Details

Time bar (total: 12.4s)

sample387.0ms

Algorithm
intervals
Results
328.0ms3132×body80valid

simplify70.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

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: 1.4b

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)

rewrite32.0ms

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)
8.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series94.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
38.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify126.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
05841144
13655959
25001912

prune681.0ms

Filtered
182 candidates to 100 candidates (54.9%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New16319182
Fresh011
Picked101
Done000
Total16420184

Merged error: 0.6b

Counts
184 → 20

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:
10.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series85.0ms

Counts
4 → 10
Calls
4 calls:
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
28.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify110.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
05351298
133211112
25001972

prune875.0ms

Filtered
203 candidates to 119 candidates (58.6%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New19112203
Fresh10919
Picked101
Done000
Total20221223

Merged error: 0.4b

Counts
223 → 21

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

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/
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
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:
104.0ms
(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (pow (fabs x) 3))) (+ (/ 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)))))
11.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series496.0ms

Counts
4 → 10
Calls
4 calls:
440.0ms
(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (pow (fabs x) 3))) (+ (/ 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)))))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify82.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
017084889
150014385

prune1.4s

Filtered
251 candidates to 174 candidates (69.3%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New23813251
Fresh17320
Picked101
Done000
Total25616272

Merged error: 0.1b

Counts
272 → 16

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
88×frac-add
78×times-frac
74×add-sqr-sqrt
67×associate-*r/
62×*-un-lft-identity
59×add-cube-cbrt
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*
18×div-exp add-cbrt-cube
14×flip3-+ associate-/r* flip-+
13×prod-exp sqrt-prod sqr-pow
11×pow1
9×pow-to-exp rec-exp 1-exp pow-exp
7×unswap-sqr
6×associate-/l*
5×cbrt-unprod
4×pow-prod-down div-inv add-log-exp
3×cbrt-undiv
2×pow-flip frac-2neg clear-num *-commutative inv-pow
Counts
4 → 240
Calls
4 calls:
5.0ms
(/ 1 (pow (fabs x) 7))
11.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
5.0ms
(/ 1 (pow (fabs x) 5))
33.0ms
(* (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))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ 1 (pow (fabs x) 7))
55.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
49.0ms
(/ 1 (pow (fabs x) 5))
397.0ms
(* (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))))

simplify74.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012224431
150014150

prune867.0ms

Filtered
252 candidates to 131 candidates (52.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2484252
Fresh9615
Picked101
Done000
Total25810268

Merged error: 0.1b

Counts
268 → 10

regimes181.0ms

bsearch0.0ms

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04224
14224

end0.0ms

sample5.9s

Algorithm
intervals
Results
5.2s51621×body80valid

Profiling

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