Details

sample75.0ms

Algorithm

intervals

Results

32.0ms	54×	body	1280	valid
16.0ms	41×	body	640	valid
12.0ms	140×	body	80	valid
4.0ms	13×	body	320	valid
2.0ms	8×	body	160	valid

simplify16.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize14.0ms

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)))
16.4b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite50.0ms

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)))
9.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
19.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series23.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
4.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
13.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (47.0ms)

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

prune531.0ms

Pruning

13 alts after pruning (13 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)))

rewrite37.0ms

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:

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

series23.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/ (sin (* 0.5 x)) (sin x))
13.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
4.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify64.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (55.0ms)

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

prune676.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize14.0ms

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))
14.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

series26.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
7.0ms	(/ (sin (* 0.5 x)) (sin x))
14.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (52.0ms)

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

prune664.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
107×	`add-sqr-sqrt`
100×	`add-exp-log`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
52×	`add-cbrt-cube`
45×	`div-exp`
44×	`associate-r`
29×	`prod-exp`
21×	`cbrt-undiv`
19×	`associate-/r*`
13×	`cbrt-unprod`
12×	`div-inv`
8×	`rec-exp` `1-exp`
7×	`pow1` `associate-l` `associate-/l*`
5×	`unswap-sqr`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative` `inv-pow`

Counts

4 → 223

Calls

4 calls:

6.0ms	(/ 1 (/ (sin x) (sin (* 0.5 x))))
5.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
4.0ms	(/ (sin x) (sin (* 0.5 x)))
32.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ 1 (/ (sin x) (sin (* 0.5 x)))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1 (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
7.0ms	(/ (sin x) (sin (* 0.5 x)))
13.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ 1 (/ (sin x) (sin (* 0.5 x)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	930	2562
1	5001	2191

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes97.0ms

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	14	9
1	16	9
2	16	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

958.0ms	1541×	body	1280	valid
543.0ms	1276×	body	640	valid
387.0ms	4215×	body	80	valid
194.0ms	649×	body	320	valid
63.0ms	319×	body	160	valid