Details

Time bar (total: 13.9s)

sample16.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055
175
2105
done105

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(- x (/ 1.0 3.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
3×*-un-lft-identity add-log-exp
2×difference-of-squares
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- times-frac diff-log add-cbrt-cube flip-- distribute-lft-out--
Counts
1 → 15
Calls
1 calls:
10.0ms
(- x (/ 1.0 3.0))

series39.0ms

Counts
1 → 3
Calls
1 calls:
39.0ms
(- x (/ 1.0 3.0))

simplify3.0s

Counts
18 → 18
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
038161
182156
2176146
3402146
41057146
53360146
done5000146

prune31.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (/ 1.0 3.0))
0.0b
(- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0)))
13.1b
(/ (- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ x (/ 1.0 3.0)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
16×times-frac
13×add-sqr-sqrt add-cube-cbrt
7×add-log-exp
6×distribute-lft-out difference-of-squares
5×add-exp-log add-cbrt-cube
4×associate-/r* associate-/l*
3×pow1
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 66
Calls
3 calls:
11.0ms
(+ x (/ 1.0 3.0))
8.0ms
(- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0)))
54.0ms
(/ (- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ x (/ 1.0 3.0)))

series207.0ms

Counts
3 → 9
Calls
3 calls:
21.0ms
(+ x (/ 1.0 3.0))
60.0ms
(- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0)))
125.0ms
(/ (- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ x (/ 1.0 3.0)))

simplify3.6s

Counts
75 → 75
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01041479
12751402
29661282
336871118
done50001024

prune289.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 3.0) (- (/ 1.0 3.0) x))
1.0b
(pow (/ 1.0 3.0) 3)
13.1b
(/ (- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0))) (/ (+ (pow x 3) (pow (/ 1.0 3.0) 3)) (+ (* (/ 1.0 3.0) (- (/ 1.0 3.0) x)) (* x x))))
17.7b
(/ (+ (pow x 3) (pow (/ 1.0 3.0) 3)) (+ (* (/ 1.0 3.0) (- (/ 1.0 3.0) x)) (* x x)))

rewrite516.0ms

Algorithm
rewrite-expression-head
Rules
332×*-un-lft-identity
323×times-frac
150×add-sqr-sqrt
140×add-cube-cbrt
95×distribute-lft-out
89×unpow-prod-down cube-prod
36×associate-/r* difference-of-squares
19×add-exp-log sum-cubes add-cbrt-cube
13×associate-*l* associate-/r/ associate-/l*
10×div-inv
7×pow1 flip3-+ flip-+
6×cbrt-undiv div-exp associate-*r*
4×associate-/l/ add-log-exp
3×pow-unpow flip3-- flip--
2×distribute-rgt-in frac-times sub-neg frac-2neg distribute-lft-in associate-*r/ pow-exp prod-exp clear-num cbrt-unprod rem-cube-cbrt unswap-sqr
1×cube-div cube-mult pow-to-exp pow-pow unpow3 div-sub pow-prod-down associate-*l/ *-commutative distribute-lft-out-- sqr-pow
Counts
4 → 331
Calls
4 calls:
74.0ms
(* (/ 1.0 3.0) (- (/ 1.0 3.0) x))
7.0ms
(pow (/ 1.0 3.0) 3)
228.0ms
(/ (- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0))) (/ (+ (pow x 3) (pow (/ 1.0 3.0) 3)) (+ (* (/ 1.0 3.0) (- (/ 1.0 3.0) x)) (* x x))))
186.0ms
(/ (+ (pow x 3) (pow (/ 1.0 3.0) 3)) (+ (* (/ 1.0 3.0) (- (/ 1.0 3.0) x)) (* x x)))

series566.0ms

Counts
4 → 10
Calls
4 calls:
50.0ms
(* (/ 1.0 3.0) (- (/ 1.0 3.0) x))
0.0ms
(pow (/ 1.0 3.0) 3)
312.0ms
(/ (- (* x x) (* (/ 1.0 3.0) (/ 1.0 3.0))) (/ (+ (pow x 3) (pow (/ 1.0 3.0) 3)) (+ (* (/ 1.0 3.0) (- (/ 1.0 3.0) x)) (* x x))))
204.0ms
(/ (+ (pow x 3) (pow (/ 1.0 3.0) 3)) (+ (* (/ 1.0 3.0) (- (/ 1.0 3.0) x)) (* x x)))

simplify1.0s

Counts
341 → 341
Iterations

Useful iterations: done (994.0ms)

IterNodesCost
043514500
1125313795
done500013117

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow x 2) (pow (/ 1.0 3.0) 2))
0.1b
(* (+ (pow x 2) (pow (/ 1.0 3.0) 2)) (+ (/ 1.0 3.0) x))
0.2b
(* (* x x) (* x x))
18.9b
(/ (- (* (* x x) (* x x)) (* (* (/ 1.0 3.0) (/ 1.0 3.0)) (* (/ 1.0 3.0) (/ 1.0 3.0)))) (* (+ (pow x 2) (pow (/ 1.0 3.0) 2)) (+ (/ 1.0 3.0) x)))

rewrite503.0ms

Algorithm
rewrite-expression-head
Rules
117×pow1
36×pow-prod-up
24×pow-prod-down
23×add-exp-log add-cbrt-cube
22×pow-sqr
18×*-un-lft-identity pow-plus
13×pow2 flip3-+ flip-+
10×add-sqr-sqrt prod-exp cbrt-unprod
8×frac-times add-cube-cbrt associate-/r/
6×associate-*l* add-log-exp
5×associate-*r* distribute-lft-out
4×unpow-prod-down times-frac associate-*r/ associate-*l/ associate-/l*
2×cbrt-undiv div-exp *-commutative associate-/l/ difference-of-squares unswap-sqr
1×+-commutative distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub swap-sqr clear-num associate-/r* sum-log flip-- div-inv
Counts
4 → 141
Calls
4 calls:
37.0ms
(+ (pow x 2) (pow (/ 1.0 3.0) 2))
219.0ms
(* (+ (pow x 2) (pow (/ 1.0 3.0) 2)) (+ (/ 1.0 3.0) x))
40.0ms
(* (* x x) (* x x))
201.0ms
(/ (- (* (* x x) (* x x)) (* (* (/ 1.0 3.0) (/ 1.0 3.0)) (* (/ 1.0 3.0) (/ 1.0 3.0)))) (* (+ (pow x 2) (pow (/ 1.0 3.0) 2)) (+ (/ 1.0 3.0) x)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(+ (pow x 2) (pow (/ 1.0 3.0) 2))
42.0ms
(* (+ (pow x 2) (pow (/ 1.0 3.0) 2)) (+ (/ 1.0 3.0) x))
61.0ms
(* (* x x) (* x x))
299.0ms
(/ (- (* (* x x) (* x x)) (* (* (/ 1.0 3.0) (/ 1.0 3.0)) (* (/ 1.0 3.0) (/ 1.0 3.0)))) (* (+ (pow x 2) (pow (/ 1.0 3.0) 2)) (+ (/ 1.0 3.0) x)))

simplify1.7s

Counts
153 → 153
Iterations

Useful iterations: 2 (553.0ms)

IterNodesCost
01863271
15542274
227571944
done50001944

prune542.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes1.0ms