Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	203×	body	80	valid
2.0ms	23×	body	640	valid
2.0ms	13×	body	1280	valid
1.0ms	10×	body	320	valid
0.0ms	7×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5001	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: 22.9b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
1.5b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

6.0ms	(* (- 1.0 x) y)
7.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series144.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* (- 1.0 x) y)
69.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	338	401
1	1456	359
2	5001	359

prune133.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0.2b

Counts

73 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
1.5b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 88

Calls

3 calls:

8.0ms	(/ y (+ y 1.0))
12.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
3.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series144.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ y (+ y 1.0))
46.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
63.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	400	572
1	1790	526
2	5002	526

prune152.0ms

Filtered

97 candidates to 69 candidates (71.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Merged error: 0.2b

Counts

102 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

1.5b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.6b	(/ (* (- 1.0 x) y) (+ y 1.0))
9.6b	(/ (* (- 1.0 x) y) (+ y 1.0))
9.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `times-frac` `associate-/r*`
10×	`add-cube-cbrt`
6×	`cbrt-undiv` `div-exp` `associate-*l/` `associate-/r/` `associate-/l/` `distribute-lft-out` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
3×	`frac-2neg` `flip3-+` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`
1×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

7.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series200.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
48.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
47.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	287	648
1	1151	575
2	5001	574

prune235.0ms

Filtered

107 candidates to 79 candidates (73.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	108	4	112

Merged error: 0.2b

Counts

112 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

1.5b	(- 1.0 (/ 1 (/ (+ y 1.0) (* (- 1.0 x) y))))
9.6b	(/ (* (- 1.0 x) y) (+ y 1.0))
9.6b	(/ (* (- 1.0 x) y) (+ y 1.0))
9.7b	(/ (+ y 1.0) (* (- 1.0 x) y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
14×	`times-frac`
10×	`add-cube-cbrt`
9×	`associate-/r*`
6×	`cbrt-undiv` `div-exp` `associate-l/` `associate-/r/` `associate-/l/` `distribute-lft-out` `associate-/l` `add-log-exp`
4×	`pow1` `flip3--` `flip--` `div-inv`
3×	`frac-2neg` `flip3-+` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `difference-of-squares`
2×	`distribute-lft-out--`
1×	`sub-neg` `diff-log`

Counts

4 → 98

Calls

4 calls:

14.0ms	(- 1.0 (/ 1 (/ (+ y 1.0) (* (- 1.0 x) y))))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
13.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms	(/ (+ y 1.0) (* (- 1.0 x) y))

series213.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- 1.0 (/ 1 (/ (+ y 1.0) (* (- 1.0 x) y))))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
48.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
38.0ms	(/ (+ y 1.0) (* (- 1.0 x) y))

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	433	757
1	1843	655
2	5002	651

prune270.0ms

Filtered

110 candidates to 80 candidates (72.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	109	5	114

Merged error: 0.2b

Counts

114 → 5

regimes103.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.2b

bsearch78.0ms

Steps

Iters	Range		Point
9	137964.03928948785	661184882896.0549	154919718.94598407
8	-591661204.423747	-45386.90934105675	-146664422.27513087

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample463.0ms

Algorithm

intervals

Results

169.0ms	6126×	body	80	valid
67.0ms	703×	body	640	valid
45.0ms	372×	body	1280	valid
39.0ms	541×	body	320	valid
13.0ms	258×	body	160	valid