Details

analyze504.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample141.0ms

Algorithm

intervals

Results

68.0ms	48×	body	2560	valid
39.0ms	79×	body	1280	valid
18.0ms	72×	body	640	valid
5.0ms	28×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	14×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	229	7
1	229	7

prune3.0ms

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: 27.4b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5058	605

prune135.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	41	16	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	16	58

Merged error: 0.4b

Counts

58 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
0.4b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
1.6b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 138

Calls

4 calls:

18.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
2.0ms	(pow (cos x) 3)
4.0ms	(+ 1.0 (cos x))
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series46.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
7.0ms	(pow (cos x) 3)
2.0ms	(+ 1.0 (cos x))
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5700	2661

prune264.0ms

Filtered

84 candidates to 150 candidates (-78.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	138	12	150
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	147	19	166

Merged error: 0.3b

Counts

166 → 19

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (* (pow (cos x) 2) (cos x))) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
0.3b	(pow (cos x) 2)
0.4b	(+ 1.0 (cos x))
1.6b	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `*-un-lft-identity`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
5×	`pow1`
4×	`times-frac` `associate-/l*` `unpow2`
3×	`difference-cubes` `unpow-prod-down` `pow-unpow` `pow3`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ (- (pow 1.0 3) (* (pow (cos x) 2) (cos x))) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
2.0ms	(pow (cos x) 2)
3.0ms	(+ 1.0 (cos x))
7.0ms	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- (pow 1.0 3) (* (pow (cos x) 2) (cos x))) (* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x)))
3.0ms	(pow (cos x) 2)
2.0ms	(+ 1.0 (cos x))
7.0ms	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4969	1157
1	4969	1157

prune207.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	80	21	101

Merged error: 0.3b

Counts

101 → 21

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (+ 1.0 (cos x)) 3))
0.4b	(pow (+ 1.0 (cos x)) 3)
0.4b	(+ 1.0 (cos x))
1.6b	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`cube-div`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`difference-cubes` `+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow3` `pow-exp` `sum-log` `flip--` `rem-cbrt-cube` `unpow2` `rem-cube-cbrt`

Counts

4 → 76

Calls

4 calls:

4.0ms	(cbrt (pow (+ 1.0 (cos x)) 3))
4.0ms	(pow (+ 1.0 (cos x)) 3)
4.0ms	(+ 1.0 (cos x))
7.0ms	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(cbrt (pow (+ 1.0 (cos x)) 3))
6.0ms	(pow (+ 1.0 (cos x)) 3)
2.0ms	(+ 1.0 (cos x))
7.0ms	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4945	738
1	4945	738

prune127.0ms

Filtered

52 candidates to 88 candidates (-69.2%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	19	20
Picked	0	1	1
Done	0	0	0
Total	88	21	109

Merged error: 0.3b

Counts

109 → 21

regimes131.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.6b

bsearch35.0ms

Steps

Iters	Range		Point
6	0.016208292679736374	0.1687105879389078	0.023890754284735707
9	-9093.216721760618	-0.014854500102091779	-0.023756317422124803

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	121	109
1	121	109

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.3s	1577×	body	2560	valid
1.4s	2790×	body	1280	valid
479.0ms	1844×	body	640	valid
163.0ms	918×	body	320	valid
66.0ms	517×	body	160	valid
31.0ms	350×	body	80	valid
16.0ms	4×	body	5120	valid

Details

analyze504.0ms

sample141.0ms

simplify10.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series12.0ms

simplify36.0ms

prune135.0ms

localize16.0ms

rewrite40.0ms

series46.0ms

simplify40.0ms

prune264.0ms

localize17.0ms

rewrite27.0ms

series45.0ms

simplify40.0ms

prune207.0ms

localize20.0ms

rewrite21.0ms

series17.0ms

simplify43.0ms

prune127.0ms

regimes131.0ms

bsearch35.0ms

simplify2.0ms

end0.0ms

sample4.6s

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