Details

Time bar (total: 6.2s)

analyze533.0ms (8.6%)

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
0%99.9%0.1%6
25%74.9%0.1%7
31.2%68.6%0.1%8
35.9%64%0.1%9
47.6%49.9%2.5%10
49.1%46.8%4%11
51.1%44.1%4.8%12
60.2%29.9%9.9%13
60.6%27.9%11.6%14
Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.2s (19.2%)

Symmetry

(sort x y)

Results
847.0ms8256×body128valid
161.0ms1569×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify91.0ms (1.5%)

Algorithm
egg-herbie
Rules
826×associate-*r/_binary64
769×associate-/l/_binary64
660×associate-*l/_binary64
522×associate-/l*_binary64
421×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01016
13016
27814
319514
431414
538314
642614
763114
8100914
9220414
10286814
11296714
12307914
13319314
14305814
15371214
16498814
17482414

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
4.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
13.3b
(/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))
Compiler

Compiled 78 to 45 computations (42.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 y (fma.f64 z z z)) z)
5.7b
(/.f64 y (fma.f64 z z z))
6.0b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series227.0ms (3.6%)

Counts
3 → 84
Calls

3 calls:

97.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
95.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
34.0ms
(/.f64 y (fma.f64 z z z))

rewrite34.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
153×times-frac_binary64
98×add-sqr-sqrt_binary64
89×*-un-lft-identity_binary64
89×add-cube-cbrt_binary64
43×associate-*r*_binary64
Counts
3 → 168
Calls

3 calls:

11.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
4.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
2.0ms
(/.f64 y (fma.f64 z z z))

simplify161.0ms (2.6%)

Algorithm
egg-herbie
Rules
805×fma-def_binary64
353×fma-neg_binary64
351×*-commutative_binary64
341×associate-/r/_binary64
275×sub-neg_binary64
Counts
252 → 296
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02874846
16874599
223044515
336074509
448174509
549634509

prune289.0ms (4.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2888296
Fresh101
Picked011
Done000
Total2899298
Error
2.0b
Counts
298 → 9
Alt Table
StatusErrorProgram
13.7b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
5.7b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
7.5b
(*.f64 (*.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
13.8b
(*.f64 (*.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) z))
30.9b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
13.6b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
22.8b
(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
34.4b
(*.f64 x (*.f64 (/.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z)) (/.f64 (/.f64 y (sqrt.f64 z)) (hypot.f64 z (sqrt.f64 z)))))
7.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
Compiler

Compiled 6239 to 1430 computations (77.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
1.5b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
5.1b
(*.f64 x (/.f64 y (fma.f64 z z z)))
5.7b
(/.f64 y (fma.f64 z z z))

series172.0ms (2.8%)

Counts
2 → 72
Calls

2 calls:

100.0ms
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
72.0ms
(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
13×associate-*r*_binary64
13×times-frac_binary64
Counts
2 → 60
Calls

2 calls:

4.0ms
(*.f64 x (/.f64 y (fma.f64 z z z)))
4.0ms
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

simplify79.0ms (1.3%)

Algorithm
egg-herbie
Rules
604×fma-neg_binary64
483×associate-*l*_binary64
433×associate-/r*_binary64
417×associate-*r*_binary64
378×associate-/r/_binary64
Counts
132 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01532289
13972096
215391990
344391990
449681990

prune142.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1714175
Fresh347
Picked011
Done011
Total17410184
Error
1.3b
Counts
184 → 10
Alt Table
StatusErrorProgram
8.5b
(/.f64 (*.f64 (*.f64 x y) (/.f64 1 (fma.f64 z z z))) z)
22.8b
(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
6.9b
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
30.9b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
13.6b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
34.4b
(*.f64 x (*.f64 (/.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z)) (/.f64 (/.f64 y (sqrt.f64 z)) (hypot.f64 z (sqrt.f64 z)))))
7.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
40.6b
(/.f64 (*.f64 x (*.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))))) z)
32.7b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
5.7b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
Compiler

Compiled 3272 to 931 computations (71.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(/.f64 z (/.f64 y (fma.f64 z z z)))
5.7b
(/.f64 y (fma.f64 z z z))
5.7b
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))

series108.0ms (1.7%)

Counts
2 → 60
Calls

2 calls:

93.0ms
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
15.0ms
(/.f64 z (/.f64 y (fma.f64 z z z)))

rewrite51.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
471×times-frac_binary64
229×*-un-lft-identity_binary64
229×add-sqr-sqrt_binary64
229×add-cube-cbrt_binary64
57×associate-/r*_binary64
Counts
2 → 270
Calls

2 calls:

8.0ms
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
6.0ms
(/.f64 z (/.f64 y (fma.f64 z z z)))

simplify236.0ms (3.8%)

Algorithm
egg-herbie
Rules
579×associate-/r/_binary64
431×associate-/l/_binary64
401×fma-def_binary64
378×associate-*l/_binary64
332×associate-*r/_binary64
Counts
330 → 488
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04879126
110858731
241368600
346398600
449898600

prune409.0ms (6.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New5363539
Fresh347
Picked101
Done022
Total5409549
Error
1.3b
Counts
549 → 9
Alt Table
StatusErrorProgram
32.7b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
5.8b
(/.f64 (/.f64 x (/.f64 z y)) (fma.f64 z z z))
34.6b
(/.f64 x (*.f64 (sqrt.f64 z) (/.f64 (sqrt.f64 z) (/.f64 y (fma.f64 z z z)))))
5.0b
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) z) (*.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 x)))
13.6b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
8.5b
(/.f64 (*.f64 (*.f64 x y) (/.f64 1 (fma.f64 z z z))) z)
7.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
40.6b
(/.f64 (*.f64 x (*.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))))) z)
5.7b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
Compiler

Compiled 12562 to 2322 computations (81.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 x)
0.8b
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) z) (*.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 x)))
2.2b
(*.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 x))
5.7b
(/.f64 y (fma.f64 z z z))

series414.0ms (6.6%)

Counts
3 → 84
Calls

3 calls:

270.0ms
(*.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 x))
112.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) z) (*.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 x)))
32.0ms
(cbrt.f64 x)

rewrite26.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
44×add-exp-log_binary64
30×add-cbrt-cube_binary64
25×add-sqr-sqrt_binary64
20×associate-*l*_binary64
20×cbrt-unprod_binary64
Counts
3 → 93
Calls

3 calls:

9.0ms
(*.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 x))
8.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) z) (*.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 x)))
1.0ms
(cbrt.f64 x)

simplify109.0ms (1.7%)

Algorithm
egg-herbie
Rules
584×associate-/r*_binary64
489×fma-neg_binary64
359×fma-def_binary64
299×cancel-sign-sub-inv_binary64
213×associate-/r/_binary64
Counts
177 → 167
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02163766
15522703
219532641
348542641
451322641

prune177.0ms (2.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2531254
Fresh156
Picked011
Done022
Total2549263
Error
1.3b
Counts
263 → 9
Alt Table
StatusErrorProgram
34.6b
(/.f64 x (*.f64 (sqrt.f64 z) (/.f64 (sqrt.f64 z) (/.f64 y (fma.f64 z z z)))))
13.3b
(pow.f64 (/.f64 (*.f64 y x) (*.f64 z (fma.f64 z z z))) 1)
32.7b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
5.8b
(/.f64 (/.f64 x (/.f64 z y)) (fma.f64 z z z))
5.0b
(*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) z) (*.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 x)))
8.5b
(/.f64 (*.f64 (*.f64 x y) (/.f64 1 (fma.f64 z z z))) z)
7.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
40.6b
(/.f64 (*.f64 x (*.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))))) z)
5.7b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
Compiler

Compiled 6087 to 1282 computations (78.9% saved)

regimes1.5s (23.5%)

Accuracy

Total 1.8b remaining (60.9%)

Threshold costs 0b (0%)

Counts
232 → 3
Compiler

Compiled 25812 to 13861 computations (46.3% saved)

bsearch7.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025124
129124
229124

end259.0ms (4.2%)

Compiler

Compiled 488 to 171 computations (65% saved)

Profiling

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