Details

Time bar (total: 11.7s)

sample342.0ms

Algorithm
intervals
Results
282.0ms3727×body80valid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune14.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

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

series97.0ms

Counts
4 → 10
Calls
4 calls:
27.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms
(pow (/ 1.0 (fabs x)) 3)
36.0ms
(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

prune681.0ms

Filtered
182 candidates to 100 candidates (54.9%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.3b

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)

rewrite37.0ms

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:
12.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
12.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(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)))
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
38.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify112.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
05351298
133211112
25001972

prune893.0ms

Filtered
203 candidates to 119 candidates (58.6%)
Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (* 1.0 (/ 1.0 (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))))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
115×add-exp-log
62×add-sqr-sqrt
61×prod-exp
58×frac-times times-frac
52×associate-*r/
49×add-cube-cbrt *-un-lft-identity
48×add-cbrt-cube
34×associate-*l/
32×div-exp
28×frac-add
22×pow1
21×cbrt-unprod
16×associate-*r*
14×associate-*l*
13×unpow-prod-down cube-prod swap-sqr
11×pow-exp
10×cbrt-undiv pow-to-exp
7×pow-prod-down
6×div-inv
4×flip3-+ flip-+ add-log-exp unswap-sqr
3×pow-unpow sqrt-prod
2×*-commutative rem-cube-cbrt
1×cube-div pow2 distribute-rgt-in cube-mult rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow-plus pow1/2 unpow3 pow-sqr pow-prod-up sqr-pow
Counts
4 → 210
Calls
4 calls:
103.0ms
(* (* (* 1.0 (/ 1.0 (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))))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series192.0ms

Counts
4 → 10
Calls
4 calls:
129.0ms
(* (* (* 1.0 (/ 1.0 (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))))
28.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify59.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
015212857
150022428

prune1.0s

Filtered
220 candidates to 129 candidates (58.6%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
76×times-frac
49×add-sqr-sqrt
48×add-cube-cbrt *-un-lft-identity
43×add-exp-log
24×add-cbrt-cube
23×prod-exp
22×associate-/r*
21×sqrt-prod
16×unpow-prod-down
13×cube-prod
9×pow-exp
8×pow-to-exp associate-*r*
7×pow1 cbrt-undiv div-exp
5×associate-*l/ cbrt-unprod div-inv associate-/l/
4×frac-add add-log-exp
3×pow-unpow pow-prod-up
2×flip3-+ flip-+ rem-cube-cbrt sqr-pow
1×cube-div cube-mult rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow-plus pow1/2 unpow3 associate-*l* clear-num associate-/r/ *-commutative associate-/l* unpow2
Counts
4 → 161
Calls
4 calls:
11.0ms
(* (* (pow (fabs x) 4) (fabs x)) (pow (fabs x) 2))
1.4s
(/ (* (+ (+ (/ (* (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))) (pow 1.0 3)) (* (* (* (pow (fabs x) 4) (fabs x)) (pow (fabs x) 2)) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series552.0ms

Counts
4 → 10
Calls
4 calls:
56.0ms
(* (* (pow (fabs x) 4) (fabs x)) (pow (fabs x) 2))
458.0ms
(/ (* (+ (+ (/ (* (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))) (pow 1.0 3)) (* (* (* (pow (fabs x) 4) (fabs x)) (pow (fabs x) 2)) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
38.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify60.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09863881
150013280

prune786.0ms

Filtered
171 candidates to 100 candidates (58.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes193.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample4.8s

Algorithm
intervals
Results
4.1s55573×body80valid