Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	205×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	11×	body	1280	valid
1.0ms	10×	body	320	valid
0.0ms	8×	body	160	valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 20.3b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.2b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.5b	(/ (* (- 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)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series137.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- 1.0 x) y)
62.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
44.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (9.0ms)

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

prune121.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0.1b

Counts

73 → 3

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)))
2.2b	(- 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:

33.0ms	(/ y (+ y 1.0))
43.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
66.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

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

prune130.0ms

Filtered

97 candidates to 69 candidates (71.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	97	3	100

Merged error: 0.1b

Counts

100 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.0b	(/ 1 (+ y 1.0))
4.2b	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
7.6b	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
32×	`add-exp-log`
27×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-*l/`
7×	`cbrt-unprod` `distribute-lft-out`
6×	`div-exp` `associate-l` `add-log-exp`
4×	`flip3--` `pow-prod-down` `associate-/r*` `associate-/r/` `flip--`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*`
2×	`frac-times` `flip3-+` `*-commutative` `flip-+` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-*r/` `clear-num` `un-div-inv` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

6.0ms	(* (- 1.0 x) y)
5.0ms	(/ 1 (+ y 1.0))
3.0ms	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
16.0ms	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (- 1.0 x) y)
22.0ms	(/ 1 (+ y 1.0))
66.0ms	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
41.0ms	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	509	737
1	2631	636
2	5001	599

prune143.0ms

Filtered

130 candidates to 74 candidates (56.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	130	3	133

Merged error: 0.1b

Counts

133 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
0.0b	(- (/ 1 y) (/ x y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`times-frac`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv` `distribute-lft-out--`
4×	`add-cube-cbrt` `associate-+l+`
3×	`sub-neg` `distribute-rgt-out--`
2×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
1×	`+-commutative` `flip3--` `flip3-+` `diff-log` `sum-log` `frac-sub` `flip--` `flip-+` `sub-div`

Counts

2 → 43

Calls

2 calls:

19.0ms	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
13.0ms	(- (/ 1 y) (/ x y))

series47.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
19.0ms	(- (/ 1 y) (/ x y))

simplify76.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	224	317
1	627	291
2	2889	282
3	5001	274

prune66.0ms

Filtered

49 candidates to 33 candidates (67.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	46	6	52

Merged error: 0.1b

Counts

52 → 6

regimes114.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.4b

bsearch81.0ms

Steps

Iters	Range		Point
9	821572.5269121197	24331955248945.938	301128037.505105
10	-591489333.2348301	-0.00011291202415345404	-127120567.1677991

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample512.0ms

Algorithm

intervals

Results

185.0ms	6090×	body	80	valid
76.0ms	713×	body	640	valid
54.0ms	398×	body	1280	valid
41.0ms	498×	body	320	valid
25.0ms	301×	body	160	valid