Details

sample63.0ms

Algorithm

intervals

Results

23.0ms	53×	body	1280	valid
13.0ms	55×	body	640	valid
9.0ms	165×	body	80	valid
4.0ms	24×	body	320	valid
3.0ms	98×	body	80	nan
1.0ms	10×	body	160	valid

simplify110.0ms

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: 12.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
7.3b	(pow (/ x (+ x y)) x)

rewrite13.0ms

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

series259.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ x (+ x y))
223.0ms	(pow (/ x (+ x y)) x)

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

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

prune133.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Merged error: 0.8b

Counts

77 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
1.7b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite20.0ms

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)

series796.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt x)
169.0ms	(cbrt x)
175.0ms	(cbrt x)
277.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify137.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (28.0ms)

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

prune225.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	85	2	87

Merged error: 0.0b

Counts

87 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
2.1b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite17.0ms

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)
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (+ x y))
173.0ms	(cbrt x)
171.0ms	(cbrt x)
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify138.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (128.0ms)

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

prune397.0ms

Filtered

115 candidates to 96 candidates (83.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	115	2	117

Merged error: 0.0b

Counts

117 → 2

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` `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)

simplify46.0ms

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

prune53.0ms

Filtered

33 candidates to 25 candidates (75.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	31	4	35

Merged error: 0b

Counts

35 → 4

regimes56.0ms

Accuracy

86% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 5.7b

bsearch113.0ms

Steps

Iters	Range		Point
9	5.359589792685655e-35	3.9546097637250077e-29	3.9066533338539774e-29
9	-1.0885082802572525e+92	-6.071934465706925e+83	-6.201981569644431e+83

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	21
1	37	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

667.0ms	1558×	body	1280	valid
352.0ms	1403×	body	640	valid
206.0ms	4912×	body	80	valid
140.0ms	886×	body	320	valid
90.0ms	3115×	body	80	nan
44.0ms	435×	body	160	valid