Details

Time bar (total: 7.8s)

sample362.0ms

Algorithm
intervals
Results
297.0ms3787×body80valid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune17.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize36.0ms

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)
1.2b
(pow (/ 1.0 (fabs x)) 6)

rewrite25.0ms

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:
9.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
5.0ms
(pow (/ 1.0 (fabs x)) 6)

series122.0ms

Counts
4 → 10
Calls
4 calls:
38.0ms
(pow (/ 1.0 (fabs x)) 3)
35.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
49.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify75.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0545752
12496663
25001647

prune873.0ms

Filtered
133 candidates to 82 candidates (61.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

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)

rewrite32.0ms

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:
16.0ms
(* (/ 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)
5.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series245.0ms

Counts
4 → 10
Calls
4 calls:
173.0ms
(* (/ 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)))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
35.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify111.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07221344
136371199
250021192

prune834.0ms

Filtered
144 candidates to 93 candidates (64.6%)
Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
114×add-sqr-sqrt
113×add-cube-cbrt *-un-lft-identity
65×unpow-prod-down cube-prod
32×associate-/r*
15×add-exp-log
11×div-inv
9×add-cbrt-cube
6×pow1 div-exp
5×cube-mult unpow3 sqr-pow
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×pow-unpow sqrt-prod associate-/l*
2×cbrt-undiv cube-div pow-to-exp rem-cube-cbrt
1×rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r/ fma-udef
Counts
4 → 222
Calls
4 calls:
10.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
1.0ms
(fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4))))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series245.0ms

Counts
4 → 10
Calls
4 calls:
98.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
113.0ms
(fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4))))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify92.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
05691951
130871632
250021620

prune1.0s

Filtered
232 candidates to 118 candidates (50.9%)
Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
90×add-exp-log
73×prod-exp
28×add-cbrt-cube
21×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac
17×pow-exp
16×pow-to-exp
13×unpow-prod-down cube-prod div-exp cbrt-unprod
8×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow sqrt-prod
2×div-inv rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 associate-*r/ associate-*r* associate-*l* pow-prod-down associate-*l/ *-commutative fma-udef sqr-pow
Counts
4 → 121
Calls
4 calls:
13.0ms
(* (* (pow (exp (fabs x)) (/ (fabs x) 2)) (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)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
1.0ms
(fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4))))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series680.0ms

Counts
4 → 10
Calls
4 calls:
528.0ms
(* (* (pow (exp (fabs x)) (/ (fabs x) 2)) (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)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
118.0ms
(fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4))))
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify93.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07152472
130551971
250011903

prune471.0ms

Filtered
131 candidates to 63 candidates (48.1%)
Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.0b

regimes308.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.6s20823×body80valid