Details

Time bar (total: 13.8s)

sample96.0ms

Algorithm
intervals
Results
33.0ms49×body1280valid
17.0ms47×body640valid
12.0ms158×body80valid
6.0ms23×body320valid
5.0ms93×body80nan
2.0ms10×body160valid

simplify1.2s

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x y))
0.0b
(/ (pow (/ x (+ x y)) x) x)
4.8b
(pow (/ x (+ x y)) x)

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
118×*-un-lft-identity
90×unpow-prod-down
80×add-sqr-sqrt add-cube-cbrt
25×associate-/l*
19×distribute-lft-out
16×add-exp-log
12×associate-/r/
7×div-exp associate-/r* add-cbrt-cube div-inv
6×flip3-+ flip-+
5×sqr-pow
4×pow1 pow-exp
3×pow-unpow add-log-exp
2×cbrt-undiv pow-to-exp frac-2neg clear-num
1×pow-pow
Counts
3 → 172
Calls
3 calls:
20.0ms
(/ x (+ x y))
86.0ms
(/ (pow (/ x (+ x y)) x) x)
24.0ms
(pow (/ x (+ x y)) x)

series620.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(/ x (+ x y))
231.0ms
(/ (pow (/ x (+ x y)) x) x)
322.0ms
(pow (/ x (+ x y)) x)

simplify987.0ms

Counts
181 → 181

prune574.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt x) (cbrt x))
0.6b
(* (cbrt (+ x y)) (cbrt (+ x y)))
0.7b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.2b
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
85×cbrt-prod
76×*-un-lft-identity
66×add-sqr-sqrt
61×unpow-prod-down
50×add-cube-cbrt
43×times-frac
26×cbrt-div
24×add-exp-log
20×pow1
15×swap-sqr
13×flip3-+ associate-*r* associate-*l* flip-+
12×pow1/3 distribute-lft-out
10×associate-/r/
8×frac-times unswap-sqr
7×pow-exp
6×pow-unpow prod-exp
5×div-exp
4×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up add-cbrt-cube add-log-exp
2×pow2 pow-to-exp pow-pow pow-plus *-commutative cbrt-unprod div-inv sqr-pow
Counts
4 → 187
Calls
4 calls:
12.0ms
(* (cbrt x) (cbrt x))
39.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
38.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
49.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.3s

Counts
4 → 12
Calls
4 calls:
272.0ms
(* (cbrt x) (cbrt x))
265.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
395.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
355.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify1.0s

Counts
199 → 199

prune577.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ x y))
0.7b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
0.7b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
0.7b
(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
144×unpow-prod-down
139×cbrt-prod
127×*-un-lft-identity
126×times-frac
89×add-sqr-sqrt add-cube-cbrt
19×distribute-lft-out
13×add-exp-log
9×pow-unpow
8×cbrt-div
7×pow1
6×pow-exp associate-/r/
4×flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow-to-exp pow-pow div-exp div-inv sqr-pow
1×pow1/3
Counts
4 → 203
Calls
4 calls:
5.0ms
(cbrt (+ x y))
23.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
19.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
38.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

series1.3s

Counts
4 → 12
Calls
4 calls:
181.0ms
(cbrt (+ x y))
403.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
379.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
357.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify645.0ms

Counts
215 → 215

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x y))
0.0b
(/ (sqrt (pow (/ x (+ x y)) x)) (/ x (sqrt (pow (/ x (+ x y)) x))))
4.8b
(pow (/ x (+ x y)) x)
4.8b
(pow (/ x (+ x y)) x)

rewrite796.0ms

Algorithm
rewrite-expression-head
Rules
5857×times-frac
3476×sqrt-prod
3255×*-un-lft-identity
2880×unpow-prod-down
2287×add-sqr-sqrt add-cube-cbrt
484×distribute-lft-out
323×associate-/r/
188×div-inv
161×flip3-+ flip-+
160×sqr-pow
83×associate-/r*
28×associate-/l*
17×add-exp-log
11×add-cbrt-cube
6×pow1 pow-unpow div-exp
4×cbrt-undiv pow-exp add-log-exp
2×pow-to-exp pow-pow frac-2neg clear-num
Counts
4 → 2193
Calls
4 calls:
26.0ms
(/ x (+ x y))
211.0ms
(/ (sqrt (pow (/ x (+ x y)) x)) (/ x (sqrt (pow (/ x (+ x y)) x))))
22.0ms
(pow (/ x (+ x y)) x)
16.0ms
(pow (/ x (+ x y)) x)

series826.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ x (+ x y))
178.0ms
(/ (sqrt (pow (/ x (+ x y)) x)) (/ x (sqrt (pow (/ x (+ x y)) x))))
245.0ms
(pow (/ x (+ x y)) x)
348.0ms
(pow (/ x (+ x y)) x)

simplify2.2s