Details

sample91.0ms

Algorithm

intervals

Results

35.0ms	44×	body	2560	valid
19.0ms	49×	body	1280	valid
12.0ms	49×	body	640	valid
7.0ms	32×	body	320	valid
4.0ms	64×	body	80	valid
2.0ms	18×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune3.0ms

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: 31.6b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
13.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite21.0ms

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 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
13.0ms	(/ (- 1.0 (cos x)) (* x x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(- 1.0 (cos x))
78.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune105.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	37	11	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	11	49

Merged error: 0.0b

Counts

49 → 11

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
40×	`sqrt-prod`
38×	`add-cube-cbrt`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
4×	`pow1` `flip3--` `sqrt-div` `flip--` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

6.0ms	(/ (sqrt (- 1.0 (cos x))) x)
6.0ms	(/ (sqrt (- 1.0 (cos x))) x)
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series222.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (sqrt (- 1.0 (cos x))) x)
91.0ms	(/ (sqrt (- 1.0 (cos x))) x)
21.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify101.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	242	1020
1	706	972
2	2968	960
3	5002	960

prune298.0ms

Filtered

138 candidates to 92 candidates (66.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	139	10	149

Merged error: 0.0b

Counts

149 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (sqrt (- 1.0 (cos x))) (/ 1 x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
37×	`times-frac`
30×	`add-cube-cbrt`
28×	`sqrt-prod`
15×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
8×	`associate-l` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `sqrt-div` `unswap-sqr`
5×	`flip3--` `flip--`
4×	`prod-exp`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `frac-times` `sub-neg` `diff-log` `associate-*l/` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`rec-exp` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative`

Counts

4 → 125

Calls

4 calls:

6.0ms	(/ (sqrt (- 1.0 (cos x))) x)
11.0ms	(* (sqrt (- 1.0 (cos x))) (/ 1 x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (sqrt (- 1.0 (cos x))) x)
92.0ms	(* (sqrt (- 1.0 (cos x))) (/ 1 x))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify45.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	398	957
1	1459	883
2	5001	871

prune295.0ms

Filtered

137 candidates to 90 candidates (65.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	137	10	147

Merged error: 0.0b

Counts

147 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ 1.0 (cos x))
0.4b	(* (sqrt (+ 1.0 (cos x))) x)
1.9b	(- (* 1.0 1.0) (* (cos x) (cos x)))
1.9b	(- 1.0 (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt` `associate-l`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sqrt-prod`
3×	`associate-r`
2×	`sub-neg` `flip3--` `flip3-+` `sqrt-div` `diff-log` `associate-*l/` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `sqr-cos` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `associate--r+` `distribute-lft-out--`

Counts

4 → 65

Calls

4 calls:

3.0ms	(+ 1.0 (cos x))
7.0ms	(* (sqrt (+ 1.0 (cos x))) x)
4.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))
7.0ms	(- 1.0 (cos x))

series145.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ 1.0 (cos x))
84.0ms	(* (sqrt (+ 1.0 (cos x))) x)
33.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))
19.0ms	(- 1.0 (cos x))

simplify119.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	320	431
1	1094	396
2	4300	396
3	5002	396

prune226.0ms

Filtered

77 candidates to 55 candidates (71.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 0.0b

Counts

87 → 10

regimes92.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.3b

bsearch74.0ms

Steps

Iters	Range		Point
8	2.0262054515877825e-05	0.3235305135594418	0.030296156057222207
10	-85019.06990604498	-4.503960361653909e-11	-0.03159820685045102

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	31
1	49	31

end0.0ms

sample1.7s

Algorithm

intervals

Results

752.0ms	1648×	body	2560	valid
290.0ms	1252×	body	1280	valid
215.0ms	1469×	body	640	valid
208.0ms	2220×	body	80	valid
103.0ms	907×	body	320	valid
36.0ms	504×	body	160	valid