Details

sample84.0ms

Algorithm

intervals

Results

55.0ms	180×	body	1280	valid
7.0ms	278×	body	80	valid
6.0ms	33×	body	640	valid
3.0ms	30×	body	320	valid
1.0ms	8×	body	160	valid

simplify135.0ms

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

prune6.0ms

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: 29.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.6b	(+ (- (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)))

simplify84.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (18.0ms)

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

prune54.0ms

Filtered

29 candidates to 41 candidates (-41.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 0.0b

Counts

42 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

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

series26.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
8.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
4.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (40.0ms)

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

prune137.0ms

Filtered

55 candidates to 87 candidates (-58.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 0.0b

Counts

89 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
28.7b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
28.7b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite28.0ms

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))
7.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
9.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/12 (pow x 4))
3.0ms	(* 1/12 (pow x 4))
7.0ms	(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)))))

simplify197.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	259	662
1	1019	626
2	4841	616
3	5001	616

prune263.0ms

Filtered

64 candidates to 94 candidates (-46.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	94	3	97

Merged error: 0.0b

Counts

97 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
0.1b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
19.0b	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite28.0ms

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:

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

series21.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* 1/360 (pow x 6))
3.0ms	(* 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))

simplify63.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

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

prune174.0ms

Filtered

62 candidates to 114 candidates (-83.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	114	3	117

Merged error: 0.0b

Counts

117 → 3

regimes30.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	17
1	19	17

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.8s	5616×	body	1280	valid
224.0ms	1271×	body	640	valid
211.0ms	7996×	body	80	valid
69.0ms	637×	body	320	valid
21.0ms	301×	body	160	valid

Details

sample84.0ms

simplify135.0ms

prune6.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify84.0ms

prune54.0ms

localize9.0ms

rewrite23.0ms

series26.0ms

simplify47.0ms

prune137.0ms

localize12.0ms

rewrite28.0ms

series22.0ms

simplify197.0ms

prune263.0ms

localize13.0ms

rewrite28.0ms

series21.0ms

simplify63.0ms

prune174.0ms

regimes30.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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