Details

sample10.0ms

Algorithm

intervals

Results

3.0ms

256×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	2
1	10	2
2	12	2
3	13	2
4	13	2

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (+ x y) x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

13.0ms

(+ (+ x y) x)

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

(+ (+ x y) x)

simplify98.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	82	65
1	241	60
2	854	58
3	4535	53
4	5002	53

prune24.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (+ x y) x)) (cbrt (+ (+ x y) x)))
0.5b	(cbrt (+ (+ x y) x))
0.5b	(cbrt (+ (+ x y) x))
0.5b	(cbrt (+ (+ x y) x))

rewrite105.0ms

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×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 105

Calls

4 calls:

73.0ms	(* (cbrt (+ (+ x y) x)) (cbrt (+ (+ x y) x)))
11.0ms	(cbrt (+ (+ x y) x))
8.0ms	(cbrt (+ (+ x y) x))
9.0ms	(cbrt (+ (+ x y) x))

series849.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(* (cbrt (+ (+ x y) x)) (cbrt (+ (+ x y) x)))
205.0ms	(cbrt (+ (+ x y) x))
202.0ms	(cbrt (+ (+ x y) x))
203.0ms	(cbrt (+ (+ x y) x))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	280	982
1	1048	931
2	5001	832

prune224.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

44×	`cbrt-prod`
31×	`*-un-lft-identity`
14×	`cbrt-div`
12×	`distribute-lft-out`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 69

Calls

4 calls:

8.0ms	(cbrt (+ (+ x y) x))
9.0ms	(cbrt (cbrt (+ (+ x y) x)))
9.0ms	(cbrt (cbrt (+ (+ x y) x)))
11.0ms	(cbrt (cbrt (+ (+ x y) x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt (+ (+ x y) x))
278.0ms	(cbrt (cbrt (+ (+ x y) x)))
276.0ms	(cbrt (cbrt (+ (+ x y) x)))
269.0ms	(cbrt (cbrt (+ (+ x y) x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	223	657
1	597	623
2	2341	611
3	5001	601

prune257.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (+ x y))
1.4b	(+ (pow (+ x y) 3) (pow x 3))
2.2b	(+ (* y (+ x y)) (* x x))
39.7b	(/ (+ (pow (+ x y) 3) (pow x 3)) (+ (* y (+ x y)) (* x x)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
66×	`distribute-lft-out`
40×	`unpow-prod-down` `cube-prod`
39×	`times-frac`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
13×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`flip3-+` `sum-cubes` `flip-+`
4×	`associate-r`
3×	`associate-l` `associate-/r*`
2×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-*r/` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 128

Calls

4 calls:

9.0ms	(* y (+ x y))
37.0ms	(+ (pow (+ x y) 3) (pow x 3))
5.0ms	(+ (* y (+ x y)) (* x x))
106.0ms	(/ (+ (pow (+ x y) 3) (pow x 3)) (+ (* y (+ x y)) (* x x)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* y (+ x y))
63.0ms	(+ (pow (+ x y) 3) (pow x 3))
20.0ms	(+ (* y (+ x y)) (* x x))
123.0ms	(/ (+ (pow (+ x y) 3) (pow x 3)) (+ (* y (+ x y)) (* x x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	401	1377
1	2050	1316
2	5001	1314

prune257.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	2
1	7	2

end0.0ms

sample232.0ms

Algorithm

intervals

Results

106.0ms

8004×

body

valid