Details

Time bar (total: 3.6s)

analyze27.0ms (0.7%)

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
48.4%1.6%50%9
48.4%1.6%50%10
48.4%1.6%50%11
48.5%1.5%50%12
48.6%1.4%50.1%13
48.6%1.3%50.1%14
Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.1s (30.5%)

Results
967.0ms8256×body128valid
0.0ms2×body128invalid
Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify122.0ms (3.4%)

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 (0.1%)

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)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series37.0ms (1%)

Counts
3 → 36
Calls

3 calls:

25.0ms
(/.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)))
5.0ms
(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

rewrite19.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
66×times-frac_binary64
37×add-sqr-sqrt_binary64
36×*-un-lft-identity_binary64
36×add-cube-cbrt_binary64
27×sqrt-prod_binary64
Counts
3 → 112
Calls

3 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)))
1.0ms
(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

simplify201.0ms (5.5%)

Algorithm
1×egg-herbie
Rules
802×fma-def_binary64
299×cancel-sign-sub-inv_binary64
239×associate-/r*_binary64
216×fma-neg_binary64
194×sub-neg_binary64
Counts
148 → 186
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03635218
19964900
232704877
349814877
449254877

prune174.0ms (4.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1833186
Fresh101
Picked101
Done000
Total1853188
Error
0b
Counts
188 → 3
Alt Table
StatusErrorProgram
0.0b
(*.f64 -4/3 (/.f64 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
1.3b
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 4/3 (*.f64 (/.f64 (*.f64 v v) (PI.f64)) (sqrt.f64 1/2)) (/.f64 (*.f64 v v) (*.f64 (PI.f64) (sqrt.f64 1/2)))))
▶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)))
Compiler

Compiled 5813 to 4398 computations (24.3% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series32.0ms (0.9%)

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)))
7.0ms
(*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))

rewrite25.0ms (0.7%)

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:

9.0ms
(/.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)))

simplify148.0ms (4.1%)

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 → 187
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03283898
19313407
233613386
347973386
449893386
549243386

prune239.0ms (6.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2241225
Fresh112
Picked101
Done000
Total2262228
Error
0b
Counts
228 → 2
Alt Table
StatusErrorProgram
▶0.0b
(*.f64 -4/3 (/.f64 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
1.0b
(exp.f64 (-.f64 (log.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))) (log.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
Compiler

Compiled 6792 to 5123 computations (24.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series57.0ms (1.6%)

Counts
3 → 36
Calls

3 calls:

30.0ms
(*.f64 -4/3 (/.f64 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
20.0ms
(/.f64 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
6.0ms
(/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))

rewrite53.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
128×times-frac_binary64
71×add-sqr-sqrt_binary64
63×*-un-lft-identity_binary64
63×add-cube-cbrt_binary64
61×add-exp-log_binary64
Counts
3 → 184
Calls

3 calls:

15.0ms
(*.f64 -4/3 (/.f64 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
6.0ms
(/.f64 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
3.0ms
(/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1)))

simplify167.0ms (4.6%)

Algorithm
1×egg-herbie
Rules
850×fma-def_binary64
303×sub-neg_binary64
219×associate-/r*_binary64
185×fma-neg_binary64
170×associate-*r/_binary64
Counts
220 → 270
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03847896
110807279
237947250
350097250

prune264.0ms (7.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New3080308
Fresh011
Picked011
Done000
Total3082310
Error
0b
Counts
310 → 2
Alt Table
StatusErrorProgram
✓0.0b
(*.f64 -4/3 (/.f64 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
▶1.0b
(exp.f64 (-.f64 (log.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))) (log.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
Compiler

Compiled 10285 to 7894 computations (23.2% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series72.0ms (2%)

Counts
3 → 36
Calls

3 calls:

40.0ms
(exp.f64 (-.f64 (log.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))) (log.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
20.0ms
(log.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
12.0ms
(log.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))))

rewrite29.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
47×pow1_binary64
42×log-pow_binary64
38×exp-sum_binary64
30×prod-diff_binary64
27×add-exp-log_binary64
Counts
3 → 103
Calls

3 calls:

10.0ms
(exp.f64 (-.f64 (log.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))) (log.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
5.0ms
(log.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))))
1.0ms
(log.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

simplify119.0ms (3.3%)

Algorithm
1×egg-herbie
Rules
835×fma-def_binary64
689×times-frac_binary64
232×sub-neg_binary64
181×associate-+r+_binary64
176×+-commutative_binary64
Counts
139 → 177
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03395928
17794527
225983925
350443925

prune219.0ms (6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New2150215
Fresh000
Picked011
Done011
Total2152217
Error
0b
Counts
217 → 2
Alt Table
StatusErrorProgram
✓0.0b
(*.f64 -4/3 (/.f64 (/.f64 1 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
✓1.0b
(exp.f64 (-.f64 (log.f64 (*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))) (log.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))
Compiler

Compiled 8458 to 6787 computations (19.8% saved)

regimes408.0ms (11.2%)

Accuracy

Total 0.0b remaining (43.2%)

Threshold costs 0.0b (43.2%)

Counts
113 → 1
Compiler

Compiled 9080 to 7300 computations (19.6% 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

end65.0ms (1.8%)

Compiler

Compiled 79 to 63 computations (20.3% saved)

Profiling

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