Details

sample80.0ms

Algorithm

intervals

Results

31.0ms	47×	body	1280	valid
17.0ms	41×	body	640	valid
11.0ms	131×	body	80	valid
7.0ms	25×	body	320	valid
2.0ms	12×	body	160	valid

simplify19.0ms

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: 12.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite158.0ms

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)))
28.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
63.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series153.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
32.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
70.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (50.0ms)

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

prune332.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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

rewrite104.0ms

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:

12.0ms	(/ (sin (* 0.5 x)) (sin x))
60.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
27.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series141.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (sin (* 0.5 x)) (sin x))
66.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify68.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (58.0ms)

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

prune424.0ms

Pruning

9 alts after pruning (9 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)))

rewrite68.0ms

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:

18.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
13.0ms	(/ (sin (* 0.5 x)) (sin x))
34.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

series139.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
35.0ms	(/ (sin (* 0.5 x)) (sin x))
70.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (55.0ms)

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

prune430.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
0.4b	(* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5))))
1.0b	(/ (sqrt 8.0) 3.0)

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-exp-log`
94×	`add-cbrt-cube`
65×	`prod-exp`
54×	`times-frac`
47×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
44×	`cbrt-unprod`
39×	`div-exp`
24×	`cbrt-undiv`
23×	`associate-l`
21×	`sqrt-prod`
18×	`pow1`
14×	`associate-r`
12×	`associate-*l/`
9×	`1-exp` `pow-prod-down` `associate-/l*`
6×	`frac-times` `associate-/r*`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 191

Calls

4 calls:

12.0ms	(/ (sin (* 0.5 x)) (sin x))
197.0ms	(* (* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
75.0ms	(* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5))))
6.0ms	(/ (sqrt 8.0) 3.0)

series334.0ms

Counts

4 → 10

Calls

4 calls:

35.0ms	(/ (sin (* 0.5 x)) (sin x))
176.0ms	(* (* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5)))) (/ (sin (* 0.5 x)) (sin x)))
123.0ms	(* (/ (sqrt 8.0) 1) (* (/ (sqrt 8.0) 3.0) (sin (* x 0.5))))
0.0ms	(/ (sqrt 8.0) 3.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	846	2222
1	4374	1675
2	5002	1471

prune592.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes50.0ms

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	15	9
1	17	9
2	17	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	1550×	body	1280	valid
558.0ms	1243×	body	640	valid
387.0ms	4272×	body	80	valid
185.0ms	608×	body	320	valid
67.0ms	327×	body	160	valid