Details

sample67.0ms

Algorithm

intervals

Results

28.0ms	52×	body	1280	valid
12.0ms	35×	body	640	valid
11.0ms	140×	body	80	valid
6.0ms	23×	body	320	valid
1.0ms	6×	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: 15.1b

localize11.0ms

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))

rewrite58.0ms

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:

24.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
20.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series181.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
84.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify62.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (53.0ms)

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

prune263.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))

rewrite40.0ms

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

Counts

3 → 104

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
22.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series166.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin (* 0.5 x)) (sin x))
83.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify71.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	474	1006
1	2505	814
2	5001	799

prune317.0ms

Pruning

10 alts after pruning (10 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	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

rewrite31.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `unswap-sqr`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

5.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
4.0ms	(/ (sin (* 0.5 x)) (sin x))
18.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

series165.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
40.0ms	(/ (sin (* 0.5 x)) (sin x))
83.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	469	1030
1	2437	847
2	5001	823

prune315.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* 0.5 x)) (sin x)))
0.2b	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

0.0ms	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
4.0ms	(/ (sin (* 0.5 x)) (sin x))
8.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* 0.5 x)) (sin x)))
0.0ms	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
40.0ms	(/ (sin (* 0.5 x)) (sin x))
353.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* 0.5 x)) (sin x)))
197.0ms	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	310	903
1	1238	791
2	5002	783

prune318.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	11
1	19	11
2	19	11

end0.0ms

sample2.0s

Algorithm

intervals

Results

816.0ms	1482×	body	1280	valid
448.0ms	1251×	body	640	valid
349.0ms	4328×	body	80	valid
166.0ms	629×	body	320	valid
58.0ms	310×	body	160	valid