Details

Time bar (total: 7.4s)

sample316.0ms

Algorithm
intervals
Results
258.0ms3273×body80valid

simplify66.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune15.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.1b

Counts
2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 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)

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:
14.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series96.0ms

Counts
4 → 10
Calls
4 calls:
28.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify128.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
05841144
13655959
25003912

prune668.0ms

Filtered
182 candidates to 100 candidates (54.9%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New16418182
Fresh011
Picked101
Done000
Total16519184

Merged error: 0.4b

Counts
184 → 19

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.4b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite41.0ms

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:
11.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
15.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series86.0ms

Counts
4 → 10
Calls
4 calls:
29.0ms
(* (/ 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)

simplify111.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
05351295
133211109
25001969

prune869.0ms

Filtered
203 candidates to 119 candidates (58.6%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New19310203
Fresh61218
Picked101
Done000
Total20022222

Merged error: 0.2b

Counts
222 → 22

localize32.0ms

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))))
0.4b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
334×add-exp-log add-cbrt-cube
184×prod-exp cbrt-unprod
90×cbrt-undiv div-exp
63×add-sqr-sqrt
59×times-frac
49×add-cube-cbrt *-un-lft-identity
18×pow1 associate-*r*
14×associate-*l*
13×unpow-prod-down cube-prod swap-sqr
7×div-inv
6×frac-times associate-*l/
5×unswap-sqr
4×associate-*r/ pow-prod-down add-log-exp
3×pow-unpow sqrt-prod
2×pow-exp *-commutative rem-cube-cbrt
1×cube-div pow2 cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow-plus pow1/2 unpow3 pow-sqr pow-prod-up sqr-pow
Counts
4 → 250
Calls
4 calls:
28.0ms
(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x))))
11.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series116.0ms

Counts
4 → 10
Calls
4 calls:
59.0ms
(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x))))
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify51.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011122858
150011431

prune770.0ms

Filtered
260 candidates to 100 candidates (38.5%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New2528260
Fresh111021
Picked101
Done000
Total26418282

Merged error: 0.1b

Counts
282 → 18

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (* 1.0 (pow 1.0 4)) (* (fabs x) (pow (fabs x) 4))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
0.4b
(/ (* (+ (+ (* (/ (* 1.0 (pow 1.0 4)) (* (fabs x) (pow (fabs x) 4))) (+ (/ 3.0 4.0) (* (/ 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)))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
77×times-frac
51×add-sqr-sqrt
48×add-cube-cbrt *-un-lft-identity
43×prod-exp
37×add-cbrt-cube
36×frac-add
23×div-exp
22×associate-/r*
21×associate-*l/ sqrt-prod
15×associate-/l/
14×frac-times associate-*r/
13×unpow-prod-down cube-prod
11×cbrt-undiv cbrt-unprod
10×pow-exp
9×pow-to-exp
8×pow1
6×flip3-+ flip-+ div-inv
5×associate-*l*
4×add-log-exp
3×pow-unpow associate-*r*
2×rem-cube-cbrt
1×cube-div distribute-rgt-in cube-mult rem-sqrt-square pow-pow frac-2neg distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down clear-num associate-/r/ *-commutative associate-/l* unswap-sqr sqr-pow
Counts
4 → 191
Calls
4 calls:
22.0ms
(* (/ (* 1.0 (pow 1.0 4)) (* (fabs x) (pow (fabs x) 4))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
91.0ms
(/ (* (+ (+ (* (/ (* 1.0 (pow 1.0 4)) (* (fabs x) (pow (fabs x) 4))) (+ (/ 3.0 4.0) (* (/ 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)))))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series655.0ms

Counts
4 → 10
Calls
4 calls:
172.0ms
(* (/ (* 1.0 (pow 1.0 4)) (* (fabs x) (pow (fabs x) 4))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
449.0ms
(/ (* (+ (+ (* (/ (* 1.0 (pow 1.0 4)) (* (fabs x) (pow (fabs x) 4))) (+ (/ 3.0 4.0) (* (/ 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)))))
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify72.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
015084559
150013997

prune926.0ms

Filtered
201 candidates to 127 candidates (63.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1938201
Fresh13417
Picked101
Done000
Total20712219

Merged error: 0.0b

Counts
219 → 12

regimes200.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.6s20989×body80valid