Details

Time bar (total: 47.1s)

sample995.0ms

Algorithm
intervals
Results
878.0ms4060×body80valid

simplify1.2s

Counts
1 → 1

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize93.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite80.0ms

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:
47.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
8.0ms
(pow (/ 1.0 (fabs x)) 3)
7.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series143.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms
(pow (/ 1.0 (fabs x)) 3)
65.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify2.3s

Counts
182 → 182

prune1.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

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)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite105.0ms

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:
25.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
49.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series108.0ms

Counts
4 → 10
Calls
4 calls:
30.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
26.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
53.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.9s

Counts
203 → 203

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite914.0ms

Algorithm
rewrite-expression-head
Rules
386×add-exp-log add-cbrt-cube
235×prod-exp cbrt-unprod
90×cbrt-undiv div-exp
74×frac-times
62×add-sqr-sqrt
58×times-frac
49×add-cube-cbrt *-un-lft-identity
46×associate-*l/
32×associate-*r/
24×frac-add
22×pow1
16×associate-*r*
14×associate-*l*
13×unpow-prod-down cube-prod swap-sqr
8×flip3-+ flip-+
7×pow-prod-down
6×div-inv
4×add-log-exp unswap-sqr
3×pow-unpow sqrt-prod
2×pow-exp *-commutative rem-cube-cbrt
1×cube-div pow2 distribute-rgt-in cube-mult pow-to-exp rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow-plus pow1/2 unpow3 pow-sqr pow-prod-up sqr-pow
Counts
4 → 292
Calls
4 calls:
818.0ms
(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
48.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series254.0ms

Counts
4 → 10
Calls
4 calls:
172.0ms
(* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (/ 1.0 (pow (fabs x) 2)) (/ 15.0 8.0))))
46.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
35.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify840.0ms

Counts
302 → 302

prune1.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (pow 1.0 4)) 1.0) (* (pow (fabs x) 6) (* (fabs x) (* 4.0 8.0))))
0.3b
(/ (* (+ (+ (/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (pow 1.0 4)) 1.0) (* (pow (fabs x) 6) (* (fabs x) (* 4.0 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)))))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
252×add-exp-log
162×prod-exp
77×times-frac
73×add-cbrt-cube
57×div-exp
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
32×cbrt-unprod
27×pow-exp
26×pow-to-exp
23×associate-/r*
21×sqrt-prod
19×cbrt-undiv
13×unpow-prod-down cube-prod
9×associate-*l/
7×associate-/l/
6×pow1 div-inv
4×frac-add add-log-exp
3×pow-unpow flip3-+ flip-+
2×frac-2neg clear-num associate-/l* rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 associate-/r/ sqr-pow
Counts
4 → 205
Calls
4 calls:
182.0ms
(/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (pow 1.0 4)) 1.0) (* (pow (fabs x) 6) (* (fabs x) (* 4.0 8.0))))
3.8s
(/ (* (+ (+ (/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (pow 1.0 4)) 1.0) (* (pow (fabs x) 6) (* (fabs x) (* 4.0 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)))))
14.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series1.0s

Counts
4 → 10
Calls
4 calls:
261.0ms
(/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (pow 1.0 4)) 1.0) (* (pow (fabs x) 6) (* (fabs x) (* 4.0 8.0))))
681.0ms
(/ (* (+ (+ (/ (* (* (+ (* 3.0 (* (pow (fabs x) 2) 8.0)) (* 4.0 (* 1.0 15.0))) (pow 1.0 4)) 1.0) (* (pow (fabs x) 6) (* (fabs x) (* 4.0 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)))))
69.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify792.0ms

Counts
215 → 215

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes303.0ms

bsearch0.0ms

simplify735.0ms

end0.0ms

sample25.5s

Algorithm
intervals
Results
23.2s88915×body80valid