Details

sample113.0ms

Algorithm

intervals

Results

31.0ms	79×	body	10240	exit
26.0ms	64×	body	1280	valid
19.0ms	352×	body	80	valid
14.0ms	42×	body	640	valid
3.0ms	21×	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: 31.8b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
2.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite64.0ms

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:

13.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
6.0ms	(* (- 1.0 eps) x)
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
22.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
27.0ms	(* (- 1.0 eps) x)
49.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
192.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1372	4120
1	5001	3814

prune455.0ms

Filtered

195 candidates to 107 candidates (54.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	2	197

Merged error: 0.2b

Counts

197 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- 2.0 (* 1.0 (pow x 2)))
5.8b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef`

Counts

2 → 30

Calls

2 calls:

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

series98.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- 2.0 (* 1.0 (pow x 2)))
39.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify67.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	126	221
1	412	193
2	2139	191
3	5001	171

prune84.0ms

Filtered

36 candidates to 27 candidates (75.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	35	3	38

Merged error: 0.2b

Counts

38 → 3

localize7.0ms

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)

series181.0ms

Counts

1 → 3

Calls

1 calls:

181.0ms

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

simplify109.0ms

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

prune28.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Merged error: 0.2b

Counts

16 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 2.0 (* 1.0 (pow x 2)))
0.0b	(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
1.9b	(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
5.8b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `prod-diff`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow-exp` `flip--` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 78

Calls

4 calls:

3.0ms	(- 2.0 (* 1.0 (pow x 2)))
2.0ms	(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
2.0ms	(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
1.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series198.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- 2.0 (* 1.0 (pow x 2)))
63.0ms	(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
38.0ms	(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
41.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	250	677
1	907	626
2	5001	618

prune183.0ms

Filtered

90 candidates to 56 candidates (62.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	1	1
Picked	0	1	1
Done	1	0	1
Total	90	3	93

Merged error: 0.2b

Counts

93 → 3

regimes49.0ms

Accuracy

96.4% (0.6b remaining)

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

bsearch146.0ms

Steps

Iters	Range		Point
10	1.9435667087631803	128700106451.34695	154.4482937142435

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	23
1	60	23
2	60	23

end0.0ms

sample2.9s

Algorithm

intervals

Results

793.0ms	1967×	body	10240	exit
773.0ms	1786×	body	1280	valid
556.0ms	10024×	body	80	valid
318.0ms	1253×	body	640	valid
97.0ms	590×	body	320	valid
34.0ms	321×	body	160	valid