Details

sample89.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

60.0ms	178×	body	1280	valid
7.0ms	39×	body	640	valid
7.0ms	230×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify138.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	65	5
5	96	5
6	140	5
7	285	5
8	1642	5
9	5001	5

prune2.0ms

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: 33.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.9b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	209	282
1	694	269
2	3196	260
3	5001	260

prune57.0ms

Filtered

29 candidates to 41 candidates (-41.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Merged error: 0.0b

Counts

42 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

7.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
4.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
7.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
12.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
5.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	438
2	5001	422

prune143.0ms

Filtered

55 candidates to 87 candidates (-58.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
24.3b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
24.3b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-exp-log` `associate-r`
12×	`add-cube-cbrt`
8×	`unpow-prod-down` `sqrt-prod` `add-cbrt-cube`
6×	`pow1` `associate-l` `prod-exp` `unswap-sqr`
4×	`sqrt-div` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
6.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
7.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series23.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/12 (pow x 4))
4.0ms	(* 1/12 (pow x 4))
8.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
8.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	260	676
1	1056	626
2	5002	616

prune266.0ms

Filtered

64 candidates to 94 candidates (-46.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	94	5	99

Merged error: 0.0b

Counts

99 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
0.2b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
22.4b	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt` `unpow-prod-down`
15×	`add-exp-log`
14×	`cbrt-prod` `associate-r`
9×	`add-cbrt-cube`
8×	`cube-prod`
6×	`associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
5×	`pow1`
4×	`cube-div` `distribute-lft-out` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`cube-mult` `cbrt-div` `flip3-+` `unpow3` `*-commutative` `cbrt-unprod` `flip-+`
1×	`pow-pow` `pow1/3` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 102

Calls

4 calls:

7.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))
8.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
7.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))
7.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
6.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

simplify61.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	419	910
1	1865	843
2	5003	830

prune175.0ms

Filtered

61 candidates to 114 candidates (-86.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	114	5	119

Merged error: 0.0b

Counts

119 → 5

regimes68.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

1.8s	5605×	body	1280	valid
228.0ms	1281×	body	640	valid
216.0ms	7866×	body	80	valid
67.0ms	620×	body	320	valid
22.0ms	300×	body	160	valid

Details

sample89.0ms

simplify138.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify87.0ms

prune57.0ms

localize10.0ms

rewrite24.0ms

series26.0ms

simplify50.0ms

prune143.0ms

localize13.0ms

rewrite25.0ms

series23.0ms

simplify44.0ms

prune266.0ms

localize12.0ms

rewrite30.0ms

series22.0ms

simplify61.0ms

prune175.0ms

regimes68.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling