Details

sample74.0ms

Algorithm

intervals

Results

27.0ms	57×	body	1280	valid
13.0ms	51×	body	640	valid
10.0ms	154×	body	80	valid
5.0ms	32×	body	320	valid
4.0ms	120×	body	80	nan
2.0ms	15×	body	160	valid

simplify133.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (12.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
7.1b	(pow (/ x (+ x y)) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 66

Calls

2 calls:

6.0ms	(/ x (+ x y))
8.0ms	(pow (/ x (+ x y)) x)

series324.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ x (+ x y))
277.0ms	(pow (/ x (+ x y)) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	309	402
1	1244	387
2	5002	386

prune149.0ms

Filtered

72 candidates to 50 candidates (69.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.3b

Counts

73 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`pow1` `cbrt-undiv` `exp-neg` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

4.0ms

(/ (exp (* -1 y)) x)

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

(/ (exp (* -1 y)) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	114	186
1	303	172
2	1465	170
3	5003	170

prune75.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	30	5	35

Merged error: 0.3b

Counts

35 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (exp y))
0.0b	(/ 1 (* x (exp y)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`pow1`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`div-exp` `prod-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `pow-flip` `1-exp` `pow-prod-down` `cbrt-unprod` `add-log-exp`
1×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `div-inv` `inv-pow` `unswap-sqr`

Counts

2 → 46

Calls

2 calls:

5.0ms	(* x (exp y))
6.0ms	(/ 1 (* x (exp y)))

series58.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(* x (exp y))
27.0ms	(/ 1 (* x (exp y)))

simplify115.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	173	203
1	786	170
2	4230	163
3	5001	163

prune79.0ms

Filtered

52 candidates to 29 candidates (55.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	51	6	57

Merged error: 0.3b

Counts

57 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.7b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
12.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
19.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt x)
201.0ms	(cbrt x)
319.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
336.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify85.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	691	1334
1	2164	1266
2	5001	1235

prune388.0ms

Filtered

128 candidates to 88 candidates (68.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	131	3	134

Merged error: 0.0b

Counts

134 → 3

regimes59.0ms

Accuracy

97.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 6.3b

bsearch140.0ms

Steps

Iters	Range		Point
9	1.2774642312839134e-06	1.9435667087631803	1.9234455677719884
10	-1.2865710840676908e+74	-2.585852377202543e+56	-2.4296307746992404e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	18
1	34	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

657.0ms	1479×	body	1280	valid
384.0ms	1488×	body	640	valid
219.0ms	4831×	body	80	valid
144.0ms	869×	body	320	valid
97.0ms	2996×	body	80	nan
46.0ms	445×	body	160	valid