Details

Time bar (total: 15.7s)

sample41.0ms

Algorithm
intervals
Results
20.0ms273×body80valid

simplify137.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12111
23711
35811
48711
511111
done11111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 2 expressions with local error:

2.8b
(* y (+ 1.0 (* z z)))
3.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
31.0ms
(* y (+ 1.0 (* z z)))
35.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series202.0ms

Counts
2 → 6
Calls
2 calls:
101.0ms
(* y (+ 1.0 (* z z)))
101.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify1.6s

Counts
76 → 76
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01561062
13951035
21322887
done5000885

prune307.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.4b
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
2.8b
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
606×times-frac
385×add-sqr-sqrt
283×add-cube-cbrt *-un-lft-identity
149×sqrt-prod
140×cbrt-prod
126×associate-*r*
63×add-exp-log
52×add-cbrt-cube
40×associate-/l*
34×associate-*l*
30×cbrt-undiv div-exp
24×unswap-sqr
15×prod-exp cbrt-unprod
13×div-inv
6×pow1
4×associate-/r/ add-log-exp
3×associate-/r*
2×flip3-+ pow1/3 flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 422
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
39.0ms
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
300.0ms
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

series1.2s

Counts
4 → 12
Calls
4 calls:
294.0ms
(cbrt x)
290.0ms
(cbrt x)
339.0ms
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
302.0ms
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

simplify1.2s

Counts
434 → 434
Iterations

Useful iterations: done (1.2s)

IterNodesCost
057611136
1177010491
done50009736

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (/ 1.0 x))
0.8b
(cbrt (/ 1.0 x))
1.4b
(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
2.8b
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
134×add-sqr-sqrt
121×cbrt-prod
110×add-cube-cbrt *-un-lft-identity
54×associate-*r*
27×add-exp-log
19×add-cbrt-cube
16×associate-/l*
12×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
7×associate-*l*
6×pow1
4×associate-/r/ add-log-exp
3×cbrt-div associate-/r*
2×flip3-+ pow1/3 flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 219
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 x))
2.0ms
(cbrt (/ 1.0 x))
17.0ms
(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
120.0ms
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))

series1.1s

Counts
4 → 12
Calls
4 calls:
295.0ms
(cbrt (/ 1.0 x))
336.0ms
(cbrt (/ 1.0 x))
314.0ms
(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
190.0ms
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))

simplify2.5s

Counts
231 → 231
Iterations

Useful iterations: done (2.5s)

IterNodesCost
03394905
18494708
232354231
done50004100

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (/ 1 x))
1.1b
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt 1.0) (sqrt (+ 1.0 (* z z)))))
15.8b
(sqrt (+ 1.0 (* z z)))
15.8b
(sqrt (+ 1.0 (* z z)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
61×times-frac
42×associate-*r*
40×add-cube-cbrt *-un-lft-identity
35×cbrt-prod
28×sqrt-prod
25×add-exp-log
18×add-cbrt-cube
10×unswap-sqr
8×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp associate-*l*
6×sqrt-div
4×add-log-exp
3×flip3-+ flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times cbrt-div pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 135
Calls
4 calls:
5.0ms
(cbrt (/ 1 x))
153.0ms
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt 1.0) (sqrt (+ 1.0 (* z z)))))
11.0ms
(sqrt (+ 1.0 (* z z)))
11.0ms
(sqrt (+ 1.0 (* z z)))

series779.0ms

Counts
4 → 12
Calls
4 calls:
306.0ms
(cbrt (/ 1 x))
345.0ms
(* (/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) y) (/ (cbrt 1.0) (sqrt (+ 1.0 (* z z)))))
68.0ms
(sqrt (+ 1.0 (* z z)))
59.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.8s

Counts
147 → 147
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02853048
17432802
225632552
done50002512

prune715.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

regimes7.0ms