Details

Time bar (total: 9.7s)

sample341.0ms

Algorithm
intervals
Results
279.0ms3561×body80valid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize26.0ms

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)

rewrite33.0ms

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:
17.0ms
(* (/ 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)

series93.0ms

Counts
4 → 10
Calls
4 calls:
28.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify125.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
05841144
13655959
25003912

prune711.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

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)

rewrite44.0ms

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:
17.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms
(* (/ 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:
28.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify107.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
05351298
133211112
25001972

prune976.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ 15.0 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)))))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
120×frac-add
116×times-frac
97×associate-*l/
87×add-sqr-sqrt
74×frac-times add-cube-cbrt *-un-lft-identity
51×associate-/l/
48×associate-*r/
31×add-cbrt-cube
29×add-exp-log
22×associate-/r*
21×sqrt-prod
13×pow1 unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
11×cbrt-undiv div-exp
10×flip3-+ flip-+
9×div-inv
6×prod-exp cbrt-unprod
4×add-log-exp unswap-sqr
3×pow-unpow
2×pow-exp rem-cube-cbrt
1×cube-div pow2 cube-mult pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow-plus pow1/2 unpow3 pow-prod-down clear-num associate-/r/ pow-sqr *-commutative pow-prod-up associate-/l* sqr-pow
Counts
4 → 241
Calls
4 calls:
1.7s
(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ 15.0 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)))))
17.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series500.0ms

Counts
4 → 10
Calls
4 calls:
444.0ms
(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ 15.0 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)))))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify84.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
017125102
150014568

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1.875 (/ 1 (pow (fabs x) 7)))
0.3b
(* (sqrt (/ 1 PI)) (* (+ (+ (+ (* 1.875 (/ 1 (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ 1 (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3)))) (exp (pow (fabs x) 2))))
0.3b
(/ 1 (pow (fabs x) 7))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 5)))

rewrite587.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt frac-add
84×times-frac
68×associate-*r/
64×*-un-lft-identity
58×add-cube-cbrt
57×add-exp-log
51×associate-*r*
46×un-div-inv
45×associate-*l/
34×unpow-prod-down
23×sqrt-div prod-exp
22×frac-times associate-*l*
21×add-cbrt-cube
18×div-exp
14×flip3-+ flip-+ unswap-sqr sqr-pow
13×pow1 sqrt-prod
9×pow-to-exp rec-exp 1-exp pow-exp
7×associate-/r* cbrt-unprod
5×pow-prod-down
4×div-inv add-log-exp
3×cbrt-undiv *-commutative associate-/l*
1×pow-flip frac-2neg clear-num inv-pow
Counts
4 → 245
Calls
4 calls:
14.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
538.0ms
(* (sqrt (/ 1 PI)) (* (+ (+ (+ (* 1.875 (/ 1 (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ 1 (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3)))) (exp (pow (fabs x) 2))))
4.0ms
(/ 1 (pow (fabs x) 7))
14.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))

series575.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
387.0ms
(* (sqrt (/ 1 PI)) (* (+ (+ (+ (* 1.875 (/ 1 (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ 1 (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3)))) (exp (pow (fabs x) 2))))
67.0ms
(/ 1 (pow (fabs x) 7))
51.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))

simplify68.0ms

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013554483
150014187

prune962.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes192.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04325
14325

end0.0ms

sample716.0ms

Algorithm
intervals
Results
607.0ms7824×body80valid