Details

sample100.0ms

Algorithm

intervals

Results

31.0ms	63×	body	1280	valid
20.0ms	52×	body	10240	exit
17.0ms	314×	body	80	valid
10.0ms	42×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify38.0ms

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

prune9.0ms

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: 31.2b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(exp (- (* (+ 1.0 eps) x)))
0.0b	(exp (- (* (- 1.0 eps) x)))
1.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
30×	`flip3-+` `flip-+`
28×	`flip3--` `flip--`
19×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube`
5×	`add-exp-log`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
3.0ms	(exp (- (* (+ 1.0 eps) x)))
4.0ms	(exp (- (* (- 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)))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
26.0ms	(exp (- (* (+ 1.0 eps) x)))
26.0ms	(exp (- (* (- 1.0 eps) x)))
194.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify143.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	1278	3905
1	4619	3606
2	5001	3568

prune396.0ms

Filtered

177 candidates to 96 candidates (54.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	177	2	179

Merged error: 0.4b

Counts

179 → 2

localize13.0ms

Local error

Found 1 expressions with local error:

5.6b	(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))))

series39.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

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

simplify30.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (28.0ms)

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

prune38.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	13	2	15

Merged error: 0.4b

Counts

15 → 2

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

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 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

series39.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

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

simplify108.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	49	82
1	132	67
2	534	67
3	3076	67
4	5001	67

prune31.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Merged error: 0.4b

Counts

15 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
0.8b	(* (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
3.9b	(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
3.9b	(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
6.0ms	(* (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
1.0ms	(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
2.0ms	(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

series195.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
41.0ms	(* (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
55.0ms	(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
60.0ms	(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

simplify186.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	181	721
1	656	625
2	4112	593
3	5001	593

prune213.0ms

Filtered

103 candidates to 60 candidates (58.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	103	3	106

Merged error: 0.4b

Counts

106 → 3

regimes50.0ms

Accuracy

96% (0.6b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 16.6b

bsearch131.0ms

Steps

Iters	Range		Point
10	9.53408654096399	1.2747519734402982e+17	22.7410926704305

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	21
1	56	21
2	56	21

end0.0ms

sample2.9s

Algorithm

intervals

Results

793.0ms	1930×	body	10240	exit
739.0ms	1708×	body	1280	valid
530.0ms	9867×	body	80	valid
339.0ms	1334×	body	640	valid
109.0ms	638×	body	320	valid
33.0ms	317×	body	160	valid