Details

Time bar (total: 6.1s)

sample391.0ms

Algorithm
intervals
Results
330.0ms3399×body80valid

simplify69.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (67.0ms)

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)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.2b

Counts
2 → 2

localize41.0ms

Local error

Found 4 expressions with local error:

0.7b
(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)

rewrite20.0ms

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

series118.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(pow (/ 1.0 (fabs x)) 3)
39.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
47.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify80.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
0545752
12496663
25001647

prune629.0ms

Filtered
133 candidates to 82 candidates (61.7%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New12013133
Fresh011
Picked101
Done000
Total12114135

Merged error: 0.3b

Counts
135 → 14

localize35.0ms

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)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite30.0ms

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:
15.0ms
(* (/ 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)

series243.0ms

Counts
4 → 10
Calls
4 calls:
172.0ms
(* (/ 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)
38.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify116.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07221344
136371199
250021192

prune732.0ms

Filtered
144 candidates to 93 candidates (64.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New13311144
Fresh9413
Picked101
Done000
Total14315158

Merged error: 0.1b

Counts
158 → 15

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
(fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
23×*-un-lft-identity
22×add-sqr-sqrt
21×add-cube-cbrt
18×times-frac
16×add-cbrt-cube
13×unpow-prod-down cube-prod prod-exp
8×pow1
7×associate-*l/
5×cbrt-unprod
4×expm1-log1p-u div-exp associate-*l* pow-exp log1p-expm1-u add-log-exp
3×frac-times pow-to-exp pow-unpow sqrt-prod
2×cbrt-undiv flip3-+ frac-add flip-+ div-inv rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 associate-*r/ associate-*r* pow-prod-down *-commutative fma-udef distribute-lft-out sqr-pow
Counts
4 → 106
Calls
4 calls:
132.0ms
(* (+ (/ 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))))
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)

series681.0ms

Counts
4 → 10
Calls
4 calls:
531.0ms
(* (+ (/ 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))))
113.0ms
(fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4))))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify96.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06901789
132061480
250021473

prune567.0ms

Filtered
116 candidates to 71 candidates (61.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1079116
Fresh10414
Picked101
Done000
Total11813131

Merged error: 0.0b

Counts
131 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.3b
(fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
45×times-frac
38×*-un-lft-identity
35×add-cube-cbrt
27×add-exp-log
25×associate-*r*
24×unpow-prod-down
13×cube-prod
12×add-cbrt-cube
10×prod-exp
8×pow1
7×div-exp unswap-sqr
6×sqr-pow
5×pow-exp
4×expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp
3×rec-exp pow-unpow 1-exp associate-*l* sqrt-prod div-inv
2×cbrt-undiv cbrt-unprod rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down un-div-inv *-commutative fma-udef
Counts
4 → 133
Calls
4 calls:
11.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
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)

series186.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
112.0ms
(fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4))))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify69.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0609889
12859730
25002719

prune564.0ms

Filtered
143 candidates to 85 candidates (59.4%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1412143
Fresh11112
Picked011
Done000
Total14214156

Merged error: 0.0b

Counts
156 → 14

regimes346.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample837.0ms

Algorithm
intervals
Results
723.0ms7552×body80valid