Details

Time bar (total: 3.5s)

analyze43.0ms (1.2%)

Algorithm
1×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
49.9%49.9%0.1%5
74.9%25%0.1%6
87.4%12.5%0.1%7
93.6%6.2%0.1%8
96.7%3.1%0.1%9
98.3%1.6%0.1%10
99.1%0.8%0.1%11
99.5%0.4%0.1%12
99.7%0.2%0.1%13
99.8%0.1%0.1%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample40.0ms (1.1%)

Algorithm
1×intervals
Results
14.0ms256×body128valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify12.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
9×fma-def_binary64
5×+-commutative_binary64
3×associate-+r+_binary64
3×associate-+l+_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01219
11717
22717
33117
43117

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
40.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶40.1b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
Compiler

Compiled 59 to 34 computations (42.4% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓37.4b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

rewrite7.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
19×times-frac_binary64
17×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
13×sqrt-prod_binary64
Counts
2 → 56
Calls

2 calls:

2.0ms
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
2.0ms
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)

series183.0ms (5.2%)

Counts
2 → 72
Calls

2 calls:

127.0ms
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
56.0ms
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)

simplify130.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
356×sub-neg_binary64
354×fma-neg_binary64
279×fma-def_binary64
227×times-frac_binary64
207×associate-*r*_binary64
Counts
128 → 246
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03854690
110024370
240434370
349954370

prune134.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2433246
Fresh000
Picked011
Done000
Total2434247
Error
0.3b
Counts
247 → 4
Alt Table
StatusErrorProgram
▶1.1b
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
29.4b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
40.2b
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
✓40.1b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
Compiler

Compiled 5977 to 3529 computations (41% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.4b
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

rewrite5.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64
6×associate-*l*_binary64
4×sqrt-prod_binary64
4×*-un-lft-identity_binary64
4×add-cube-cbrt_binary64
Counts
1 → 25
Calls

1 calls:

4.0ms
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

series23.0ms (0.6%)

Counts
1 → 24
Calls

1 calls:

22.0ms
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

simplify71.0ms (2%)

Algorithm
1×egg-herbie
Rules
635×distribute-rgt-neg-in_binary64
498×times-frac_binary64
397×distribute-neg-frac_binary64
345×associate-*r*_binary64
302×associate-/l*_binary64
Counts
49 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0991097
12691061
29051057
339231057
452791057

prune46.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New73578
Fresh022
Picked011
Done011
Total73982
Error
0.0b
Counts
82 → 9
Alt Table
StatusErrorProgram
✓1.1b
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
1.4b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))))
1.2b
(*.f64 (*.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
1.8b
(*.f64 (*.f64 (sqrt.f64 1/3) (*.f64 (cbrt.f64 (hypot.f64 x z)) (cbrt.f64 (hypot.f64 x z)))) (cbrt.f64 (hypot.f64 x z)))
▶0.9b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
29.4b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
40.2b
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
1.9b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z)))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))
✓40.1b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
Compiler

Compiled 1273 to 914 computations (28.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
✓0.3b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

rewrite16.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
21×sqrt-prod_binary64
18×associate-*l*_binary64
15×add-sqr-sqrt_binary64
9×*-un-lft-identity_binary64
9×add-cube-cbrt_binary64
Counts
2 → 56
Calls

2 calls:

7.0ms
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
5.0ms
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))

series48.0ms (1.4%)

Counts
2 → 48
Calls

2 calls:

26.0ms
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
22.0ms
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

simplify106.0ms (3%)

Algorithm
1×egg-herbie
Rules
785×fma-neg_binary64
710×times-frac_binary64
483×associate-/l*_binary64
470×fma-def_binary64
235×cancel-sign-sub-inv_binary64
Counts
104 → 183
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01602514
14632398
216572278
347852274
453012274

prune100.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1803183
Fresh516
Picked011
Done022
Total1857192
Error
0b
Counts
192 → 7
Alt Table
StatusErrorProgram
1.2b
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
✓40.1b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
✓0.9b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
✓1.1b
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
29.4b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
1.2b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (hypot.f64 x z))))
▶1.0b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
Compiler

Compiled 2885 to 2253 computations (21.9% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
✓0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
✓0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
✓1.0b
(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

rewrite36.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
25×associate-*l*_binary64
25×add-sqr-sqrt_binary64
24×pow1_binary64
20×sqrt-prod_binary64
19×cbrt-prod_binary64
Counts
3 → 100
Calls

3 calls:

16.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
10.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
4.0ms
(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

series134.0ms (3.8%)

Counts
3 → 48
Calls

3 calls:

74.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
60.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
0.0ms
(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

simplify159.0ms (4.5%)

Algorithm
1×egg-herbie
Rules
607×fma-neg_binary64
568×cancel-sign-sub-inv_binary64
400×times-frac_binary64
365×associate-*r*_binary64
296×associate-*l*_binary64
Counts
148 → 261
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02324743
16304293
222934285
348994285
450404285

prune248.0ms (7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New3490349
Fresh033
Picked011
Done033
Total3497356
Error
0b
Counts
356 → 7
Alt Table
StatusErrorProgram
1.2b
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
✓40.1b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
✓0.9b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
✓1.1b
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
29.4b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
1.2b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (hypot.f64 x z))))
✓1.0b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
Compiler

Compiled 7958 to 6870 computations (13.7% saved)

regimes613.0ms (17.3%)

Accuracy

Total 0.7b remaining (82.1%)

Threshold costs 0.7b (82.1%)

Compiler

Compiled 10183 to 8061 computations (20.8% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0918
11118
21118

end15.0ms (0.4%)

Compiler

Compiled 42 to 36 computations (14.3% saved)

sample1.3s (37.5%)

Algorithm
1×intervals
Results
482.0ms8000×body128valid
Compiler

Compiled 145 to 119 computations (17.9% saved)

Profiling

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