Details

sample21.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	82
1	6	82
2	8	82
3	11	82
4	12	82
done	12	82

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (+ x y) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity` `add-log-exp`
3×	`sum-log` `distribute-lft-out`
1×	`add-sqr-sqrt` `pow1` `+-commutative` `associate-+l+` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `flip-+`

Counts

1 → 15

Calls

1 calls:

47.0ms

(+ (+ x y) x)

series29.0ms

Counts

1 → 3

Calls

1 calls:

29.0ms

(+ (+ x y) x)

simplify4.1s

Counts

18 → 18

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	32	2962
1	80	2521
2	243	2521
3	885	2478
4	4295	2357
done	5027	2357

prune71.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (+ x y) x)) (cbrt (+ (+ x y) x)))
0.6b	(cbrt (+ (+ x y) x))
0.6b	(cbrt (+ (+ x y) x))
0.6b	(cbrt (+ (+ x y) x))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
51×	`cbrt-prod`
33×	`distribute-lft-out`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
14×	`swap-sqr`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 105

Calls

4 calls:

173.0ms	(* (cbrt (+ (+ x y) x)) (cbrt (+ (+ x y) x)))
12.0ms	(cbrt (+ (+ x y) x))
22.0ms	(cbrt (+ (+ x y) x))
25.0ms	(cbrt (+ (+ x y) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

340.0ms	(* (cbrt (+ (+ x y) x)) (cbrt (+ (+ x y) x)))
274.0ms	(cbrt (+ (+ x y) x))
260.0ms	(cbrt (+ (+ x y) x))
281.0ms	(cbrt (+ (+ x y) x))

simplify2.0s

Counts

117 → 117

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	130	44533
1	307	36175
2	780	36015
3	2312	35174
done	5006	34209

prune565.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt (+ (+ x y) x))
0.6b	(cbrt (+ (+ x y) x))
25.9b	(cbrt (* y (+ (+ x y) x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `distribute-lft-out`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`associate-*r/`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt y)
16.0ms	(cbrt (+ (+ x y) x))
13.0ms	(cbrt (+ (+ x y) x))
15.0ms	(cbrt (* y (+ (+ x y) x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt y)
267.0ms	(cbrt (+ (+ x y) x))
312.0ms	(cbrt (+ (+ x y) x))
290.0ms	(cbrt (* y (+ (+ x y) x)))

simplify1.7s

Counts

64 → 64

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	105	21079
1	232	17888
2	577	17769
3	1969	17009
done	5006	16491

prune421.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (+ x y) x))
0.0b	(+ (+ x y) x)
0.0b	(+ (+ x y) x)
0.3b	(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
43×	`sqrt-prod`
33×	`distribute-lft-out`
26×	`add-sqr-sqrt`
20×	`pow1`
16×	`swap-sqr`
14×	`sqrt-div` `add-log-exp`
13×	`add-cube-cbrt`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
8×	`associate-r` `associate-l`
6×	`sum-log` `add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `associate-+l+` `associate-l/` `associate-r/`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

48.0ms	(sqrt (+ (+ x y) x))
43.0ms	(+ (+ x y) x)
43.0ms	(+ (+ x y) x)
144.0ms	(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (+ (+ x y) x))
24.0ms	(+ (+ x y) x)
25.0ms	(+ (+ x y) x)
45.0ms	(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

simplify324.0ms

Iterations

Useful iterations: 1 (135.0ms)

Iter	Nodes	Cost
0	119	30916
1	268	21651