Details

Time bar (total: 2.6s)

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)

sample150.0ms (5.8%)

Algorithm
1×intervals
Results
21.0ms256×body128valid
Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify118.0ms (4.5%)

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

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)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series48.0ms (1.9%)

Counts
4 → 48
Calls

4 calls:

31.0ms
(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
7.0ms
(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
1×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:

7.0ms
(/.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))

simplify161.0ms (6.2%)

Algorithm
1×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

prune208.0ms (8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2252227
Fresh101
Picked011
Done000
Total2263229
Error
0b
Counts
229 → 3
Alt Table
StatusErrorProgram
▶0.0b
(/.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (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 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 6672 to 4985 computations (25.3% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series33.0ms (1.3%)

Counts
2 → 24
Calls

2 calls:

25.0ms
(/.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
8.0ms
(*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))

rewrite26.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
56×add-exp-log_binary64
37×add-sqr-sqrt_binary64
32×add-cbrt-cube_binary64
31×times-frac_binary64
25×div-exp_binary64
Counts
2 → 100
Calls

2 calls:

10.0ms
(*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))
8.0ms
(/.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

simplify151.0ms (5.8%)

Algorithm
1×egg-herbie
Rules
723×fma-def_binary64
258×cancel-sign-sub-inv_binary64
197×associate-/r*_binary64
195×fma-neg_binary64
192×associate-/l*_binary64
Counts
124 → 188
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03283898
19313407
233613386
347973386
449893386
549243386

prune261.0ms (10%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2260226
Fresh011
Picked011
Done011
Total2263229
Error
0b
Counts
229 → 3
Alt Table
StatusErrorProgram
✓0.0b
(/.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (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 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 6802 to 5125 computations (24.7% saved)

localize12.0ms (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 1 (*.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))))

series41.0ms (1.6%)

Counts
3 → 36
Calls

3 calls:

26.0ms
(/.f64 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
8.0ms
(*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))))
6.0ms
(/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))

rewrite25.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
61×add-exp-log_binary64
31×add-cbrt-cube_binary64
23×prod-exp_binary64
20×div-exp_binary64
14×add-sqr-sqrt_binary64
Counts
3 → 103
Calls

3 calls:

7.0ms
(/.f64 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
7.0ms
(*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))))
4.0ms
(/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))

simplify128.0ms (4.9%)

Algorithm
1×egg-herbie
Rules
716×fma-def_binary64
263×distribute-rgt-in_binary64
256×cancel-sign-sub-inv_binary64
194×associate-/r*_binary64
173×sub-neg_binary64
Counts
139 → 185
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03133978
18713526
229723440
350173440

prune206.0ms (7.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2230223
Fresh000
Picked011
Done022
Total2233226
Error
0b
Counts
226 → 3
Alt Table
StatusErrorProgram
✓0.0b
(/.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (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 (*.f64 -4/3 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Compiler

Compiled 6462 to 4899 computations (24.2% saved)

regimes92.0ms (3.5%)

Accuracy

Total 0.0b remaining (43.9%)

Threshold costs 0.0b (43.9%)

Counts
22 → 1
Compiler

Compiled 2100 to 1702 computations (19% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01627
12027
21927

end1.0ms (0%)

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample883.0ms (33.9%)

Algorithm
1×intervals
Results
621.0ms8000×body128valid
0.0ms3×body128nan
Compiler

Compiled 97 to 76 computations (21.6% saved)

Profiling

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