Details

Time bar (total: 13.5s)

sample333.0ms

Algorithm
intervals
Results
275.0ms3326×body80valid

simplify70.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b
(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)

rewrite21.0ms

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)

series123.0ms

Counts
4 → 10
Calls
4 calls:
36.0ms
(pow (/ 1.0 (fabs x)) 3)
35.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
52.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify79.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
0545752
12496663
25001647

prune654.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

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)
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)

series242.0ms

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)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
37.0ms
(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

prune785.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
213×times-frac
144×add-sqr-sqrt
131×*-un-lft-identity
128×add-cube-cbrt
76×unpow-prod-down
65×cube-prod
35×add-exp-log
32×associate-/r*
25×associate-*r*
14×add-cbrt-cube
12×div-exp div-inv
10×prod-exp sqr-pow
8×pow1
7×pow-exp unswap-sqr
5×cube-mult pow-to-exp unpow3
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp pow-unpow 1-exp associate-*l* sqrt-prod associate-/l*
2×cube-div cbrt-unprod rem-cube-cbrt
1×rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r/ un-div-inv *-commutative
Counts
4 → 272
Calls
4 calls:
13.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
11.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series177.0ms

Counts
4 → 10
Calls
4 calls:
99.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
44.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify117.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
08182184
144381804
250011775

prune1.2s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (fabs x)) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0))
0.7b
(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
62×add-exp-log
43×add-sqr-sqrt
40×times-frac
39×add-cbrt-cube
37×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down
24×div-exp
20×prod-exp
13×cbrt-undiv cube-prod associate-*l*
12×cbrt-unprod
9×pow1
7×associate-*r*
6×pow-unpow pow-exp
5×div-inv
4×expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow-pow rem-cube-cbrt unswap-sqr sqr-pow
1×cube-div cube-mult frac-times rem-sqrt-square sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 149
Calls
4 calls:
15.0ms
(* (/ 1.0 (fabs x)) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series138.0ms

Counts
4 → 10
Calls
4 calls:
65.0ms
(* (/ 1.0 (fabs x)) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0))
39.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify122.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
07841170
141851000
25001995

prune726.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.1b

regimes347.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04333
14333

end0.0ms

sample8.0s

Algorithm
intervals
Results
6.9s86600×body80valid