Details

Time bar (total: 2.5s)

analyze6.0ms (0.2%)

Algorithm
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)

sample146.0ms (5.9%)

Algorithm
intervals
Results
18.0ms256×body128valid
Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify119.0ms (4.8%)

Algorithm
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

prune5.0ms (0.2%)

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

Compiled 113 to 85 computations (24.8% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series43.0ms (1.8%)

Counts
4 → 48
Calls

4 calls:

25.0ms
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
9.0ms
(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))

rewrite24.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
66×times-frac_binary64
42×add-sqr-sqrt_binary64
39×*-un-lft-identity_binary64
39×add-cube-cbrt_binary64
27×sqrt-prod_binary64
Counts
4 → 134
Calls

4 calls:

6.0ms
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
3.0ms
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
3.0ms
(*.f64 (PI.f64) (fma.f64 v v -1))
1.0ms
(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

simplify154.0ms (6.2%)

Algorithm
egg-herbie
Rules
880×fma-def_binary64
306×associate-/r*_binary64
254×sub-neg_binary64
223×fma-neg_binary64
173×associate-*r*_binary64
Counts
182 → 227
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03865649
110285260
236165237
347985236
449555236

prune206.0ms (8.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2261227
Fresh011
Picked101
Done000
Total2272229
Error
0b
Counts
229 → 2
Alt Table
StatusErrorProgram
0.0b
(/.f64 (cbrt.f64 (pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3)) (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 6661 to 4976 computations (25.3% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (PI.f64) (fma.f64 v v -1))
1.0b
(cbrt.f64 (pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3))
1.0b
(pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3)
1.0b
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series40.0ms (1.6%)

Counts
2 → 24
Calls

2 calls:

25.0ms
(cbrt.f64 (pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3))
14.0ms
(pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3)

rewrite10.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
20×cbrt-prod_binary64
14×cube-prod_binary64
14×unpow-prod-down_binary64
12×*-un-lft-identity_binary64
12×times-frac_binary64
Counts
2 → 70
Calls

2 calls:

4.0ms
(pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3)
3.0ms
(cbrt.f64 (pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3))

simplify88.0ms (3.5%)

Algorithm
egg-herbie
Rules
725×fma-def_binary64
586×associate-/r*_binary64
382×associate-*l/_binary64
319×times-frac_binary64
250×associate-/l*_binary64
Counts
94 → 109
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01732229
14152060
214182030
349142026
453702026

prune190.0ms (7.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1850185
Fresh011
Picked011
Done000
Total1852187
Error
0b
Counts
187 → 2
Alt Table
StatusErrorProgram
0.0b
(/.f64 (cbrt.f64 (pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3)) (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 4942 to 3676 computations (25.6% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))
0.0b
(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
0.2b
(*.f64 6 (*.f64 v v))
1.0b
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))

series49.0ms (2%)

Counts
4 → 48
Calls

4 calls:

25.0ms
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
15.0ms
(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
7.0ms
(sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))
2.0ms
(*.f64 6 (*.f64 v v))

rewrite37.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube_binary64
32×add-exp-log_binary64
19×pow1_binary64
16×associate-*r/_binary64
15×cbrt-unprod_binary64
Counts
4 → 107
Calls

4 calls:

13.0ms
(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
9.0ms
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
4.0ms
(*.f64 6 (*.f64 v v))
2.0ms
(sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))

simplify124.0ms (5%)

Algorithm
egg-herbie
Rules
401×associate-*l*_binary64
387×associate-*r*_binary64
378×fma-neg_binary64
290×associate-/r*_binary64
228×fma-def_binary64
Counts
155 → 237
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04205211
112024683
248754683
351284683

prune173.0ms (7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New2370237
Fresh000
Picked011
Done011
Total2372239
Error
0b
Counts
239 → 2
Alt Table
StatusErrorProgram
0.0b
(/.f64 (cbrt.f64 (pow.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) 3)) (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 8348 to 5970 computations (28.5% saved)

regimes264.0ms (10.6%)

Accuracy

Total 0.0b remaining (55.9%)

Threshold costs 0.0b (55.9%)

Counts
78 → 1
Compiler

Compiled 5969 to 4745 computations (20.5% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01627
12027
21927

end1.0ms (0%)

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample769.0ms (31%)

Algorithm
intervals
Results
531.0ms8000×body128valid
0.0msbody128nan
Compiler

Compiled 83 to 65 computations (21.7% saved)

Profiling

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