Details

Time bar (total: 7.5s)

sample399.0ms

Algorithm
intervals
Results
333.0ms4192×body80valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune16.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.2b
(pow (/ 1.0 (fabs x)) 6)

rewrite19.0ms

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:
5.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
5.0ms
(pow (/ 1.0 (fabs x)) 6)

series120.0ms

Counts
4 → 10
Calls
4 calls:
33.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
53.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify78.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0545752
12496663
25001647

prune629.0ms

Filtered
133 candidates to 82 candidates (61.7%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 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)))
0.6b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite29.0ms

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:
14.0ms
(* (/ 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)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series240.0ms

Counts
4 → 10
Calls
4 calls:
170.0ms
(* (/ 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)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
37.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify114.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
07221344
136371203
250021198

prune790.0ms

Filtered
144 candidates to 94 candidates (65.3%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (fabs x) 6))
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))))
0.6b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity times-frac
38×add-sqr-sqrt
37×add-cube-cbrt
35×add-exp-log
25×unpow-prod-down
18×add-cbrt-cube
13×cube-prod prod-exp
10×div-exp
8×pow1
7×associate-*l/ pow-exp associate-/r*
6×pow-to-exp
5×cbrt-unprod sqr-pow
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
3×cbrt-undiv frac-times rec-exp pow-unpow 1-exp sqrt-prod div-inv associate-/l*
2×flip3-+ frac-add flip-+ rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-flip pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*r/ associate-*r* pow-prod-down clear-num *-commutative distribute-lft-out inv-pow
Counts
4 → 151
Calls
4 calls:
5.0ms
(/ 1 (pow (fabs x) 6))
131.0ms
(* (+ (/ 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))))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series595.0ms

Counts
4 → 10
Calls
4 calls:
51.0ms
(/ 1 (pow (fabs x) 6))
511.0ms
(* (+ (/ 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))))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify100.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07981993
137041627
250031611

prune697.0ms

Filtered
161 candidates to 84 candidates (52.2%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
0.3b
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (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))))
0.6b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
116×*-un-lft-identity
115×add-sqr-sqrt
114×add-cube-cbrt
65×unpow-prod-down cube-prod
34×add-exp-log
32×associate-/r*
18×add-cbrt-cube
13×prod-exp
11×div-inv
9×div-exp
8×pow1
7×associate-*l/
6×pow-exp
5×cube-mult unpow3 cbrt-unprod sqr-pow
4×expm1-log1p-u pow-to-exp associate-*l* log1p-expm1-u add-log-exp
3×cbrt-undiv frac-times pow-unpow sqrt-prod associate-/l*
2×cube-div flip3-+ frac-add flip-+ rem-cube-cbrt
1×rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*r* pow-prod-down clear-num associate-/r/ *-commutative distribute-lft-out
Counts
4 → 245
Calls
4 calls:
10.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
132.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (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))))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series661.0ms

Counts
4 → 10
Calls
4 calls:
98.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
530.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (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
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify133.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
08943056
147272534
250012533

prune986.0ms

Filtered
255 candidates to 134 candidates (52.5%)
Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes247.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04333
14333

end0.0ms

sample1.1s

Algorithm
intervals
Results
931.0ms11944×body80valid