Details

Time bar (total: 3.2s)

analyze6.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50.1%13
49.9%0%50.1%14
Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.2s (37.4%)

Results
1.0s8256×body128valid
0.0ms3×body128invalid
Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify134.0ms (4.2%)

Algorithm
1×egg-herbie
Rules
1332×fma-def_binary64
889×associate-/r*_binary64
605×neg-sub0_binary64
599×neg-mul-1_binary64
576×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01731
14228
210226
326126
468426
5108824
6180124
7354124
8391424
9400224
10441624
11440924
12441524
13515924

prune9.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.0b
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
1.0b
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Compiler

Compiled 113 to 85 computations (24.8% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (PI.f64) (fma.f64 v v -1))
✓0.0b
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
✓1.0b
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series33.0ms (1.1%)

Counts
3 → 36
Calls

3 calls:

24.0ms
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
6.0ms
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
3.0ms
(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite202.0ms (6.4%)

Algorithm
3×egg-rewrite
Rules
62×egg
51×egg
36×egg
Counts
3 → 149
Calls

3 calls:

84.0ms
(*.f64 (PI.f64) (fma.f64 v v -1))
67.0ms
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
47.0ms
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
116312
2188112
3490012
01424
129324
2350424
3488924
069
11139
212409
349289
464839

simplify86.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
672×fma-def_binary64
660×times-frac_binary64
581×fma-neg_binary64
252×cancel-sign-sub-inv_binary64
132×sub-neg_binary64
Counts
185 → 193
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01781475
15651444
220051340
347171334
450801334

prune171.0ms (5.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1912193
Fresh101
Picked101
Done000
Total1932195
Error
0b
Counts
195 → 2
Alt Table
StatusErrorProgram
0.0b
(*.f64 -4/3 (/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
▶0.0b
(/.f64 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 5048 to 3744 computations (25.8% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))
0.0b
(*.f64 (PI.f64) (fma.f64 v v -1))
✓0.0b
(/.f64 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
✓0.0b
(*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))))

series34.0ms (1.1%)

Counts
3 → 36
Calls

3 calls:

23.0ms
(/.f64 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
6.0ms
(*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))))
5.0ms
(/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))

rewrite168.0ms (5.3%)

Algorithm
3×egg-rewrite
Rules
60×egg
39×egg
33×egg
Counts
3 → 132
Calls

3 calls:

67.0ms
(/.f64 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
51.0ms
(*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))))
47.0ms
(/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
119612
2211012
3516512
01624
132624
2372624
3493624
0812
115312
2166612
3504612

simplify91.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
676×fma-def_binary64
660×times-frac_binary64
582×fma-neg_binary64
248×cancel-sign-sub-inv_binary64
150×distribute-neg-in_binary64
Counts
168 → 183
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01911677
16031653
221171563
347281557
450901557

prune198.0ms (6.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2400240
Fresh011
Picked011
Done000
Total2402242
Error
0b
Counts
242 → 2
Alt Table
StatusErrorProgram
▶0.0b
(*.f64 -4/3 (/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
✓0.0b
(/.f64 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 6353 to 4725 computations (25.6% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (PI.f64) (fma.f64 v v -1))
✓0.0b
(*.f64 -4/3 (/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
✓0.0b
(*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
✓0.0b
(/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))

series56.0ms (1.8%)

Counts
3 → 36
Calls

3 calls:

25.0ms
(*.f64 -4/3 (/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
19.0ms
(/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
12.0ms
(*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

rewrite188.0ms (6%)

Algorithm
3×egg-rewrite
Rules
41×egg
40×egg
37×egg
Counts
3 → 118
Calls

3 calls:

68.0ms
(*.f64 -4/3 (/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
61.0ms
(/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
56.0ms
(*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01424
127724
2301524
3503424
01221
123721
2259421
3489421
01624
132024
2346124
3576124

simplify98.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
501×cancel-sign-sub-inv_binary64
387×sub-neg_binary64
336×fma-neg_binary64
229×fma-def_binary64
180×+-commutative_binary64
Counts
154 → 188
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02592642
18772599
234742595
350382595

prune223.0ms (7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New2450245
Fresh000
Picked011
Done011
Total2452247
Error
0b
Counts
247 → 2
Alt Table
StatusErrorProgram
✓0.0b
(*.f64 -4/3 (/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
✓0.0b
(/.f64 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 7721 to 5896 computations (23.6% saved)

regimes175.0ms (5.5%)

Accuracy

Total 0.0b remaining (50.1%)

Threshold costs 0.0b (50.1%)

Counts
51 → 1
Compiler

Compiled 3791 to 3066 computations (19.1% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01627
12127
22027

end69.0ms (2.2%)

Compiler

Compiled 76 to 60 computations (21.1% saved)

Profiling

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