Details

Time bar (total: 19.5s)

sample24.0ms

Algorithm
intervals
Results
12.0ms345×body80valid

simplify5.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12711
27711
317411
426411
533111
640311
755111
8114511
9459511
done500011

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (* z z) (+ z 1.0))
14.5b
(/ (* x y) (* (* z z) (+ z 1.0)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log add-cbrt-cube
12×prod-exp cbrt-unprod
7×pow1
6×cbrt-undiv div-exp
5×*-un-lft-identity
4×add-sqr-sqrt associate-*r/ associate-*r*
3×add-cube-cbrt pow-prod-down
2×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in times-frac associate-*l* clear-num associate-/r* *-commutative div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
2 → 55
Calls
2 calls:
42.0ms
(* (* z z) (+ z 1.0))
42.0ms
(/ (* x y) (* (* z z) (+ z 1.0)))

series158.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(* (* z z) (+ z 1.0))
91.0ms
(/ (* x y) (* (* z z) (+ z 1.0)))

simplify1.3s

Counts
61 → 61
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0116898
1349826
21932663
done5000661

prune181.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ z 1.0))
5.6b
(* (/ x (* z z)) (/ y (+ z 1.0)))
8.5b
(/ x (* z z))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
34×add-sqr-sqrt times-frac
31×add-exp-log add-cbrt-cube
24×add-cube-cbrt
18×associate-*r*
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod
7×associate-*l* distribute-lft-out
6×associate-/l*
5×pow1 associate-/r*
4×associate-/r/ div-inv unswap-sqr
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg flip3-+ clear-num flip-+
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
3 → 113
Calls
3 calls:
17.0ms
(/ y (+ z 1.0))
53.0ms
(* (/ x (* z z)) (/ y (+ z 1.0)))
16.0ms
(/ x (* z z))

series171.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(/ y (+ z 1.0))
75.0ms
(* (/ x (* z z)) (/ y (+ z 1.0)))
32.0ms
(/ x (* z z))

simplify1.9s

Counts
122 → 122
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01861549
14961460
218721271
done50001259

prune408.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(* (/ (cbrt x) z) (/ y (+ z 1.0)))
0.9b
(* (/ (* (cbrt x) (cbrt x)) z) (* (/ (cbrt x) z) (/ y (+ z 1.0))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
85×add-exp-log
67×add-cbrt-cube
48×add-sqr-sqrt
40×times-frac
36×prod-exp cbrt-unprod
35×*-un-lft-identity
29×add-cube-cbrt associate-*l*
26×cbrt-undiv div-exp
19×associate-*r*
17×cbrt-prod
11×pow1
6×frac-times associate-*r/ unswap-sqr
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out
2×pow1/3 associate-/r/ *-commutative
1×flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
2.0ms
(cbrt x)
2.0ms
(cbrt x)
75.0ms
(* (/ (cbrt x) z) (/ y (+ z 1.0)))
105.0ms
(* (/ (* (cbrt x) (cbrt x)) z) (* (/ (cbrt x) z) (/ y (+ z 1.0))))

series823.0ms

Counts
4 → 12
Calls
4 calls:
282.0ms
(cbrt x)
252.0ms
(cbrt x)
171.0ms
(* (/ (cbrt x) z) (/ y (+ z 1.0)))
118.0ms
(* (/ (* (cbrt x) (cbrt x)) z) (* (/ (cbrt x) z) (/ y (+ z 1.0))))

simplify2.4s

Counts
163 → 163
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02712848
18082700
233081981
done50001772

prune645.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (/ (* (cbrt x) (cbrt x)) z) (* (* (/ (cbrt x) z) (* (cbrt (/ y (+ z 1.0))) (cbrt (/ y (+ z 1.0))))) (cbrt (/ y (+ z 1.0)))))
10.5b
(cbrt (/ y (+ z 1.0)))
10.5b
(cbrt (/ y (+ z 1.0)))
10.5b
(cbrt (/ y (+ z 1.0)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
97×add-exp-log
57×prod-exp cbrt-unprod
54×cbrt-prod
52×add-cbrt-cube
51×cbrt-div
49×frac-times
48×*-un-lft-identity
39×times-frac
37×associate-*r/
30×add-sqr-sqrt add-cube-cbrt
27×associate-*l/
18×pow1 cbrt-undiv div-exp
10×pow-prod-down
9×distribute-lft-out
7×associate-*l*
6×associate-/r/
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×flip3-+ pow1/3 flip-+
1×associate-*r* *-commutative
Counts
4 → 176
Calls
4 calls:
1.0s
(* (/ (* (cbrt x) (cbrt x)) z) (* (* (/ (cbrt x) z) (* (cbrt (/ y (+ z 1.0))) (cbrt (/ y (+ z 1.0))))) (cbrt (/ y (+ z 1.0)))))
19.0ms
(cbrt (/ y (+ z 1.0)))
11.0ms
(cbrt (/ y (+ z 1.0)))
11.0ms
(cbrt (/ y (+ z 1.0)))

series778.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (/ (* (cbrt x) (cbrt x)) z) (* (* (/ (cbrt x) z) (* (cbrt (/ y (+ z 1.0))) (cbrt (/ y (+ z 1.0))))) (cbrt (/ y (+ z 1.0)))))
252.0ms
(cbrt (/ y (+ z 1.0)))
201.0ms
(cbrt (/ y (+ z 1.0)))
226.0ms
(cbrt (/ y (+ z 1.0)))

simplify2.8s

Counts
188 → 188
Iterations

Useful iterations: done (2.8s)

IterNodesCost
03295356
19425125
236643589
done50002862

prune738.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes4.0ms