Details

Time bar (total: 14.5s)

sample348.0ms

Algorithm
intervals
Results
274.0ms3514×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: 1.5b

localize31.0ms

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)

rewrite41.0ms

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:
21.0ms
(* (/ 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)

series87.0ms

Counts
4 → 10
Calls
4 calls:
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
30.0ms
(pow (/ 1.0 (fabs x)) 3)
35.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify124.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
05841144
13655959
25003912

prune683.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.6b

localize27.0ms

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)

rewrite61.0ms

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:
21.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series80.0ms

Counts
4 → 10
Calls
4 calls:
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
35.0ms
(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

prune869.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (+ (+ (* (* (* (* 1.0 1.0) (/ 1 (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3))) (+ (/ 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)

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
162×frac-add
119×associate-*l/
116×times-frac
96×frac-times
87×add-sqr-sqrt
74×add-cube-cbrt *-un-lft-identity
63×associate-/l/
58×associate-*r/
31×add-cbrt-cube
29×add-exp-log
22×associate-/r*
21×sqrt-prod
20×un-div-inv
13×pow1 unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
11×cbrt-undiv div-exp
9×div-inv
8×flip3-+ flip-+
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 → 253
Calls
4 calls:
2.9s
(/ (* (+ (+ (* (* (* (* 1.0 1.0) (/ 1 (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3))) (+ (/ 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)))))
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series458.0ms

Counts
4 → 10
Calls
4 calls:
401.0ms
(/ (* (+ (+ (* (* (* (* 1.0 1.0) (/ 1 (pow (fabs x) 2))) (/ 1.0 (pow (fabs x) 3))) (+ (/ 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)))))
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
35.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify81.0ms

Algorithm
egg-herbie
Counts
263 → 263
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
016455342
150014829

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1.875 (/ 1 (pow (fabs x) 7)))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 5)))
0.3b
(/ 1 (pow (fabs x) 7))
0.5b
(* (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))))

rewrite852.0ms

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:
22.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
21.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
8.0ms
(/ 1 (pow (fabs x) 7))
788.0ms
(* (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))))

series533.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
51.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
57.0ms
(/ 1 (pow (fabs x) 7))
362.0ms
(* (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))))

simplify66.0ms

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013554483
150024187

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes168.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04325
14325

end0.0ms

sample4.2s

Algorithm
intervals
Results
3.5s45843×body80valid