Details

Time bar (total: 10.0m)

sample50.0ms

Algorithm
intervals
Results
15.0ms52×body1280valid
10.0ms47×body640valid
8.0ms129×body80valid
2.0ms15×body320valid
1.0ms13×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
11213
21613
31913
42113
52713
63913
75813
87913
918313
1053513
11170613
12358413
done500013

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ 1.0 x) (- x 1.0))
3.4b
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
22.0ms
(/ x (+ x 1.0))
48.0ms
(/ (+ 1.0 x) (- x 1.0))
171.0ms
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

series278.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(/ x (+ x 1.0))
49.0ms
(/ (+ 1.0 x) (- x 1.0))
172.0ms
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

simplify996.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (290.0ms)

IterNodesCost
01861584
14481503
219021427
done50001427

prune344.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ 1.0 x))
0.2b
(cbrt (+ 1.0 x))
0.2b
(cbrt (+ 1.0 x))
20.6b
(- (/ x (+ x 1.0)) (* (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))) (/ (cbrt (+ 1.0 x)) (- x 1.0))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-div
17×frac-sub
16×frac-times
15×flip3-+ flip-+
13×*-un-lft-identity
12×cbrt-prod associate-*l/
7×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×associate-*r/
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3 distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
4 → 71
Calls
4 calls:
4.0ms
(cbrt (+ 1.0 x))
4.0ms
(cbrt (+ 1.0 x))
4.0ms
(cbrt (+ 1.0 x))
86.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))) (/ (cbrt (+ 1.0 x)) (- x 1.0))))

series621.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(cbrt (+ 1.0 x))
142.0ms
(cbrt (+ 1.0 x))
138.0ms
(cbrt (+ 1.0 x))
204.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))) (/ (cbrt (+ 1.0 x)) (- x 1.0))))

simplify1.0s

Counts
83 → 83
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02102230
15512128
221361895
done50011796

prune343.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (+ (* 1.0 1.0) (* x (- x 1.0))))
15.0b
(cbrt (- (* 1.0 1.0) (* x x)))
20.4b
(cbrt (+ (pow 1.0 3) (pow x 3)))
25.2b
(- (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (+ 1.0 x)))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
7098×cbrt-div
5776×frac-times
4020×associate-*r/
2828×flip3-+ flip-+
2264×associate-*l/
2144×flip3-- flip--
2080×frac-sub
17×*-un-lft-identity
16×cbrt-prod
8×distribute-rgt-in distribute-lft-in associate--l+
7×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×sub-neg distribute-lft-out
4×pow1 add-exp-log unpow-prod-down cube-prod add-cbrt-cube
3×pow1/3
1×diff-log sum-cubes difference-of-squares
Counts
4 → 2146
Calls
4 calls:
5.0ms
(cbrt (+ (* 1.0 1.0) (* x (- x 1.0))))
6.0ms
(cbrt (- (* 1.0 1.0) (* x x)))
18.0ms
(cbrt (+ (pow 1.0 3) (pow x 3)))
569.0ms
(- (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (+ 1.0 x)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
176.0ms
(cbrt (+ (* 1.0 1.0) (* x (- x 1.0))))
355.0ms
(cbrt (- (* 1.0 1.0) (* x x)))
598.0ms
(cbrt (+ (pow 1.0 3) (pow x 3)))
458.0ms
(- (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (+ 1.0 x)))))

simplify4.9s

Counts
2158 → 2158
Iterations

Useful iterations: 0 (1.5s)

IterNodesCost
08871402602
done8871402602

prune48.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (- (* 1.0 1.0) (* x x)))
15.1b
(/ (- (* (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- (pow x 3) (pow 1.0 3)))) (cbrt (- 1.0 x))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (- (* 1.0 1.0) (* x x))))))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (cbrt (- 1.0 x))))
20.4b
(cbrt (+ (pow 1.0 3) (pow x 3)))
29.1b
(- (* (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- (pow x 3) (pow 1.0 3)))) (cbrt (- 1.0 x))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (- (* 1.0 1.0) (* x x)))))))

rewrite25.9s

Algorithm
rewrite-expression-head
Rules
156708×frac-times
156178×cbrt-div
87138×associate-*r/
65130×flip3-- flip--
54354×associate-*l/
51952×flip3-+ flip-+
38720×frac-sub
19362×associate-/l/
18×*-un-lft-identity
13×cbrt-prod
9×add-exp-log
8×add-sqr-sqrt add-cube-cbrt associate-/r/ add-cbrt-cube
6×add-log-exp
5×distribute-lft-out
4×pow1 unpow-prod-down cube-prod
3×times-frac associate-/l*
2×cbrt-undiv pow1/3 div-exp
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* sum-cubes cbrt-unprod div-inv difference-of-squares
Counts
4 → 38797
Calls
4 calls:
6.0ms
(cbrt (- (* 1.0 1.0) (* x x)))
6.8s
(/ (- (* (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- (pow x 3) (pow 1.0 3)))) (cbrt (- 1.0 x))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (- (* 1.0 1.0) (* x x))))))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (cbrt (- 1.0 x))))
33.0ms
(cbrt (+ (pow 1.0 3) (pow x 3)))
3.2s
(- (* (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- (pow x 3) (pow 1.0 3)))) (cbrt (- 1.0 x))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (- (* 1.0 1.0) (* x x)))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
199.0ms
(cbrt (- (* 1.0 1.0) (* x x)))
583.0ms
(/ (- (* (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- (pow x 3) (pow 1.0 3)))) (cbrt (- 1.0 x))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (- (* 1.0 1.0) (* x x))))))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (cbrt (- 1.0 x))))
399.0ms
(cbrt (+ (pow 1.0 3) (pow x 3)))
409.0ms
(- (* (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- (pow x 3) (pow 1.0 3)))) (cbrt (- 1.0 x))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (- (* 1.0 1.0) (* x x)))))))

simplify40.6s

Counts
38809 → 38809
Iterations

Useful iterations: 0 (12.8s)

IterNodesCost
0894687756447
done894687756447

prune7.8m