Details

sample488.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 48.311013%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

33.0ms	63×	body	1280	valid
10.0ms	131×	body	80	valid
9.0ms	30×	body	640	valid
7.0ms	24×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	2×	body	1280	invalid
0.0ms	1×	body	640	invalid
0.0ms	3×	body	80	invalid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (33.0ms)

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

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 29.7b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (neg (* (- 1.0 eps) x)))
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
1.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

81×	`exp-neg` `frac-sub`
80×	`frac-times`
61×	`neg-sub0` `exp-diff`
40×	`associate-r/` `associate-l/`
31×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
20×	`un-div-inv`
18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`associate-l`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `exp-prod` `associate-r`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `difference-of-squares` `unswap-sqr`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `times-frac` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

3.0ms	(exp (neg (* (- 1.0 eps) x)))
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
15.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
16.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(exp (neg (* (- 1.0 eps) x)))
10.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
15.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
45.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify139.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	1201	4059
1	4400	3786
2	5002	3771

prune379.0ms

Filtered

96 candidates to 180 candidates (-87.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	177	3	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	3	181

Merged error: 0.4b

Counts

181 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

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)))

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* 0.6666666666666667 (pow x 3))
4.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify33.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (28.0ms)

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

prune85.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Merged error: 0.4b

Counts

54 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

7.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
12.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
12.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
12.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite27.0ms

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:

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

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
10.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
9.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify129.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	252	983
1	905	918
2	4255	839
3	5002	839

prune364.0ms

Filtered

59 candidates to 65 candidates (-10.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	65	4	69

Merged error: 0.4b

Counts

69 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

7.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
7.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
12.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
12.9b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite29.0ms

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:

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

series30.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
4.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
11.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify129.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	252	862
1	905	800
2	4255	738
3	5002	738

prune419.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

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: 0.4b

Counts

70 → 4

regimes147.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 16.7b

bsearch105.0ms

Steps

Iters	Range		Point
9	1.5938854338342312e-06	5.883618671938579	0.8410446680516683

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	33
1	57	33
2	57	33

end0.0ms

sample2.4s

Algorithm

intervals

sampling

Space saved by range analysis: 48.311013%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

903.0ms	1697×	body	1280	valid
424.0ms	1255×	body	640	valid
314.0ms	4096×	body	80	valid
140.0ms	615×	body	320	valid
49.0ms	337×	body	160	valid
8.0ms	97×	body	80	invalid
7.0ms	14×	body	1280	invalid
7.0ms	91×	body	80	overflowed
6.0ms	12×	body	640	invalid
1.0ms	2×	body	320	invalid
0.0ms	1×	body	160	invalid

Details

sample488.0ms

simplify35.0ms

prune7.0ms

localize16.0ms

rewrite57.0ms

series75.0ms

simplify139.0ms

prune379.0ms

localize10.0ms

rewrite14.0ms

series8.0ms

simplify33.0ms

prune85.0ms

localize16.0ms

rewrite27.0ms

series33.0ms

simplify129.0ms

prune364.0ms

localize17.0ms

rewrite29.0ms

series30.0ms

simplify129.0ms

prune419.0ms

regimes147.0ms

bsearch105.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling