Details

analyze235.0ms

Algorithm: search

sample73.0ms

Algorithm

intervals

Results

30.0ms	54×	body	1280	valid
17.0ms	50×	body	640	valid
10.0ms	126×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	8×	body	80	invalid
0.0ms	4×	body	80	overflowed

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 (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: 30.6b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

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)))
13.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(exp (neg (* (- 1.0 eps) x)))
11.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
10.0ms	(* (+ 1.0 (/ 1.0 eps)) (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)))))

simplify141.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (104.0ms)

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

prune360.0ms

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: 0.6b

Counts

181 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.6666666666666667 (pow x 3))
6.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite16.0ms

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:

8.0ms	(* 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

prune84.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0.6b

Counts

54 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 0.6666666666666667 (pow x 3)))
0.0b	(* 0.6666666666666667 (pow x 3))
2.0b	(log (exp (* 0.6666666666666667 (pow x 3))))
6.8b	(- (+ (log (exp (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

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

series16.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify37.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	252	420
1	1041	358
2	5001	351

prune135.0ms

Filtered

51 candidates to 81 candidates (-58.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	81	4	85

Merged error: 0.6b

Counts

85 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
3.3b	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
6.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
6.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

6.0ms	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
6.0ms	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
9.0ms	(- (+ (* 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)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
6.0ms	(sqrt (- (+ (* 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)))
4.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify107.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	199	708
1	707	666
2	3357	652
3	5001	650

prune192.0ms

Filtered

54 candidates to 70 candidates (-29.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	70	4	74

Merged error: 0.6b

Counts

74 → 4

regimes148.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 17.3b

bsearch142.0ms

Steps

Iters	Range		Point
8	0.013539988030895631	5.883327029445557	1.508259436498545

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	35
1	59	35
2	59	35

end0.0ms

analyze233.0ms

Algorithm: search

sample2.1s

Algorithm

intervals

Results

910.0ms	1632×	body	1280	valid
418.0ms	1213×	body	640	valid
342.0ms	4182×	body	80	valid
153.0ms	639×	body	320	valid
52.0ms	334×	body	160	valid
19.0ms	235×	body	80	invalid
14.0ms	178×	body	80	overflowed
9.0ms	16×	body	1280	invalid
5.0ms	13×	body	640	invalid
2.0ms	6×	body	320	invalid

Details

analyze235.0ms

sample73.0ms

simplify36.0ms

prune9.0ms

localize17.0ms

rewrite58.0ms

series72.0ms

simplify141.0ms

prune360.0ms

localize9.0ms

rewrite16.0ms

series8.0ms

simplify33.0ms

prune84.0ms

localize12.0ms

rewrite20.0ms

series16.0ms

simplify37.0ms

prune135.0ms

localize12.0ms

rewrite30.0ms

series20.0ms

simplify107.0ms

prune192.0ms

regimes148.0ms

bsearch142.0ms

simplify2.0ms

end0.0ms

analyze233.0ms

sample2.1s

Profiling