Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	197×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	14×	body	1280	valid
1.0ms	18×	body	320	valid
0.0ms	8×	body	160	valid

simplify61.0ms

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

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.6b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.5b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite26.0ms

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:

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

series135.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* (- 1.0 x) y)
66.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
41.0ms	(/ (* (- 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

prune128.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 0.2b

Counts

73 → 6

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.6b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite23.0ms

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:

5.0ms	(/ y (+ y 1.0))
12.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
3.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series142.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ y (+ y 1.0))
41.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
65.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

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

prune136.0ms

Filtered

97 candidates to 70 candidates (72.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Merged error: 0.2b

Counts

103 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* y y) (* 1.0 1.0))
0.1b	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
4.3b	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
18.0b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

4.0ms	(- (* y y) (* 1.0 1.0))
14.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
10.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* y y) (* 1.0 1.0))
73.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
147.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
84.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	528	1020
1	2773	891
2	5001	891

prune179.0ms

Filtered

108 candidates to 78 candidates (72.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	109	5	114

Merged error: 0.1b

Counts

114 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))))
3.6b	(- 1.0 (* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))))
18.0b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))
18.0b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

12.0ms	(* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))))
3.0ms	(- 1.0 (* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))))
11.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))
11.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))))
98.0ms	(- 1.0 (* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))))
84.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))
87.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	436	1007
1	2320	858
2	5002	858

prune209.0ms

Filtered

108 candidates to 83 candidates (76.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	107	6	113

Merged error: 0.0b

Counts

113 → 6

regimes140.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 14.8b

bsearch107.0ms

Steps

Iters	Range		Point
9	573.0632436401448	118875297.13418089	60021882.29519812
9	-39495616121.36297	-27949.393755151574	-68835468.42054991

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	36
1	57	36
2	64	36
3	70	36
4	83	36
5	92	36
6	94	36
7	94	36

end0.0ms

sample426.0ms

Algorithm

intervals

Results

143.0ms	6052×	body	80	valid
62.0ms	745×	body	640	valid
43.0ms	546×	body	320	valid
38.0ms	356×	body	1280	valid
13.0ms	301×	body	160	valid