12.3%)

Counts
1 → 72
Calls

1 calls:

2.7s
(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))) 2)

rewrite55.0ms (0.3%)

Algorithm
batch-egg-rewrite
Rules
323×log1p-udef_binary64
264×prod-diff_binary64
184×add-sqr-sqrt_binary64
172×add-cbrt-cube_binary64
171×add-cube-cbrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01929
137829
2434829
Stop Event
node limit
Counts
1 → 18
Calls

1 calls:

54.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))) 2)

simplify212.0ms (1%)

Algorithm
egg-herbie
Rules
596×fma-def_binary64
425×associate-/l*_binary64
371×times-frac_binary64
74×sqr-pow_binary64
56×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0262234143
Stop Event
node limit
Counts
90 → 142

prune2.8s (13%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New6931694
Fresh044
Picked011
Done033
Total6939702
Error
0.0b
Counts
702 → 9
Alt Table
StatusErrorProgram
51.8b
(+.f64 z (+.f64 t (cbrt.f64 (pow.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))) 3))))
1.3b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) (*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))) 2) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))))) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))))
21.0b
(+.f64 z (+.f64 t (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))
1.5b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) 3) (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))))
0.9b
(+.f64 z (+.f64 t (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 3)))
1.1b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))))
42.7b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) (cbrt.f64 (pow.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))) 2))))))
1.5b
(+.f64 z (+.f64 t (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))) 2) (*.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))) 2) (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a))))))))) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))) 2)))))
0.1b
(+.f64 z (+.f64 t (fma.f64 x (log.f64 y) (fma.f64 y i (fma.f64 (+.f64 b -1/2) (log.f64 c) a)))))
Compiler

Compiled 160807 to 93884 computations (41.6% saved)

regimes748.0ms (3.4%)

Accuracy

Total 0.0b remaining (48.1%)

Threshold costs 0.0b (48.1%)

Counts
47 → 1
Compiler

Compiled 19471 to 12829 computations (34.1% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01826
12126
Stop Event
saturated

end289.0ms (1.3%)

Remove

(sort z t a)

Compiler

Compiled 588 to 363 computations (38.3% saved)

Profiling

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