Details

sample95.0ms

Algorithm

intervals

Results

31.0ms	55×	body	1280	valid
21.0ms	303×	body	80	valid
14.0ms	45×	body	640	valid
5.0ms	26×	body	320	valid
5.0ms	61×	body	80	overflowed
1.0ms	6×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (36.0ms)

Iter	Nodes	Cost
0	47	16
1	124	16
2	365	16
3	1376	16
4	5001	15

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 31.6b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
2.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out`

Counts

4 → 183

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
16.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
7.0ms	(* (- 1.0 eps) x)
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
53.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
28.0ms	(* (- 1.0 eps) x)
193.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1372	4120
1	5001	3814

prune464.0ms

Filtered

195 candidates to 107 candidates (54.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	194	3	197

Merged error: 0.8b

Counts

197 → 3

localize10.0ms

Local error

Found 1 expressions with local error:

5.2b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series43.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify29.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	42	89
1	136	78
2	722	78
3	5002	75

prune43.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Merged error: 0.8b

Counts

16 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

5.2b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
155.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
149.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
154.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	190	752
1	639	693
2	2777	627
3	5001	621

prune245.0ms

Filtered

61 candidates to 58 candidates (95.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	59	6	65

Merged error: 0.8b

Counts

65 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

5.2b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
10.4b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
157.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
156.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
152.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	190	752
1	639	693
2	2777	627
3	5001	621

prune400.0ms

Filtered

61 candidates to 58 candidates (95.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	61	6	67

Merged error: 0.8b

Counts

67 → 6

regimes108.0ms

Accuracy

96.6% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.6b

bsearch164.0ms

Steps

Iters	Range		Point
10	121.55286302593997	3002406562115.273	357.6465136238462

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	21
1	42	21
2	42	21

end0.0ms

sample2.6s

Algorithm

intervals

Results

856.0ms	1703×	body	1280	valid
712.0ms	10160×	body	80	valid
374.0ms	1212×	body	640	valid
138.0ms	660×	body	320	valid
130.0ms	1869×	body	80	overflowed
44.0ms	328×	body	160	valid