Details

sample74.0ms

Algorithm

intervals

Results

43.0ms	88×	body	5120	exit
13.0ms	274×	body	80	valid
3.0ms	5×	body	1280	valid
2.0ms	6×	body	640	valid
1.0ms	7×	body	320	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	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: 0.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.3b	(log (+ 1.0 (exp x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `log-div` `associate--l+`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series129.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
55.0ms	(- (log (+ 1.0 (exp x))) (* x y))
66.0ms	(log (+ 1.0 (exp x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune105.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	3	55

Merged error: 0b

Counts

55 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.0b	(log (sqrt (+ 1.0 (exp x))))
1.0b	(log (sqrt (+ 1.0 (exp x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
6×	`add-exp-log` `log-pow`
4×	`log-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`+-commutative` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log`

Counts

4 → 64

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
7.0ms	(+ 1.0 (exp x))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ 1.0 (exp x))
8.0ms	(+ 1.0 (exp x))
105.0ms	(log (sqrt (+ 1.0 (exp x))))
107.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	155	476
1	390	434
2	1073	422
3	5002	414

prune188.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Merged error: 0b

Counts

79 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* x y))) (cbrt (- (log (+ 1.0 (exp x))) (* x y)))) (cbrt (- (log (+ 1.0 (exp x))) (* x y))))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
23×	`pow1`
14×	`associate-*l/`
13×	`cbrt-prod`
12×	`pow1/3`
11×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-up`
8×	`associate-*r/`
6×	`pow-plus` `associate-r`
5×	`pow-prod-down` `add-cbrt-cube`
4×	`add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod`
2×	`pow2` `unswap-sqr`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 100

Calls

4 calls:

14.0ms	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* x y))) (cbrt (- (log (+ 1.0 (exp x))) (* x y)))) (cbrt (- (log (+ 1.0 (exp x))) (* x y))))
3.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
2.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
3.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

series986.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* x y))) (cbrt (- (log (+ 1.0 (exp x))) (* x y)))) (cbrt (- (log (+ 1.0 (exp x))) (* x y))))
309.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
301.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
316.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

simplify60.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	444	2629
1	1609	2345
2	5001	2216

prune272.0ms

Filtered

112 candidates to 78 candidates (69.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	3	115

Merged error: 0b

Counts

115 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.0b	(* 1/2 (pow x 2))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
8.8b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

6.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
5.0ms	(* 1/2 (pow x 2))
8.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
24.0ms	(* 1/2 (pow x 2))
78.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
56.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	371	575
1	1439	529
2	5001	520

prune152.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	83	3	86

Merged error: 0b

Counts

86 → 3

regimes254.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	2491×	body	5120	exit
430.0ms	8485×	body	80	valid
77.0ms	241×	body	640	valid
76.0ms	128×	body	1280	valid
36.0ms	180×	body	320	valid
13.0ms	110×	body	160	valid