Details

Time bar (total: 14.3s)

sample508.0ms

Algorithm
intervals
Results
446.0ms3289×body80valid

simplify64.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite31.0ms

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:
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series90.0ms

Counts
4 → 10
Calls
4 calls:
22.0ms
(* (/ 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)

simplify121.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
05841144
13655959
25003912

prune690.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.6b

localize31.0ms

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

rewrite39.0ms

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:
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series81.0ms

Counts
4 → 10
Calls
4 calls:
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
27.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify108.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
05351295
133211109
25001969

prune888.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (+ (+ (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 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)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite3.3s

Algorithm
rewrite-expression-head
Rules
216×frac-add
181×associate-*l/
154×frac-times
116×times-frac
87×add-sqr-sqrt
83×associate-/l/
74×add-cube-cbrt *-un-lft-identity
64×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 → 273
Calls
4 calls:
3.3s
(/ (* (+ (+ (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 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)))))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series704.0ms

Counts
4 → 10
Calls
4 calls:
644.0ms
(/ (* (+ (+ (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 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)))))
27.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify94.0ms

Algorithm
egg-herbie
Counts
283 → 283
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
022476406
150015835

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))
0.3b
(/ 1 (pow (fabs x) 3))
0.3b
(* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))
0.4b
(* (sqrt (/ 1 PI)) (* (exp (pow (fabs x) 2)) (+ (+ (+ (* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3))))))

rewrite782.0ms

Algorithm
rewrite-expression-head
Rules
214×times-frac
182×unpow-prod-down
166×add-sqr-sqrt
130×add-cube-cbrt *-un-lft-identity
82×associate-*r*
63×associate-*r/
61×sqrt-prod
52×add-exp-log
50×sqr-pow
36×frac-add
24×div-exp
19×associate-*l* associate-/r*
18×add-cbrt-cube unpow2
16×unswap-sqr
15×pow-to-exp pow-exp
14×associate-/l*
13×sqrt-div prod-exp
12×frac-times cube-prod
11×pow1
10×flip3-+ un-div-inv flip-+
5×cbrt-unprod
4×distribute-rgt-in cube-mult distribute-lft-in unpow3 pow-prod-down div-inv add-log-exp
3×cbrt-undiv rec-exp 1-exp
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*l/ inv-pow
Counts
4 → 370
Calls
4 calls:
8.0ms
(/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))
5.0ms
(/ 1 (pow (fabs x) 3))
33.0ms
(* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))
715.0ms
(* (sqrt (/ 1 PI)) (* (exp (pow (fabs x) 2)) (+ (+ (+ (* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3))))))

series859.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))
34.0ms
(/ 1 (pow (fabs x) 3))
136.0ms
(* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))
572.0ms
(* (sqrt (/ 1 PI)) (* (exp (pow (fabs x) 2)) (+ (+ (+ (* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
382 → 382
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
016215758
150015168

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes262.0ms

bsearch0.0ms

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05744
15744

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.9s14008×body80valid