Details

sample115.0ms

Algorithm

intervals

Results

32.0ms	321×	body	80	valid
27.0ms	42×	body	1280	valid
21.0ms	50×	body	640	valid
7.0ms	73×	body	80	overflowed
6.0ms	20×	body	320	valid
2.0ms	11×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 eps))
0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
2.5b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
72×	`exp-neg` `frac-times`
54×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip3-+` `flip--` `flip-+`
18×	`un-div-inv`
14×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`associate-l`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-r`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 148

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 eps))
6.0ms	(* (+ 1.0 eps) x)
7.0ms	(* (- 1.0 eps) x)
18.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ 1.0 (/ 1.0 eps))
26.0ms	(* (+ 1.0 eps) x)
28.0ms	(* (- 1.0 eps) x)
195.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify144.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	1203	3643
1	4629	3381
2	5001	3372

prune345.0ms

Filtered

160 candidates to 78 candidates (48.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	2	161

Merged error: 0.6b

Counts

161 → 2

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
6.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* 0.6666666666666667 (pow x 3))
38.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify35.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	207	270
1	894	242
2	5002	238

prune89.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Merged error: 0.6b

Counts

53 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

6.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
10.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 53

Calls

4 calls:

8.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
157.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
146.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
148.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify136.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	252	983
1	905	918
2	4257	836
3	5002	836

prune234.0ms

Filtered

65 candidates to 59 candidates (90.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	64	4	68

Merged error: 0.6b

Counts

68 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

6.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
6.4b	(- (+ (* 0.1111111111111111 (pow x 3)) 1) (* 0.16666666666666666 (pow x 2)))
10.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-div` `flip3--` `diff-log` `add-cbrt-cube` `flip--`
2×	`sub-neg` `pow1/3` `associate--l+` `sum-log`

Counts

4 → 54

Calls

4 calls:

8.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
11.0ms	(- (+ (* 0.1111111111111111 (pow x 3)) 1) (* 0.16666666666666666 (pow x 2)))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series374.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
43.0ms	(- (+ (* 0.1111111111111111 (pow x 3)) 1) (* 0.16666666666666666 (pow x 2)))
150.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
144.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify41.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	336	862
1	1254	800
2	5001	746

prune256.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	66	4	70

Merged error: 0.6b

Counts

70 → 4

regimes93.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.9b

bsearch178.0ms

Steps

Iters	Range		Point
10	8.159003009805276e-07	18724.121991280714	21.9973522139557

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	25
1	53	25
2	53	25

end0.0ms

sample2.7s

Algorithm

intervals

Results

880.0ms	1708×	body	1280	valid
744.0ms	10224×	body	80	valid
398.0ms	1243×	body	640	valid
137.0ms	615×	body	320	valid
136.0ms	1850×	body	80	overflowed
47.0ms	333×	body	160	valid