Details

Time bar (total: 23.9s)

sample848.0ms

Algorithm
intervals
Results
716.0ms3515×body80valid

simplify64.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt times-frac
63×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down cube-prod
22×add-exp-log add-cbrt-cube
14×pow1
13×swap-sqr associate-*r* associate-*l*
8×div-inv
6×cbrt-undiv pow-unpow div-exp
4×pow-exp prod-exp cbrt-unprod add-log-exp rem-cube-cbrt unswap-sqr
3×sqrt-prod
2×cube-div cube-mult pow-to-exp pow-pow unpow3 sqr-pow
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up
Counts
4 → 172
Calls
4 calls:
20.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series80.0ms

Counts
4 → 10
Calls
4 calls:
21.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms
(pow (/ 1.0 (fabs x)) 3)
29.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify124.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
05841144
13655959
25003912

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
98×times-frac
76×add-cube-cbrt *-un-lft-identity
31×add-exp-log add-cbrt-cube
26×swap-sqr associate-*r* associate-*l*
20×pow1
13×unpow-prod-down cube-prod
10×div-inv
9×cbrt-undiv div-exp
8×prod-exp cbrt-unprod unswap-sqr
4×add-log-exp
3×pow-unpow sqrt-prod
2×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ pow-exp pow-sqr *-commutative pow-prod-up rem-cube-cbrt
1×cube-div cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 sqr-pow
Counts
4 → 193
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
20.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series78.0ms

Counts
4 → 10
Calls
4 calls:
21.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
27.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify132.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
05911333
137711145
250011075

prune2.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (* (* 1.0 1.0) (/ 1.0 (pow (fabs x) 3)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0))))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite361.0ms

Algorithm
rewrite-expression-head
Rules
247×add-exp-log
143×prod-exp add-cbrt-cube
79×cbrt-unprod
65×div-exp
62×add-sqr-sqrt
58×frac-times times-frac
52×associate-*r/
49×add-cube-cbrt *-un-lft-identity
34×associate-*l/
33×cbrt-undiv
28×frac-add
27×pow1
16×associate-*r*
14×associate-*l*
13×unpow-prod-down cube-prod swap-sqr
11×pow-prod-down
10×pow-exp
9×pow-to-exp
6×div-inv
4×flip3-+ flip-+ add-log-exp unswap-sqr
3×pow-unpow sqrt-prod
2×*-commutative rem-cube-cbrt
1×cube-div pow2 distribute-rgt-in cube-mult rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow-plus pow1/2 unpow3 pow-sqr pow-prod-up sqr-pow
Counts
4 → 241
Calls
4 calls:
315.0ms
(* (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (* (* 1.0 1.0) (/ 1.0 (pow (fabs x) 3)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0))))
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series173.0ms

Counts
4 → 10
Calls
4 calls:
111.0ms
(* (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (* (* 1.0 1.0) (/ 1.0 (pow (fabs x) 3)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0))))
21.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify75.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
018694214
150013243

prune2.1s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (* 1.0 (/ 1.0 (fabs x))) (* (pow 1.0 3) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))))) (* (pow (fabs x) 6) 4.0))
0.4b
(/ (* (+ (+ (/ (* (* 1.0 (/ 1.0 (fabs x))) (* (pow 1.0 3) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))))) (* (pow (fabs x) 6) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
267×add-exp-log
157×prod-exp
84×add-cbrt-cube
77×times-frac
75×div-exp
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
35×cbrt-unprod
27×pow-exp
26×pow-to-exp
25×cbrt-undiv
23×associate-/r*
21×sqrt-prod
13×unpow-prod-down cube-prod
10×associate-/l/
9×associate-*r/
6×pow1 associate-*l/ div-inv
4×flip3-+ frac-add flip-+ add-log-exp
3×pow-unpow
2×frac-times frac-2neg clear-num associate-/l* rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 associate-/r/ sqr-pow
Counts
4 → 212
Calls
4 calls:
94.0ms
(/ (* (* 1.0 (/ 1.0 (fabs x))) (* (pow 1.0 3) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))))) (* (pow (fabs x) 6) 4.0))
1.5s
(/ (* (+ (+ (/ (* (* 1.0 (/ 1.0 (fabs x))) (* (pow 1.0 3) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))))) (* (pow (fabs x) 6) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
8.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series580.0ms

Counts
4 → 10
Calls
4 calls:
156.0ms
(/ (* (* 1.0 (/ 1.0 (fabs x))) (* (pow 1.0 3) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))))) (* (pow (fabs x) 6) 4.0))
394.0ms
(/ (* (+ (+ (/ (* (* 1.0 (/ 1.0 (fabs x))) (* (pow 1.0 3) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))))) (* (pow (fabs x) 6) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
29.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify72.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
014065748
150015008

prune1.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes498.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample11.0s

Algorithm
intervals
Results
10.3s49789×body80valid