Details

Time bar (total: 8.1s)

analyze331.0ms (4.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
25%74.9%0.1%6
25%74.9%0.1%7
43.7%56.2%0.1%8
62.4%37.4%0.1%9
65.5%34.3%0.1%10
71.8%27.7%0.5%11
79.2%19.7%1.1%12
80.2%18.7%1.1%13
82.8%15%2.2%14
Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.0s (12.4%)

Symmetry

(sort x y)

Results
893.0ms8256×body128valid
65.0ms524×body128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify11.0ms (0.1%)

Algorithm
egg-herbie
Rules
44×fma-def_binary64
37×associate-*l*_binary64
36×associate-*r*_binary64
20×*-commutative_binary64
19×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01016
12414
24114
39414
412214
514914
615314
714614

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
7.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
7.3b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
Compiler

Compiled 50 to 34 computations (32% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
3.3b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
4.5b
(*.f64 y (fma.f64 z z 1))

series92.0ms (1.1%)

Counts
2 → 60
Calls

2 calls:

82.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
10.0ms
(*.f64 y (fma.f64 z z 1))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
31×times-frac_binary64
26×add-exp-log_binary64
20×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
Counts
2 → 74
Calls

2 calls:

5.0ms
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
2.0ms
(*.f64 y (fma.f64 z z 1))

simplify119.0ms (1.5%)

Algorithm
egg-herbie
Rules
469×associate-/r*_binary64
451×associate-*l*_binary64
414×associate-/l*_binary64
336×associate-/l/_binary64
296×associate-*r*_binary64
Counts
134 → 122
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01542203
13301967
211071965
339561963
444821963
548061963
649381963

prune124.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1139122
Fresh000
Picked011
Done000
Total11310123
Error
2.2b
Counts
123 → 10
Alt Table
StatusErrorProgram
7.1b
(*.f64 (/.f64 1 y) (/.f64 1 (*.f64 (fma.f64 z z 1) x)))
20.9b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
7.3b
(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
27.2b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1))) (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
8.0b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
7.1b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
24.3b
(*.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
7.1b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
7.3b
(/.f64 (/.f64 1 x) (*.f64 (*.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
7.0b
(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
Compiler

Compiled 2437 to 1522 computations (37.5% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (/.f64 1 x) y)
6.8b
(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))

series86.0ms (1.1%)

Counts
2 → 60
Calls

2 calls:

79.0ms
(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
7.0ms
(/.f64 (/.f64 1 x) y)

rewrite47.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
468×times-frac_binary64
228×*-un-lft-identity_binary64
228×add-sqr-sqrt_binary64
228×add-cube-cbrt_binary64
56×associate-/l*_binary64
Counts
2 → 270
Calls

2 calls:

9.0ms
(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
5.0ms
(/.f64 (/.f64 1 x) y)

simplify270.0ms (3.3%)

Algorithm
egg-herbie
Rules
603×fma-def_binary64
536×times-frac_binary64
385×associate-*l*_binary64
378×associate-/l/_binary64
368×associate-/l*_binary64
Counts
330 → 383
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02868112
16477481
216747473
339647471
446287471
549967471
649527471

prune430.0ms (5.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3758383
Fresh628
Picked101
Done101
Total38310393
Error
0.0b
Counts
393 → 10
Alt Table
StatusErrorProgram
7.3b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z 1)) (cbrt.f64 (fma.f64 z z 1)))) (/.f64 (/.f64 1 (*.f64 y x)) (cbrt.f64 (fma.f64 z z 1))))
1.9b
(*.f64 (/.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 y)) (hypot.f64 1 z)))
7.1b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
20.1b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 y)) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 y)) (hypot.f64 1 z)))
18.7b
(*.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (sqrt.f64 y)) (hypot.f64 1 z)) (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (sqrt.f64 y)) (hypot.f64 1 z)))
1.6b
(*.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (/.f64 (/.f64 1 (hypot.f64 1 z)) y))
8.0b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
2.2b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) y) (hypot.f64 1 z)))
7.7b
(/.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 1 x) y)) (cbrt.f64 (/.f64 (/.f64 1 x) y))) (/.f64 (fma.f64 z z 1) (cbrt.f64 (/.f64 (/.f64 1 x) y))))
4.3b
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)))
Compiler

Compiled 9181 to 5431 computations (40.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 1 z))
0.1b
(/.f64 (/.f64 1 (hypot.f64 1 z)) y)
0.1b
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
1.5b
(*.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (/.f64 (/.f64 1 (hypot.f64 1 z)) y))

series174.0ms (2.1%)

Counts
4 → 96
Calls

4 calls:

93.0ms
(*.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (/.f64 (/.f64 1 (hypot.f64 1 z)) y))
39.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
38.0ms
(/.f64 (/.f64 1 (hypot.f64 1 z)) y)
3.0ms
(/.f64 1 (hypot.f64 1 z))

rewrite77.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
331×times-frac_binary64
230×add-sqr-sqrt_binary64
174×*-un-lft-identity_binary64
166×add-cube-cbrt_binary64
126×add-exp-log_binary64
Counts
4 → 331
Calls

4 calls:

29.0ms
(*.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (/.f64 (/.f64 1 (hypot.f64 1 z)) y))
4.0ms
(/.f64 (/.f64 1 (hypot.f64 1 z)) y)
4.0ms
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
2.0ms
(/.f64 1 (hypot.f64 1 z))

simplify287.0ms (3.5%)

Algorithm
egg-herbie
Rules
566×fma-def_binary64
473×associate-/r/_binary64
364×associate-*l/_binary64
357×associate-*r/_binary64
277×fma-neg_binary64
Counts
427 → 545
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03939644
110708755
232298619
345118593
449308593
549678593

prune674.0ms (8.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New5405545
Fresh369
Picked101
Done000
Total54411555
Error
0b
Counts
555 → 11
Alt Table
StatusErrorProgram
8.0b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
2.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) 1) (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z))))
20.1b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 y)) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 y)) (hypot.f64 1 z)))
25.1b
(cbrt.f64 (pow.f64 (/.f64 (/.f64 1 x) (*.f64 (hypot.f64 1 z) (*.f64 y (hypot.f64 1 z)))) 3))
7.1b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
1.9b
(*.f64 (/.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 y)) (hypot.f64 1 z)))
2.3b
(*.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 1 (hypot.f64 1 z)) (cbrt.f64 y))))
2.2b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) y) (hypot.f64 1 z)))
1.7b
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
4.3b
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)))
1.8b
(*.f64 (/.f64 1 (*.f64 x (hypot.f64 1 z))) (/.f64 (/.f64 1 (hypot.f64 1 z)) y))
Compiler

Compiled 14514 to 10562 computations (27.2% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 1 z)
0.0b
(*.f64 y (hypot.f64 1 z))
0.1b
(/.f64 (/.f64 1 x) (hypot.f64 1 z))
1.7b
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))

series115.0ms (1.4%)

Counts
3 → 72
Calls

3 calls:

97.0ms
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
16.0ms
(*.f64 y (hypot.f64 1 z))
2.0ms
(hypot.f64 1 z)

rewrite27.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
175×times-frac_binary64
77×add-sqr-sqrt_binary64
75×*-un-lft-identity_binary64
75×add-cube-cbrt_binary64
43×associate-/l*_binary64
Counts
3 → 146
Calls

3 calls:

9.0ms
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
2.0ms
(*.f64 y (hypot.f64 1 z))
2.0ms
(hypot.f64 1 z)

simplify131.0ms (1.6%)

Algorithm
egg-herbie
Rules
805×associate-/l*_binary64
575×fma-def_binary64
472×associate-*l/_binary64
439×associate-/r/_binary64
229×associate-/r*_binary64
Counts
218 → 267
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02944922
17224369
222424049
346694045
449514045

prune490.0ms (6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New4160416
Fresh01010
Picked011
Done000
Total41611427
Error
0b
Counts
427 → 11
Alt Table
StatusErrorProgram
8.0b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
2.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) 1) (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z))))
20.1b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 y)) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 y)) (hypot.f64 1 z)))
25.1b
(cbrt.f64 (pow.f64 (/.f64 (/.f64 1 x) (*.f64 (hypot.f64 1 z) (*.f64 y (hypot.f64 1 z)))) 3))
7.1b
(/.f64 1 (*.f64 y (*.f64 (+.f64 1 (pow.f64 z 2)) x)))
1.9b
(*.f64 (/.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 y)) (hypot.f64 1 z)))
2.3b
(*.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 1 (hypot.f64 1 z)) (cbrt.f64 y))))
2.2b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) y) (hypot.f64 1 z)))
1.7b
(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
4.3b
(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)))
1.8b
(*.f64 (/.f64 1 (*.f64 x (hypot.f64 1 z))) (/.f64 (/.f64 1 (hypot.f64 1 z)) y))
Compiler

Compiled 9621 to 6655 computations (30.8% saved)

regimes3.3s (40.3%)

Accuracy

Total 1.3b remaining (98.2%)

Threshold costs 0b (0%)

Counts
344 → 1
Compiler

Compiled 58278 to 42852 computations (26.5% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01435
11835
21735

end307.0ms (3.8%)

Compiler

Compiled 344 to 257 computations (25.3% saved)

Profiling

Loading profile data...