Details

analyze4.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 99.993896%

sample25.0ms

Algorithm

intervals

Results

8.0ms	58×	body	1280	valid
5.0ms	41×	body	640	valid
4.0ms	127×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

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: 30.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
3.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

2 → 71

Calls

2 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
36.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series11.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
8.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify143.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	317	591
1	1003	565
2	4494	559
3	5003	559

prune122.0ms

Filtered

50 candidates to 77 candidates (-54.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	3	78

Merged error: 0.2b

Counts

78 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.0b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

376×	`*-un-lft-identity`
208×	`times-frac`
120×	`distribute-lft-out`
70×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
24×	`swap-sqr` `distribute-lft-out--`
18×	`add-exp-log` `associate-r` `associate-l` `frac-sub` `add-cbrt-cube`
14×	`difference-of-squares`
13×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`pow1` `associate-/r/` `associate-/l/`
8×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`flip3--` `frac-add` `flip--`
1×	`+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `clear-num` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 222

Calls

4 calls:

30.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
50.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
19.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
15.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
18.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify149.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	906	3775
1	4571	3560
2	5001	3547

prune381.0ms

Filtered

126 candidates to 234 candidates (-85.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	232	2	234
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	235	2	237

Merged error: 0.2b

Counts

237 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.0b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
16.6b	(* (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))) (* (+ x 1.0) (- x 1.0)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
88×	`times-frac`
69×	`add-sqr-sqrt`
65×	`associate-*r/`
57×	`add-cube-cbrt`
52×	`associate-l`
45×	`frac-times`
44×	`associate-/r/`
36×	`flip3-+` `flip-+`
32×	`frac-add`
30×	`add-exp-log` `add-cbrt-cube`
26×	`associate-*l/`
24×	`flip3--` `swap-sqr` `flip--`
19×	`associate-r`
18×	`frac-sub` `distribute-lft-out`
16×	`pow1`
11×	`associate-/l/`
10×	`prod-exp` `cbrt-unprod`
8×	`distribute-rgt-in` `distribute-lft-in` `difference-of-squares`
7×	`cbrt-undiv` `div-exp`
6×	`div-inv` `add-log-exp`
5×	`sub-neg`
4×	`pow-prod-down` `associate-/l*` `unswap-sqr`
3×	`associate-/r*`
2×	`*-commutative`
1×	`pow2` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `pow-sqr` `pow-prod-up`

Counts

4 → 249

Calls

4 calls:

23.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))))
18.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
35.0ms	(* (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))) (* (+ x 1.0) (- x 1.0)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))))
3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
11.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
22.0ms	(* (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))) (* (+ x 1.0) (- x 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1619	5151
1	5001	4817

prune903.0ms

Filtered

187 candidates to 261 candidates (-39.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	259	2	261
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	260	3	263

Merged error: 0.1b

Counts

263 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (pow x 3))
0.2b	(/ 1 (pow x 2))
0.3b	(* 3.0 (/ 1 x))
7.8b	(+ (* 1.0 (/ 1 (pow x 2))) (+ (* 3.0 (/ 1 x)) (* 3.0 (/ 1 (pow x 3)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
61×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
54×	`add-cube-cbrt`
31×	`add-exp-log`
24×	`unpow-prod-down`
20×	`frac-add` `associate-/r*`
15×	`associate-*r/` `un-div-inv`
14×	`div-exp`
13×	`associate-r` `add-cbrt-cube`
12×	`cube-prod`
9×	`add-log-exp`
8×	`sqr-pow`
7×	`rec-exp` `1-exp`
6×	`pow1` `pow-to-exp` `pow-exp` `associate-/l*`
4×	`cube-mult` `unpow3` `prod-exp` `unpow2`
3×	`cbrt-undiv` `flip3-+` `associate-l` `sum-log` `flip-+` `div-inv` `unswap-sqr`
2×	`pow-flip` `frac-2neg` `clear-num` `cbrt-unprod` `inv-pow`
1×	`+-commutative` `associate-+r+` `pow-prod-down` `*-commutative`

Counts

4 → 191

Calls

4 calls:

6.0ms	(/ 1 (pow x 3))
5.0ms	(/ 1 (pow x 2))
10.0ms	(* 3.0 (/ 1 x))
14.0ms	(+ (* 1.0 (/ 1 (pow x 2))) (+ (* 3.0 (/ 1 x)) (* 3.0 (/ 1 (pow x 3)))))

series12.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 1 (pow x 3))
2.0ms	(/ 1 (pow x 2))
2.0ms	(* 3.0 (/ 1 x))
4.0ms	(+ (* 1.0 (/ 1 (pow x 2))) (+ (* 3.0 (/ 1 x)) (* 3.0 (/ 1 (pow x 3)))))

simplify131.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	721	1139
1	4089	881
2	5001	857

prune235.0ms

Filtered

85 candidates to 203 candidates (-138.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	203	3	206

Merged error: 0b

Counts

206 → 3

Details

analyze4.0ms

sample25.0ms

simplify17.0ms

prune2.0ms

localize6.0ms

rewrite47.0ms

series11.0ms

simplify143.0ms

prune122.0ms

localize11.0ms

rewrite133.0ms

series39.0ms

simplify149.0ms

prune381.0ms

localize15.0ms

rewrite102.0ms

series52.0ms

simplify81.0ms

prune903.0ms

localize15.0ms

rewrite41.0ms

series12.0ms

simplify131.0ms

prune235.0ms

regimes38.0ms

bsearch1.0ms

Profiling

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6