Details

sample60.0ms

Algorithm

intervals

Results

26.0ms	61×	body	1280	valid
10.0ms	39×	body	640	valid
6.0ms	156×	body	80	valid
3.0ms	21×	body	320	valid
3.0ms	90×	body	80	nan
1.0ms	9×	body	160	valid

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4

prune4.0ms

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: 11.7b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
5.8b	(pow (/ x (+ x y)) x)

rewrite14.0ms

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×	`expm1-log1p-u` `flip3-+` `div-exp` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 70

Calls

2 calls:

5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series260.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ x (+ x y))
222.0ms	(pow (/ x (+ x y)) x)

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	320	413
1	1304	399
2	5002	398

prune159.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	4	77

Merged error: 0.5b

Counts

77 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
13×	`unpow-prod-down`
12×	`cbrt-div`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/r/`
6×	`flip3-+` `flip-+`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-pow` `times-frac` `div-inv` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series799.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt x)
183.0ms	(cbrt x)
173.0ms	(cbrt x)
270.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify144.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	378	644
1	1170	603
2	4673	584
3	5001	584

prune277.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Merged error: 0b

Counts

88 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
2.6b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

55×	`cbrt-prod`
48×	`log-prod` `*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log` `distribute-lft-out`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `rem-log-exp` `associate-/r/` `flip-+`
1×	`log-div` `div-exp` `log-pow` `div-inv`

Counts

4 → 103

Calls

4 calls:

3.0ms	(cbrt (+ x y))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (+ x y))
172.0ms	(cbrt x)
172.0ms	(cbrt x)
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify132.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	370	887
1	1014	855
2	4230	835
3	5002	830

prune432.0ms

Filtered

115 candidates to 96 candidates (83.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	115	3	118

Merged error: 0b

Counts

118 → 3

localize4.0ms

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` `expm1-log1p-u` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

4.0ms

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

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

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

simplify47.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	118	194
1	313	179
2	1512	177
3	5001	177

prune59.0ms

Filtered

33 candidates to 25 candidates (75.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	33	3	36

Merged error: 0b

Counts

36 → 3

regimes50.0ms

Accuracy

99.6% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.7b

bsearch78.0ms

Steps

Iters	Range		Point
9	0.0014765281187882199	322798.86593566654	6.015440873046695
9	-0.4506066524886072	-1.4365382038701608e-08	-0.4445338161431805

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample1.7s

Algorithm

intervals

Results

662.0ms	1551×	body	1280	valid
367.0ms	1470×	body	640	valid
202.0ms	4855×	body	80	valid
134.0ms	827×	body	320	valid
89.0ms	3076×	body	80	nan
39.0ms	396×	body	160	valid