Details

sample60.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
14.0ms	45×	body	640	valid
8.0ms	135×	body	80	valid
4.0ms	17×	body	320	valid
2.0ms	11×	body	160	valid

simplify20.0ms

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: 14.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
14.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite156.0ms

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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 85

Calls

3 calls:

63.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
27.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
63.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series164.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
34.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
75.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify60.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	412	862
1	2127	656
2	5001	637

prune237.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-l`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/l*`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 116

Calls

3 calls:

32.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
15.0ms	(/ (sin x) (sin (* 0.5 x)))
26.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series150.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
37.0ms	(/ (sin x) (sin (* 0.5 x)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify71.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	550	1204
1	2727	1016
2	5001	992

prune342.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

217×	`times-frac`
97×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
25×	`div-inv`
19×	`associate-/r*`
16×	`cbrt-undiv` `div-exp`
11×	`associate-/l*`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `associate-/l/`

Counts

3 → 189

Calls

3 calls:

21.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
24.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* 0.5 x))))
12.0ms	(/ (sin x) (sin (* 0.5 x)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
75.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* 0.5 x))))
40.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify140.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1007	2777
1	4941	2580
2	5001	2580

prune571.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 8.0 (sin (* x 0.5))) 3.0)
0.1b	(/ (sin (* 0.5 x)) (sin x))
0.1b	(/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ 1 (/ (sin (* 0.5 x)) (sin x))))
0.2b	(/ 1 (/ (sin (* 0.5 x)) (sin x)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

1058×	`times-frac`
426×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
100×	`add-exp-log`
85×	`div-inv`
66×	`div-exp`
63×	`associate-/r*`
52×	`add-cbrt-cube`
30×	`cbrt-undiv`
14×	`associate-/l*`
10×	`associate-/r/`
8×	`rec-exp` `1-exp` `prod-exp`
5×	`pow1`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

4 → 533

Calls

4 calls:

21.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
12.0ms	(/ (sin (* 0.5 x)) (sin x))
33.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ 1 (/ (sin (* 0.5 x)) (sin x))))
15.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
35.0ms	(/ (sin (* 0.5 x)) (sin x))
72.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ 1 (/ (sin (* 0.5 x)) (sin x))))
45.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))

simplify133.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2697	9454
1	5002	8751

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	9
1	16	9
2	16	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

782.0ms	1596×	body	1280	valid
404.0ms	1259×	body	640	valid
282.0ms	4231×	body	80	valid
131.0ms	614×	body	320	valid
44.0ms	300×	body	160	valid