Details

sample78.0ms

Algorithm

intervals

Results

26.0ms	45×	body	1280	valid
19.0ms	141×	body	80	valid
15.0ms	40×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	8×	body	160	valid

simplify23.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
16.0b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite60.0ms

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:

25.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
21.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series190.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
87.0ms	(/ (* (* (/ 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

prune283.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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:

11.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series179.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
43.0ms	(/ (sin x) (sin (* 0.5 x)))
47.0ms	(* (/ 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

prune402.0ms

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

rewrite29.0ms

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:

5.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
11.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))

series169.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
83.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* 0.5 x))))
49.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify158.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (40.0ms)

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

prune681.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

2326×	`times-frac`
904×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
424×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
242×	`neg-mul-1`
82×	`div-inv`
73×	`associate-/l*`
26×	`associate-/r*`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `div-sub` `distribute-frac-neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`neg-sub0`
1×	`associate-/r/` `associate-/l/`

Counts

3 → 1054

Calls

3 calls:

7.0ms	(/ (- (* 8.0 (sin (* x 0.5)))) (- 3.0))
36.0ms	(/ (/ (- (* 8.0 (sin (* x 0.5)))) (- 3.0)) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- (* 8.0 (sin (* x 0.5)))) (- 3.0))
88.0ms	(/ (/ (- (* 8.0 (sin (* x 0.5)))) (- 3.0)) (/ (sin x) (sin (* 0.5 x))))
44.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify208.0ms

Algorithm

egg-herbie

Counts

1063 → 1063

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5002	22128

prune4.3s

Pruning

8 alts after pruning (7 fresh and 1 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	22	11
1	33	11
2	33	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

894.0ms	1487×	body	1280	valid
499.0ms	1242×	body	640	valid
447.0ms	4343×	body	80	valid
174.0ms	633×	body	320	valid
61.0ms	295×	body	160	valid