Details

Time bar (total: 4.2s)

analyze173.0ms (4.1%)

Algorithm
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%50%50%4
0%50%50%5
12.5%37.5%50%6
18.7%31.2%50%7
28.1%21.9%50%8
32.8%17.2%50%9
38.2%11.7%50%10
41%9%50%11
43.9%6%50%12
45.4%4.6%50%13
46.9%3.1%50%14
Compiler

Compiled 31 to 22 computations (29% saved)

sample1.3s (29.9%)

Results
1.2s8256×body128valid
1.0ms10×body128invalid
Compiler

Compiled 92 to 65 computations (29.3% saved)

simplify32.0ms (0.8%)

Algorithm
egg-herbie
Rules
826×times-frac_binary64
592×fma-def_binary64
509×associate-/r*_binary64
353×associate-/l*_binary64
343×div-sub_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02043
15843
217938
382436
4388236
5502936

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.5b
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.5b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
Compiler

Compiled 166 to 115 computations (30.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
0.3b
(*.f64 (PI.f64) t)
0.3b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
0.5b
(*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

series158.0ms (3.8%)

Counts
4 → 72
Calls

4 calls:

106.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
33.0ms
(*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
15.0ms
(*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
2.0ms
(*.f64 (PI.f64) t)

rewrite86.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
193×add-sqr-sqrt_binary64
186×prod-diff_binary64
183×log1p-expm1-u_binary64
183×expm1-log1p-u_binary64
182×add-log-exp_binary64
Counts
4 → 102
Calls

4 calls:

83.0ms
(*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
83.0ms
(*.f64 (PI.f64) t)
83.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
83.0ms
(*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01981
139981
2478481
3504281

simplify84.0ms (2%)

Algorithm
egg-herbie
Rules
756×cancel-sign-sub-inv_binary64
309×fma-neg_binary64
302×sub-neg_binary64
266×associate-/r*_binary64
229×fma-def_binary64
Counts
174 → 157
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02713301
18763173
237293173
353513173

prune163.0ms (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1498157
Fresh101
Picked101
Done000
Total1518159
Error
0.0b
Counts
159 → 8
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (*.f64 (PI.f64) t))) (/.f64 (fma.f64 v (*.f64 v -5) 1) (-.f64 1 (*.f64 v v))))
1.4b
(/.f64 (sqrt.f64 1/2) (*.f64 (PI.f64) t))
0.5b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (-.f64 (*.f64 (PI.f64) t) (*.f64 (pow.f64 v 2) (*.f64 (PI.f64) t)))))
0.7b
(*.f64 (/.f64 (-.f64 1 (*.f64 5 (pow.f64 v 2))) (*.f64 (-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
28.2b
(*.f64 (/.f64 1 (cbrt.f64 (*.f64 (fma.f64 v (*.f64 v -6) 2) (pow.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) 2)))) (/.f64 (fma.f64 v (*.f64 v -5) 1) (cbrt.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))))
0.4b
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
0.3b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 t (-.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))))
1.1b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))
Compiler

Compiled 6563 to 4348 computations (33.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (pow.f64 v 2) (PI.f64))
0.2b
(*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))
0.2b
(*.f64 t (-.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))))
0.3b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 t (-.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))))

series250.0ms (5.9%)

Counts
4 → 48
Calls

4 calls:

181.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 t (-.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))))
57.0ms
(*.f64 t (-.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))))
9.0ms
(*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))
3.0ms
(*.f64 (pow.f64 v 2) (PI.f64))

rewrite74.0ms (1.8%)

Algorithm
batch-egg-rewrite
Rules
303×prod-diff_binary64
214×add-sqr-sqrt_binary64
205×log1p-expm1-u_binary64
205×expm1-log1p-u_binary64
201×add-log-exp_binary64
Counts
4 → 81
Calls

4 calls:

72.0ms
(*.f64 (pow.f64 v 2) (PI.f64))
72.0ms
(*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))
72.0ms
(*.f64 t (-.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))))
72.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 t (-.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02098
144098
2480898
3526798

simplify75.0ms (1.8%)

Algorithm
egg-herbie
Rules
812×cancel-sign-sub-inv_binary64
400×fma-neg_binary64
343×sub-neg_binary64
261×associate-/r*_binary64
205×associate-*r*_binary64
Counts
129 → 150
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02332987
18192944
235652942
353262942

prune178.0ms (4.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1473150
Fresh347
Picked101
Done000
Total1517158
Error
0.0b
Counts
158 → 7
Alt Table
StatusErrorProgram
0.3b
(pow.f64 (/.f64 (*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))))) (fma.f64 v (*.f64 v -5) 1)) -1)
0.7b
(*.f64 (/.f64 (-.f64 1 (*.f64 5 (pow.f64 v 2))) (*.f64 (-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
1.1b
(/.f64 1 (*.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))
0.5b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (-.f64 (*.f64 (PI.f64) t) (*.f64 (pow.f64 v 2) (*.f64 (PI.f64) t)))))
1.4b
(/.f64 (sqrt.f64 1/2) (*.f64 (PI.f64) t))
0.6b
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) t) (/.f64 1 (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))))))
0.4b
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
Compiler

Compiled 6916 to 4709 computations (31.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 6 (*.f64 v v))
0.2b
(*.f64 (PI.f64) (*.f64 v v))
0.2b
(*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v)))))
0.3b
(pow.f64 (/.f64 (*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))))) (fma.f64 v (*.f64 v -5) 1)) -1)

series219.0ms (5.2%)

Counts
4 → 72
Calls

4 calls:

178.0ms
(pow.f64 (/.f64 (*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))))) (fma.f64 v (*.f64 v -5) 1)) -1)
36.0ms
(*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v)))))
3.0ms
(*.f64 (PI.f64) (*.f64 v v))
2.0ms
(*.f64 6 (*.f64 v v))

rewrite69.0ms (1.6%)

Algorithm
batch-egg-rewrite
Rules
222×add-sqr-sqrt_binary64
212×log1p-expm1-u_binary64
212×expm1-log1p-u_binary64
208×add-cbrt-cube_binary64
208×add-log-exp_binary64
Counts
4 → 61
Calls

4 calls:

67.0ms
(*.f64 6 (*.f64 v v))
67.0ms
(*.f64 (PI.f64) (*.f64 v v))
67.0ms
(*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v)))))
67.0ms
(pow.f64 (/.f64 (*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))))) (fma.f64 v (*.f64 v -5) 1)) -1)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02186
145786
2483186
3493686

simplify82.0ms (2%)

Algorithm
egg-herbie
Rules
691×cancel-sign-sub-inv_binary64
304×sub-neg_binary64
295×fma-neg_binary64
242×associate-/r*_binary64
201×distribute-neg-frac_binary64
Counts
133 → 113
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02043098
17123071
231873071
350203071

prune126.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1130113
Fresh066
Picked011
Done000
Total1137120
Error
0.0b
Counts
120 → 7
Alt Table
StatusErrorProgram
0.3b
(pow.f64 (/.f64 (*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))))) (fma.f64 v (*.f64 v -5) 1)) -1)
0.7b
(*.f64 (/.f64 (-.f64 1 (*.f64 5 (pow.f64 v 2))) (*.f64 (-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
1.1b
(/.f64 1 (*.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))
0.5b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)) (-.f64 (*.f64 (PI.f64) t) (*.f64 (pow.f64 v 2) (*.f64 (PI.f64) t)))))
1.4b
(/.f64 (sqrt.f64 1/2) (*.f64 (PI.f64) t))
0.6b
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) t) (/.f64 1 (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))))))
0.4b
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
Compiler

Compiled 5262 to 3533 computations (32.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (PI.f64) t)
0.3b
(/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
0.5b
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
1.0b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

series155.0ms (3.7%)

Counts
3 → 60
Calls

3 calls:

105.0ms
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
41.0ms
(/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
9.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

rewrite75.0ms (1.8%)

Algorithm
batch-egg-rewrite
Rules
360×log1p-udef_binary64
209×add-sqr-sqrt_binary64
198×log1p-expm1-u_binary64
198×expm1-log1p-u_binary64
197×add-log-exp_binary64
Counts
3 → 117
Calls

3 calls:

72.0ms
(/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
72.0ms
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
72.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02073
143173
2471673
3538173

simplify78.0ms (1.9%)

Algorithm
egg-herbie
Rules
438×cancel-sign-sub-inv_binary64
291×associate-/r*_binary64
272×distribute-neg-in_binary64
256×sub-neg_binary64
217×fma-def_binary64
Counts
177 → 180
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02933056
18982953
235222946
351442946

prune184.0ms (4.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1923195
Fresh415
Picked101
Done011
Total1975202
Error
0b
Counts
202 → 5
Alt Table
StatusErrorProgram
0.3b
(pow.f64 (/.f64 (*.f64 t (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))))) (fma.f64 v (*.f64 v -5) 1)) -1)
0.7b
(*.f64 (/.f64 (-.f64 1 (*.f64 5 (pow.f64 v 2))) (*.f64 (-.f64 (PI.f64) (*.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
1.4b
(*.f64 (*.f64 (/.f64 1 (pow.f64 (fma.f64 v (*.f64 v -6) 2) 1/4)) (/.f64 (fma.f64 v (*.f64 v -5) 1) (pow.f64 (fma.f64 v (*.f64 v -6) 2) 1/4))) (/.f64 1 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
0.1b
(/.f64 (/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (PI.f64)) (*.f64 t (-.f64 1 (*.f64 v v))))
0.4b
(/.f64 (/.f64 1 (*.f64 (PI.f64) t)) (*.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (fma.f64 v (*.f64 v -5) 1)) (-.f64 1 (*.f64 v v))))
Compiler

Compiled 7436 to 5003 computations (32.7% saved)

regimes403.0ms (9.6%)

Accuracy

Total 0.1b remaining (93.4%)

Threshold costs 0.1b (93.4%)

Counts
64 → 1
Compiler

Compiled 10597 to 7879 computations (25.6% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01936
12936
23536
33936
44136
54036

end228.0ms (5.4%)

Compiler

Compiled 205 to 154 computations (24.9% saved)

Profiling

Loading profile data...