Details

sample19.0ms

Algorithm

intervals

Results

11.0ms

285×

body

valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	5
1	42	5
2	87	5
3	175	5
4	310	5
5	500	5
6	720	5
7	948	5
8	1148	5
9	1148	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (- y 1.0))
0.0b	(- (* x (- y 1.0)) (* y 0.5))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity`
5×	`sub-neg` `associate-r`
4×	`pow1` `add-exp-log` `distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in` `associate--l+` `add-cbrt-cube` `add-log-exp`
3×	`associate-l`
2×	`flip3--` `associate-*r/` `flip--`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

2 → 42

Calls

2 calls:

6.0ms	(* x (- y 1.0))
6.0ms	(- (* x (- y 1.0)) (* y 0.5))

series62.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(* x (- y 1.0))
24.0ms	(- (* x (- y 1.0)) (* y 0.5))

simplify90.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	186	217
1	673	197
2	2660	196
3	5003	196

prune61.0ms

Filtered

48 candidates to 29 candidates (60.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	3	49

Merged error: 0.0b

Counts

49 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series756.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (cbrt x) (cbrt x))
173.0ms	(cbrt x)
182.0ms	(cbrt x)
168.0ms	(cbrt x)

simplify91.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune163.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	84	4	88

Merged error: 0b

Counts

88 → 4

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (* x (- (* y y) (* 1.0 1.0))) (+ y 1.0)) (* y 0.5))
5.7b	(* x (- (* y y) (* 1.0 1.0)))
9.0b	(/ (* x (- (* y y) (* 1.0 1.0))) (+ y 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`times-frac` `associate-r/` `associate-r` `associate-/r`
3×	`sub-neg` `flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l` `difference-of-squares` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

10.0ms	(- (/ (* x (- (* y y) (* 1.0 1.0))) (+ y 1.0)) (* y 0.5))
6.0ms	(* x (- (* y y) (* 1.0 1.0)))
9.0ms	(/ (* x (- (* y y) (* 1.0 1.0))) (+ y 1.0))

series211.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(- (/ (* x (- (* y y) (* 1.0 1.0))) (+ y 1.0)) (* y 0.5))
62.0ms	(* x (- (* y y) (* 1.0 1.0)))
98.0ms	(/ (* x (- (* y y) (* 1.0 1.0))) (+ y 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	368	564
1	1721	488
2	5001	484

prune130.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	73	4	77

Merged error: 0b

Counts

77 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt x) (- y 1.0))
0.2b	(* (pow x 2/3) (* (cbrt x) (- y 1.0)))
0.6b	(cbrt x)
3.0b	(pow x 2/3)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`associate-l`
12×	`add-cube-cbrt`
10×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
9×	`add-cbrt-cube`
7×	`pow1` `cbrt-prod`
6×	`sub-neg` `unpow-prod-down` `associate-r/` `associate-r*`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`flip3--` `*-commutative` `flip--` `unswap-sqr` `sqr-pow`
1×	`pow-pow` `pow1/3` `pow-prod-down` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

7.0ms	(* (cbrt x) (- y 1.0))
13.0ms	(* (pow x 2/3) (* (cbrt x) (- y 1.0)))
1.0ms	(cbrt x)
2.0ms	(pow x 2/3)

series2.5m

Calls

2 calls:

170.0ms	(cbrt x)
166.0ms	(pow x 2/3)

Details

sample19.0ms

simplify39.0ms

prune2.0ms

localize7.0ms

rewrite13.0ms

series62.0ms

simplify90.0ms

prune61.0ms

localize10.0ms

rewrite10.0ms

series756.0ms

simplify91.0ms

prune163.0ms

localize14.0ms

rewrite26.0ms

series211.0ms

simplify51.0ms

prune130.0ms

localize12.0ms

rewrite25.0ms

series2.5m

Profiling