Details

Time bar (total: 21.9s)

sample841.0ms

Algorithm
intervals
Results
740.0ms3515×body80valid

simplify71.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.3b
(pow (/ 1.0 (fabs x)) 6)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
37×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
13×add-exp-log cube-prod
9×pow-unpow
8×pow1
7×add-cbrt-cube
6×pow-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×pow-to-exp pow-pow div-exp sqrt-prod sqr-pow
2×rem-cube-cbrt
1×cbrt-undiv cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3
Counts
4 → 123
Calls
4 calls:
7.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
6.0ms
(pow (/ 1.0 (fabs x)) 6)

series107.0ms

Counts
4 → 10
Calls
4 calls:
29.0ms
(pow (/ 1.0 (fabs x)) 3)
30.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
48.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify77.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
0545752
12496663
25001647

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
38×*-un-lft-identity
37×times-frac
36×add-cube-cbrt
26×unpow-prod-down
15×add-exp-log
13×cube-prod associate-*l*
12×add-cbrt-cube
9×pow1
6×pow-unpow
4×expm1-log1p-u associate-*r* pow-exp log1p-expm1-u div-inv add-log-exp
3×div-exp sqrt-prod
2×cbrt-undiv frac-times pow-to-exp pow-pow flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+ rem-cube-cbrt unswap-sqr sqr-pow
1×cube-div distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down associate-*l/ *-commutative distribute-lft-out
Counts
4 → 134
Calls
4 calls:
71.0ms
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
7.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series214.0ms

Counts
4 → 10
Calls
4 calls:
152.0ms
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
29.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify112.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07221344
136371199
250021192

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite935.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
46×add-exp-log
45×times-frac
41×*-un-lft-identity
36×add-cube-cbrt
26×associate-*r*
24×unpow-prod-down
23×prod-exp
21×add-cbrt-cube
13×cube-prod
10×pow1 div-exp
7×associate-*l* associate-*l/ pow-exp cbrt-unprod unswap-sqr
6×pow-to-exp sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv frac-times rec-exp pow-unpow 1-exp sqrt-prod div-inv
2×flip3-+ associate-*r/ pow-prod-down frac-add *-commutative flip-+ rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 un-div-inv distribute-lft-out
Counts
4 → 156
Calls
4 calls:
900.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
22.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series557.0ms

Counts
4 → 10
Calls
4 calls:
488.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
33.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
35.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify120.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
09402032
144841663
250021662

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.3b
(* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (pow (exp (fabs x)) (* 2 (/ (fabs x) 2))) (/ 1.0 (sqrt PI))))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
46×add-exp-log
45×times-frac
39×*-un-lft-identity
36×add-cube-cbrt
26×associate-*r*
24×unpow-prod-down
23×prod-exp
21×add-cbrt-cube
13×cube-prod
10×pow1 div-exp
7×pow-exp cbrt-unprod unswap-sqr
6×pow-to-exp associate-*l* sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp pow-unpow 1-exp associate-*r/ sqrt-prod div-inv
2×pow-prod-down *-commutative rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 un-div-inv
Counts
4 → 149
Calls
4 calls:
24.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
38.0ms
(* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (pow (exp (fabs x)) (* 2 (/ (fabs x) 2))) (/ 1.0 (sqrt PI))))
10.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series525.0ms

Counts
4 → 10
Calls
4 calls:
34.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
461.0ms
(* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (pow (exp (fabs x)) (* 2 (/ (fabs x) 2))) (/ 1.0 (sqrt PI))))
30.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify104.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
08181728
138401385
250021368

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes444.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample11.0s

Algorithm
intervals
Results
10.4s49789×body80valid