Details

sample88.0ms

Algorithm

intervals

Results

55.0ms	170×	body	1280	valid
11.0ms	295×	body	80	valid
8.0ms	46×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	12×	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

Filtered

1 candidates to 0 candidates (0.0%)

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: 30.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.2b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite13.0ms

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)
8.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series73.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
60.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify90.0ms

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

prune91.0ms

Filtered

41 candidates to 29 candidates (70.7%)

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

localize10.0ms

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))

rewrite29.0ms

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))))
9.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series273.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
52.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
52.0ms	(* 1/360 (pow x 6))
35.0ms	(* 1/12 (pow x 4))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (43.0ms)

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

prune172.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Merged error: 0.0b

Counts

89 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
26.4b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
26.4b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite27.0ms

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

series283.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* 1/12 (pow x 4))
36.0ms	(* 1/12 (pow x 4))
105.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
99.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify202.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (32.0ms)

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

prune259.0ms

Filtered

94 candidates to 64 candidates (68.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	94	5	99

Merged error: 0.0b

Counts

99 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (log (exp (* 1/12 (pow x 4))))))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
3.0b	(log (exp (* 1/12 (pow x 4))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

10.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (log (exp (* 1/12 (pow x 4))))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))
2.0ms	(log (exp (* 1/12 (pow x 4))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (log (exp (* 1/12 (pow x 4))))))
46.0ms	(* 1/360 (pow x 6))
42.0ms	(* 1/12 (pow x 4))
38.0ms	(log (exp (* 1/12 (pow x 4))))

simplify46.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	308	461
1	1313	413
2	5002	400

prune199.0ms

Filtered

90 candidates to 57 candidates (63.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	90	5	95

Merged error: 0.0b

Counts

95 → 5

regimes30.0ms

Accuracy

69.2% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.6b

bsearch26.0ms

Steps

Iters	Range		Point
6	-0.24198949490186406	-0.015327944483214716	-0.030068988456940456

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.8s	5581×	body	1280	valid
230.0ms	1283×	body	640	valid
223.0ms	8199×	body	80	valid
74.0ms	623×	body	320	valid
27.0ms	366×	body	160	valid

Details

sample88.0ms

simplify138.0ms

prune2.0ms

localize6.0ms

rewrite13.0ms

series73.0ms

simplify90.0ms

prune91.0ms

localize10.0ms

rewrite29.0ms

series273.0ms

simplify51.0ms

prune172.0ms

localize12.0ms

rewrite27.0ms

series283.0ms

simplify202.0ms

prune259.0ms

localize17.0ms

rewrite25.0ms

series184.0ms

simplify46.0ms

prune199.0ms

regimes30.0ms

bsearch26.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling