Details

Time bar (total: 6.2s)

analyze1.5s (24.5%)

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
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
9.4%90.4%0.2%11
9.4%90.4%0.2%12
10.1%89.6%0.2%13
20.8%78.9%0.2%14
Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.6s (25.3%)

Symmetry

(sort x y)

(sort z t)

Results
1.1s8256×body128valid
417.0ms3249×body128invalid
Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify206.0ms (3.3%)

Algorithm
egg-herbie
Rules
2966×fma-def_binary64
757×fma-neg_binary64
541×cancel-sign-sub-inv_binary64
473×associate-/l/_binary64
472×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01419
13117
210317
331817
479417
5152617
6205417
7228117
8297517
9354017
10395417
11415817
12409717
13410817
14411817
15446217
16453117
17453617
18453617
19647417

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Compiler

Compiled 100 to 69 computations (31% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
7.5b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series53.0ms (0.9%)

Counts
2 → 108
Calls

2 calls:

41.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
12.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

5.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
0.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

simplify109.0ms (1.8%)

Algorithm
egg-herbie
Rules
937×fma-def_binary64
487×associate-*l*_binary64
418×associate-*r*_binary64
225×associate-*r/_binary64
211×associate-*l/_binary64
Counts
152 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082547
12482243
28122243
332062242
449372242
550192242

prune84.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New761288
Fresh011
Picked101
Done000
Total771390
Error
7.6b
Counts
90 → 13
Alt Table
StatusErrorProgram
8.8b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.4b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
8.0b
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (/.f64 1/2 a))
8.8b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
33.7b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
33.7b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
7.9b
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
7.9b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
31.6b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
36.0b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
33.2b
(*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
31.2b
(*.f64 (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
Compiler

Compiled 2206 to 1216 computations (44.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 1/2 (*.f64 y x))
0.3b
(fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x)))
7.5b
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)

series54.0ms (0.9%)

Counts
3 → 108
Calls

3 calls:

33.0ms
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
16.0ms
(fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x)))
4.0ms
(*.f64 1/2 (*.f64 y x))

rewrite10.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
Counts
3 → 59
Calls

3 calls:

4.0ms
(*.f64 1/2 (*.f64 y x))
2.0ms
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
0.0ms
(fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x)))

simplify79.0ms (1.3%)

Algorithm
egg-herbie
Rules
455×associate-*l*_binary64
428×distribute-rgt-in_binary64
425×distribute-lft-in_binary64
423×fma-def_binary64
320×associate-*r*_binary64
Counts
167 → 77
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01142934
12342627
26112624
318562624
449452624

prune77.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New76177
Fresh11112
Picked011
Done000
Total771390
Error
7.6b
Counts
90 → 13
Alt Table
StatusErrorProgram
8.8b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.4b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
8.0b
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (/.f64 1/2 a))
8.8b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
33.7b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
31.6b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
35.9b
(/.f64 (/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) (sqrt.f64 a)) (sqrt.f64 a))
33.7b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
7.9b
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
7.9b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
33.2b
(*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
31.2b
(*.f64 (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
Compiler

Compiled 1976 to 1068 computations (46% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
0.2b
(*.f64 9/2 (/.f64 (*.f64 t z) a))
5.1b
(/.f64 (*.f64 y x) a)
7.2b
(/.f64 (*.f64 t z) a)

series78.0ms (1.3%)

Counts
4 → 24
Calls

4 calls:

38.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
15.0ms
(*.f64 9/2 (/.f64 (*.f64 t z) a))
13.0ms
(/.f64 (*.f64 y x) a)
12.0ms
(/.f64 (*.f64 t z) a)

rewrite23.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
4 → 93
Calls

4 calls:

6.0ms
(/.f64 (*.f64 t z) a)
5.0ms
(*.f64 9/2 (/.f64 (*.f64 t z) a))
5.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
3.0ms
(/.f64 (*.f64 y x) a)

simplify74.0ms (1.2%)

Algorithm
egg-herbie
Rules
676×times-frac_binary64
581×fma-def_binary64
359×*-commutative_binary64
335×associate-/l/_binary64
254×associate-/r*_binary64
Counts
117 → 134
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01681744
14231541
215231530
341621530
449411530

prune130.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1286134
Fresh8311
Picked101
Done011
Total13710147
Error
0.7b
Counts
147 → 10
Alt Table
StatusErrorProgram
8.4b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
8.0b
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (/.f64 1/2 a))
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
35.5b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 (/.f64 t (sqrt.f64 a)) (/.f64 z (sqrt.f64 a)))))
8.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 t 9/2) (/.f64 z a)))
7.9b
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
8.7b
(-.f64 (*.f64 1/2 (/.f64 y (/.f64 a x))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(-.f64 (*.f64 1/2 (*.f64 y (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.1b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.3b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
Compiler

Compiled 3195 to 1386 computations (56.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y x (*.f64 (*.f64 t z) -9))
0.2b
(*.f64 (*.f64 t z) -9)
7.5b
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (/.f64 1/2 a))

series56.0ms (0.9%)

Counts
3 → 132
Calls

3 calls:

39.0ms
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (/.f64 1/2 a))
12.0ms
(fma.f64 y x (*.f64 (*.f64 t z) -9))
4.0ms
(*.f64 (*.f64 t z) -9)

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
16×associate-*r*_binary64
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
12×*-un-lft-identity_binary64
Counts
3 → 64
Calls

3 calls:

5.0ms
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (/.f64 1/2 a))
4.0ms
(*.f64 (*.f64 t z) -9)
0.0ms
(fma.f64 y x (*.f64 (*.f64 t z) -9))

simplify115.0ms (1.9%)

Algorithm
egg-herbie
Rules
692×fma-def_binary64
483×div-sub_binary64
323×*-commutative_binary64
239×associate-*l/_binary64
238×associate-*r/_binary64
Counts
196 → 106
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01422836
13272584
211712583
330632583
445922583
555592583

prune95.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1051106
Fresh178
Picked011
Done011
Total10610116
Error
0.7b
Counts
116 → 10
Alt Table
StatusErrorProgram
8.4b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
8.0b
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (/.f64 1/2 a))
8.1b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.2b
(*.f64 1/2 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) a))
35.5b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 (/.f64 t (sqrt.f64 a)) (/.f64 z (sqrt.f64 a)))))
8.4b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 t 9/2) (/.f64 z a)))
7.9b
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
8.7b
(-.f64 (*.f64 1/2 (/.f64 y (/.f64 a x))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(-.f64 (*.f64 1/2 (*.f64 y (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.3b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
Compiler

Compiled 2200 to 1251 computations (43.1% saved)

regimes1.3s (21.5%)

Accuracy

Total 3.9b remaining (89.5%)

Threshold costs 0b (0%)

Counts
52 → 3
Compiler

Compiled 14074 to 9631 computations (31.6% saved)

bsearch2.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03396
15096
26496
38096
410096
511296
611996
712196
812096

end453.0ms (7.3%)

Compiler

Compiled 617 to 363 computations (41.2% saved)

Profiling

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