Details

Time bar (total: 8.0s)

sample321.0ms

Algorithm
intervals
Results
266.0ms3289×body80valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune18.0ms

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: 1.4b

Counts
2 → 2

localize28.0ms

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:
11.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series95.0ms

Counts
4 → 10
Calls
4 calls:
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
38.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify131.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
05841144
13655959
25003912

prune737.0ms

Filtered
182 candidates to 100 candidates (54.9%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New16022182
Fresh011
Picked101
Done000
Total16123184

Merged error: 0.6b

Counts
184 → 23

localize30.0ms

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:
11.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
12.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series85.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify114.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
05351295
133211109
25001969

prune916.0ms

Filtered
203 candidates to 119 candidates (58.6%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New1949203
Fresh71522
Picked101
Done000
Total20224226

Merged error: 0.5b

Counts
226 → 24

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (+ (+ (* (* (/ 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)

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
116×times-frac
108×frac-add
87×add-sqr-sqrt
77×associate-*l/
74×add-cube-cbrt *-un-lft-identity
58×frac-times
43×associate-/l/
32×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
9×div-inv
6×flip3-+ prod-exp cbrt-unprod flip-+
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 → 233
Calls
4 calls:
111.0ms
(/ (* (+ (+ (* (* (/ 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)))))
12.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series500.0ms

Counts
4 → 10
Calls
4 calls:
443.0ms
(/ (* (+ (+ (* (* (/ 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)))))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify85.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
016555083
150014510

prune1.4s

Filtered
243 candidates to 167 candidates (68.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New22914243
Fresh21223
Picked101
Done000
Total25116267

Merged error: 0.1b

Counts
267 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (fabs x) 7))
0.3b
(/ 1 (pow (fabs x) 3))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 5)))
0.4b
(* (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))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
93×times-frac
88×frac-add
83×add-sqr-sqrt
71×*-un-lft-identity
68×add-cube-cbrt
67×associate-*r/
46×add-exp-log
45×associate-*l/ un-div-inv
35×unpow-prod-down
26×associate-*r*
23×sqrt-div
22×frac-times
19×associate-*l* associate-/r*
18×div-exp add-cbrt-cube
14×flip3-+ flip-+
13×prod-exp sqrt-prod sqr-pow
12×cube-prod
11×pow1
9×pow-to-exp rec-exp 1-exp pow-exp
7×unswap-sqr
6×associate-/l*
5×cbrt-unprod
4×cube-mult unpow3 pow-prod-down div-inv add-log-exp
3×cbrt-undiv
2×pow-flip frac-2neg clear-num *-commutative inv-pow
Counts
4 → 260
Calls
4 calls:
6.0ms
(/ 1 (pow (fabs x) 7))
6.0ms
(/ 1 (pow (fabs x) 3))
12.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
37.0ms
(* (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))))

series740.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ 1 (pow (fabs x) 7))
35.0ms
(/ 1 (pow (fabs x) 3))
55.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
584.0ms
(* (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))))

simplify78.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013404542
150014125

prune782.0ms

Filtered
272 candidates to 122 candidates (44.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2675272
Fresh8715
Picked101
Done000
Total27612288

Merged error: 0.0b

Counts
288 → 12

regimes231.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04325
14325

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s14008×body80valid