Details

Time bar (total: 11.3s)

sample296.0ms

Algorithm
intervals
Results
242.0ms3083×body80valid

simplify64.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 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)

rewrite30.0ms

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:
16.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series91.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms
(pow (/ 1.0 (fabs x)) 3)
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify119.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
05841144
13655959
25003912

prune686.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite37.0ms

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:
12.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
12.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series84.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
27.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify105.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
05351295
133211109
25001969

prune887.0ms

Pruning

23 alts after pruning (22 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 (fabs x))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
386×add-exp-log add-cbrt-cube
235×prod-exp cbrt-unprod
90×cbrt-undiv div-exp
74×frac-times
62×add-sqr-sqrt
58×times-frac
49×add-cube-cbrt *-un-lft-identity
46×associate-*l/
32×associate-*r/
24×frac-add
22×pow1
16×associate-*r*
14×associate-*l*
13×unpow-prod-down cube-prod swap-sqr
8×flip3-+ flip-+
7×pow-prod-down
6×div-inv
4×add-log-exp unswap-sqr
3×pow-unpow sqrt-prod
2×pow-exp *-commutative rem-cube-cbrt
1×cube-div pow2 distribute-rgt-in cube-mult pow-to-exp rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow-plus pow1/2 unpow3 pow-sqr pow-prod-up sqr-pow
Counts
4 → 292
Calls
4 calls:
239.0ms
(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series185.0ms

Counts
4 → 10
Calls
4 calls:
130.0ms
(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify80.0ms

Algorithm
egg-herbie
Counts
302 → 302
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
020785873
150013776

prune993.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* (+ (+ (/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (/ 1.0 (fabs x))) (pow 1.0 4)) (* (pow (fabs x) 6) (* 4.0 8.0))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.4b
(/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (/ 1.0 (fabs x))) (pow 1.0 4)) (* (pow (fabs x) 6) (* 4.0 8.0)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
332×add-exp-log
197×prod-exp
98×div-exp
77×times-frac
73×add-cbrt-cube
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
43×pow-exp
42×pow-to-exp
29×cbrt-unprod
23×associate-/r*
22×cbrt-undiv
21×sqrt-prod
13×unpow-prod-down cube-prod
12×associate-*l/
10×associate-/l/
6×pow1 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/ associate-/r/ sqr-pow
Counts
4 → 228
Calls
4 calls:
1.4s
(/ (* (+ (+ (/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (/ 1.0 (fabs x))) (pow 1.0 4)) (* (pow (fabs x) 6) (* 4.0 8.0))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
43.0ms
(/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (/ 1.0 (fabs x))) (pow 1.0 4)) (* (pow (fabs x) 6) (* 4.0 8.0)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series620.0ms

Counts
4 → 10
Calls
4 calls:
421.0ms
(/ (* (+ (+ (/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (/ 1.0 (fabs x))) (pow 1.0 4)) (* (pow (fabs x) 6) (* 4.0 8.0))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
167.0ms
(/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (/ 1.0 (fabs x))) (pow 1.0 4)) (* (pow (fabs x) 6) (* 4.0 8.0)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify75.0ms

Algorithm
egg-herbie
Counts
238 → 238
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013775584
150024941

prune796.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes196.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample4.1s

Algorithm
intervals
Results
3.5s45233×body80valid