Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	198×	body	80	valid
2.0ms	27×	body	640	valid
2.0ms	14×	body	1280	valid
1.0ms	9×	body	320	valid
0.0ms	8×	body	160	valid

simplify62.0ms

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: 20.7b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.1b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.4b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite24.0ms

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:

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

series143.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- 1.0 x) y)
64.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
47.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (11.0ms)

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

prune146.0ms

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: 0.1b

Counts

73 → 5

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
0.0b	(/ y (+ y 1.0))
2.1b	(- 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:

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

series148.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
35.0ms	(/ y (+ y 1.0))
68.0ms	(- 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

prune166.0ms

Filtered

97 candidates to 70 candidates (72.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Merged error: 0.1b

Counts

102 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
0.1b	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
2.1b	(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
10.6b	(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

49×	`frac-times`
43×	`pow1`
42×	`add-exp-log` `add-cbrt-cube`
29×	`associate-*l/`
26×	`flip3--` `flip--`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/` `pow-prod-down`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
5×	`difference-of-squares`
4×	`pow-sqr` `pow-prod-up` `associate-/l*`
3×	`associate-/r*`
2×	`flip3-+` `pow-plus` `associate-/r/` `flip-+` `associate-/l/`
1×	`+-commutative` `pow2` `sub-neg` `frac-2neg` `diff-log` `div-sub` `swap-sqr` `associate-r` `associate-l` `clear-num` `sum-log` `*-commutative` `div-inv`

Counts

4 → 139

Calls

4 calls:

3.0ms	(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
19.0ms	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
4.0ms	(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
8.0ms	(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

series565.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
53.0ms	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
81.0ms	(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
385.0ms	(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	827	2225
1	4190	1935
2	5002	1931

prune269.0ms

Filtered

151 candidates to 87 candidates (57.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	151	5	156

Merged error: 0.1b

Counts

156 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1.0 1.0) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
0.1b	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
2.1b	(- (/ (* 1.0 1.0) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
10.6b	(/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

98×	`frac-times`
92×	`add-exp-log` `add-cbrt-cube`
58×	`associate-*l/`
49×	`flip3--` `flip--`
43×	`pow1` `prod-exp` `cbrt-unprod`
35×	`associate-/l/`
34×	`associate-*r/`
24×	`cbrt-undiv` `div-exp`
17×	`pow-prod-down`
16×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `times-frac`
8×	`add-cube-cbrt` `associate-/r/`
6×	`associate-/r*` `add-log-exp`
4×	`flip3-+` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `pow-plus` `clear-num` `associate-/l*`
1×	`pow2` `sub-neg` `diff-log` `swap-sqr` `associate-r` `associate-l` `*-commutative` `frac-sub` `distribute-lft-out--` `sub-div`

Counts

4 → 198

Calls

4 calls:

5.0ms	(/ (* 1.0 1.0) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
22.0ms	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
11.0ms	(- (/ (* 1.0 1.0) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
27.0ms	(/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (* 1.0 1.0) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
57.0ms	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
919.0ms	(- (/ (* 1.0 1.0) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
513.0ms	(/ (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1076	3302
1	5001	2781

prune425.0ms

Filtered

210 candidates to 127 candidates (60.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	210	5	215

Merged error: 0.1b

Counts

215 → 5

regimes97.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.3b

bsearch88.0ms

Steps

Iters	Range		Point
9	29019769.916827235	7152780495357.076	371097375.1162559
10	-113800757124221.17	-6.308761783247451	-189812180.78608567

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample449.0ms

Algorithm

intervals

Results

154.0ms	6110×	body	80	valid
63.0ms	698×	body	640	valid
45.0ms	377×	body	1280	valid
37.0ms	507×	body	320	valid
14.0ms	308×	body	160	valid