Details

sample144.0ms

Algorithm

intervals

Results

80.0ms	57×	body	2560	valid
32.0ms	75×	body	1280	valid
17.0ms	71×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	14×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

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: 30.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.3b	(- 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 → 52

Calls

2 calls:

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

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune153.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	45	13	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	13	59

Merged error: 0.1b

Counts

59 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.9b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.3b	(- 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 → 112

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))

series136.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
42.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
41.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify94.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune279.0ms

Filtered

124 candidates to 90 candidates (72.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	122	15	137

Merged error: 0.0b

Counts

137 → 15

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.3b	(- 1.0 (cos x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`flip3--` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

4.0ms	(/ 1 (sin x))
10.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
4.0ms	(- 1.0 (cos x))

series70.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ 1 (sin x))
34.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
18.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	320	548
1	1393	482
2	5001	456

prune156.0ms

Filtered

96 candidates to 57 candidates (59.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	96	15	111

Merged error: 0.0b

Counts

111 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.3b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

25.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series218.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
28.0ms	(pow (cos x) 3)
16.0ms	(+ (cos x) 1.0)
47.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	617	2953
1	2699	2889
2	5001	2810

prune357.0ms

Filtered

201 candidates to 105 candidates (52.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	199	17	216

Merged error: 0.0b

Counts

216 → 17

regimes152.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.5b

bsearch68.0ms

Steps

Iters	Range		Point
6	0.011261476250181132	0.06406876111163662	0.02361334001762777
9	-3.7752751361666412	-2.6386627092684764e-08	-0.01928967347682116

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	48	27

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1597×	body	2560	valid
1.2s	2707×	body	1280	valid
458.0ms	1924×	body	640	valid
155.0ms	913×	body	320	valid
60.0ms	489×	body	160	valid
28.0ms	6×	body	5120	valid
24.0ms	364×	body	80	valid