Details

sample63.0ms

Algorithm

intervals

Results

26.0ms	52×	body	1280	valid
12.0ms	35×	body	640	valid
10.0ms	140×	body	80	valid
5.0ms	23×	body	320	valid
1.0ms	6×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
14.9b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
5×	`associate-*l/`
4×	`pow-prod-down`
3×	`associate-/r*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 79

Calls

3 calls:

19.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
24.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series173.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
79.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	402	818
1	2097	614
2	5002	599

prune215.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
14×	`associate-l`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `associate-*l/`
3×	`associate-/r` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 98

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
21.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (sin (* 0.5 x)) (sin x))
79.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify65.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	463	970
1	2477	779
2	5002	764

prune264.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 8.0 (sin (* x 0.5))) 3.0)
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`add-log-exp`
2×	`frac-2neg` `clear-num` `unswap-sqr`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 94

Calls

3 calls:

5.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
3.0ms	(/ (sin (* 0.5 x)) (sin x))
15.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
42.0ms	(/ (sin (* 0.5 x)) (sin x))
77.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	458	994
1	2409	812
2	5001	788

prune254.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(* (* 8.0 (sin (* x 0.5))) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-exp-log`
58×	`add-cbrt-cube`
51×	`prod-exp`
42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`*-un-lft-identity` `cbrt-unprod`
25×	`add-cube-cbrt` `div-exp`
17×	`pow1`
14×	`associate-r` `associate-l`
13×	`cbrt-undiv`
9×	`pow-prod-down`
6×	`rec-exp` `1-exp` `unswap-sqr`
5×	`associate-*r/`
3×	`associate-/r` `div-inv` `associate-/l` `add-log-exp`
2×	`frac-times` `associate-l/` `-commutative`
1×	`frac-2neg` `clear-num`

Counts

3 → 128

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
14.0ms	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
24.0ms	(* (* 8.0 (sin (* x 0.5))) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

series173.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (sin (* 0.5 x)) (sin x))
59.0ms	(* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x)))
76.0ms	(* (* 8.0 (sin (* x 0.5))) (* (/ 1 3.0) (/ (sin (* 0.5 x)) (sin x))))

simplify79.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	635	1440
1	2955	1113
2	5001	1057

prune269.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	17	9
2	17	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

881.0ms	1482×	body	1280	valid
485.0ms	1251×	body	640	valid
362.0ms	4328×	body	80	valid
167.0ms	629×	body	320	valid
55.0ms	310×	body	160	valid