Details

sample63.0ms

Algorithm

intervals

Results

29.0ms	59×	body	1280	valid
10.0ms	32×	body	640	valid
8.0ms	134×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify28.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize18.0ms

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)))
13.4b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite53.0ms

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:

20.0ms	(* (* (/ 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))

series187.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
86.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify68.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (58.0ms)

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

prune262.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite43.0ms

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))
25.0ms	(* (* (/ 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:

44.0ms	(/ (sin (* 0.5 x)) (sin x))
82.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify76.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (65.0ms)

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

prune329.0ms

Filtered

113 candidates to 81 candidates (71.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.1b	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
0.2b	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
33×	`associate-l`
28×	`sqrt-prod`
20×	`pow1`
17×	`associate-r`
16×	`prod-exp` `cbrt-unprod`
13×	`sqrt-div` `associate-*l/`
10×	`pow-prod-down`
6×	`frac-times`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-*r/` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 147

Calls

4 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
13.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
83.0ms	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
29.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (sin (* 0.5 x)) (sin x))
72.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
173.0ms	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
102.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

simplify95.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	601	1552
1	3040	1250
2	5002	1217

prune515.0ms

Filtered

159 candidates to 117 candidates (73.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (/ (sin (* 0.5 x)) (sin x))))
0.2b	(expm1 (/ (sin (* 0.5 x)) (sin x)))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (log1p (expm1 (/ (sin (* 0.5 x)) (sin x)))))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (sin (* 0.5 x)) (sin x))))
0.0ms	(expm1 (/ (sin (* 0.5 x)) (sin x)))
17.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (log1p (expm1 (/ (sin (* 0.5 x)) (sin x)))))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series610.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(log1p (expm1 (/ (sin (* 0.5 x)) (sin x))))
95.0ms	(expm1 (/ (sin (* 0.5 x)) (sin x)))
281.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (log1p (expm1 (/ (sin (* 0.5 x)) (sin x)))))
45.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify57.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	361	776
1	1536	620
2	5001	598

prune286.0ms

Filtered

91 candidates to 66 candidates (72.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

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

sample1.8s

Algorithm

intervals

Results

801.0ms	1579×	body	1280	valid
403.0ms	1210×	body	640	valid
288.0ms	4328×	body	80	valid
133.0ms	602×	body	320	valid
41.0ms	281×	body	160	valid