Details

analyze224.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample134.0ms

Algorithm

intervals

Results

23.0ms	48×	body	2560	valid
9.0ms	58×	body	640	valid
9.0ms	35×	body	1280	valid
3.0ms	80×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	13×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	500	8
1	500	8

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: 29.5b

Counts

2 → 1

localize25.0ms

Local error

Found 2 expressions with local error:

13.6b	(/ (- 1.0 (cos x)) (* x x))
15.0b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 41

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (* x x))
4.0ms	(- 1.0 (cos x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ (- 1.0 (cos x)) (* x x))
4.0ms	(- 1.0 (cos x))

simplify45.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4894	437
1	4894	437

prune95.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	38	9	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	9	48

Merged error: 0.1b

Counts

48 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

12.9b	(sqrt (- 1.0 (cos x)))
12.9b	(sqrt (- 1.0 (cos x)))
15.0b	(- 1.0 (cos x))
15.0b	(- 1.0 (cos x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (cos x)))
3.0ms	(sqrt (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series19.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (cos x)))
5.0ms	(sqrt (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))
5.0ms	(- 1.0 (cos x))

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4900	584
1	4900	584

prune133.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	70	11	81

Merged error: 0.1b

Counts

81 → 11

localize78.0ms

Local error

Found 4 expressions with local error:

12.9b	(sqrt (- 1.0 (cos x)))
15.0b	(- 1.0 (cos x))
15.0b	(- 1.0 (cos x))
15.0b	(log (exp (- 1.0 (cos x))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `log-pow`
5×	`exp-prod` `sqrt-prod`
4×	`add-exp-log` `log-prod` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`sqrt-div` `diff-log`
1×	`rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `rem-log-exp` `exp-sum`

Counts

4 → 62

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
6.0ms	(log (exp (- 1.0 (cos x))))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5039	553

prune154.0ms

Filtered

54 candidates to 74 candidates (-37.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 0.1b

Counts

85 → 10

localize87.0ms

Local error

Found 4 expressions with local error:

12.9b	(sqrt (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x))))))
14.8b	(- (pow 1.0 3) (pow (cos x) 3))
15.0b	(- 1.0 (cos x))
15.0b	(log (exp (- 1.0 (cos x))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

138×	`add-sqr-sqrt`
81×	`sqrt-prod`
79×	`*-un-lft-identity`
76×	`times-frac`
66×	`difference-of-squares`
48×	`unpow-prod-down` `cube-prod`
35×	`add-cube-cbrt`
32×	`sqr-pow`
22×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1` `log-pow`
5×	`exp-prod`
4×	`difference-cubes` `add-exp-log` `log-prod` `add-cbrt-cube`
3×	`sub-neg`
2×	`rem-sqrt-square` `flip3--` `diff-log` `associate-/r/` `flip--`
1×	`log-div` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `sqrt-div` `rem-log-exp` `exp-sum` `flip-+` `div-inv`

Counts

4 → 158

Calls

4 calls:

21.0ms	(sqrt (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x))))))
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x))))))
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))
3.0ms	(- 1.0 (cos x))
3.0ms	(log (exp (- 1.0 (cos x))))

simplify94.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4937	4493
1	4937	4493

prune364.0ms

Filtered

94 candidates to 170 candidates (-80.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	168	12	180

Merged error: 0.1b

Counts

180 → 12

regimes84.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch48.0ms

Steps

Iters	Range		Point
8	0.00010925368023973285	0.5988921853613554	0.03595994027748503
9	-10382199.762014683	-0.003551435546146371	-0.036336696848678435

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	91
1	72	91

end0.0ms

sample3.8s

Algorithm

intervals

Results

810.0ms	1612×	body	2560	valid
310.0ms	1198×	body	1280	valid
245.0ms	1563×	body	640	valid
110.0ms	938×	body	320	valid
72.0ms	2259×	body	80	valid
33.0ms	430×	body	160	valid

Details

analyze224.0ms

sample134.0ms

simplify20.0ms

prune2.0ms

localize25.0ms

rewrite11.0ms

series9.0ms

simplify45.0ms

prune95.0ms

localize27.0ms

rewrite15.0ms

series19.0ms

simplify74.0ms

prune133.0ms

localize78.0ms

rewrite17.0ms

series17.0ms

simplify37.0ms

prune154.0ms

localize87.0ms

rewrite51.0ms

series43.0ms

simplify94.0ms

prune364.0ms

regimes84.0ms

bsearch48.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling