Details

analyze540.0ms

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

sample145.0ms

Algorithm

intervals

Results

67.0ms	50×	body	2560	valid
38.0ms	73×	body	1280	valid
17.0ms	64×	body	640	valid
7.0ms	38×	body	320	valid
6.0ms	2×	body	5120	valid
2.0ms	15×	body	160	valid
1.0ms	14×	body	80	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	7
1	9	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: 30.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.5b	(- 1.0 (cos x))

rewrite16.0ms

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:

10.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 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))

simplify38.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5247	606

prune119.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	44	13	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	13	58

Merged error: 0.2b

Counts

58 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/240 (pow x 5)) (* x 1/2))
0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
0.1b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

4.0ms	(+ (* 1/240 (pow x 5)) (* x 1/2))
7.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series27.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (* 1/240 (pow x 5)) (* x 1/2))
6.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
4.0ms	(* 1/240 (pow x 5))
4.0ms	(* 1/24 (pow x 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4993	868
1	4993	868

prune164.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Merged error: 0.2b

Counts

105 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5))) (* x 1/2))
0.0b	(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
0.1b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+l+` `unpow3`

Counts

4 → 80

Calls

4 calls:

7.0ms	(+ (+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5))) (* x 1/2))
4.0ms	(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5))) (* x 1/2))
11.0ms	(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
4.0ms	(* 1/240 (pow x 5))
4.0ms	(* 1/24 (pow x 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4914	902
1	4914	902

prune162.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	92	13	105

Merged error: 0.2b

Counts

105 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.7b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.5b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series31.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
10.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

simplify73.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4949	1214
1	4949	1214

prune153.0ms

Filtered

89 candidates to 123 candidates (-38.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	122	14	136

Merged error: 0.1b

Counts

136 → 14

regimes207.0ms

Accuracy

98% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	71
1	47	71

end0.0ms

analyze533.0ms

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

sample4.6s

Algorithm

intervals

Results

2.3s	1553×	body	2560	valid
1.4s	2730×	body	1280	valid
530.0ms	1895×	body	640	valid
173.0ms	955×	body	320	valid
68.0ms	524×	body	160	valid
26.0ms	338×	body	80	valid
14.0ms	5×	body	5120	valid

Details

analyze540.0ms

sample145.0ms

simplify2.0ms

prune3.0ms

localize7.0ms

rewrite16.0ms

series12.0ms

simplify38.0ms

prune119.0ms

localize11.0ms

rewrite25.0ms

series27.0ms

simplify53.0ms

prune164.0ms

localize13.0ms

rewrite25.0ms

series25.0ms

simplify43.0ms

prune162.0ms

localize11.0ms

rewrite27.0ms

series31.0ms

simplify73.0ms

prune153.0ms

regimes207.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

analyze533.0ms

sample4.6s

Profiling