Details

sample68.0ms

Algorithm

intervals

Results

28.0ms	53×	body	1280	valid
15.0ms	42×	body	640	valid
10.0ms	127×	body	80	valid
4.0ms	17×	body	320	valid
3.0ms	17×	body	160	valid

simplify17.0ms

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: 16.3b

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)))
16.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite56.0ms

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:

24.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
19.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series170.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
77.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (45.0ms)

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

prune205.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)))

rewrite27.0ms

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

Counts

3 → 110

Calls

3 calls:

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

series153.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
43.0ms	(/ (sin x) (sin (* 0.5 x)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify64.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	540	1166
1	2701	980
2	5001	956

prune294.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
5×	`div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

3 → 105

Calls

3 calls:

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

series146.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ (sin (* 0.5 x)) 3.0)
75.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
37.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	504	1132
1	2553	976
2	5002	950

prune445.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 3.0 (sin (* 0.5 x)))
0.2b	(/ (* 8.0 (/ 1 (/ 3.0 (sin (* 0.5 x))))) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.3b	(/ 1 (/ 3.0 (sin (* 0.5 x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

124×	`times-frac`
83×	`add-exp-log`
76×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
47×	`div-exp`
45×	`add-cbrt-cube`
32×	`associate-/r*`
23×	`cbrt-undiv`
14×	`prod-exp`
10×	`div-inv` `associate-/l*`
6×	`rec-exp` `1-exp` `cbrt-unprod`
5×	`pow1`
4×	`frac-2neg` `clear-num` `add-log-exp`
2×	`associate-/r/` `associate-/l/`
1×	`pow-flip` `associate-*r/` `un-div-inv` `inv-pow`

Counts

4 → 194

Calls

4 calls:

2.0ms	(/ 3.0 (sin (* 0.5 x)))
13.0ms	(/ (* 8.0 (/ 1 (/ 3.0 (sin (* 0.5 x))))) (/ (sin x) (sin (* 0.5 x))))
7.0ms	(/ (sin x) (sin (* 0.5 x)))
6.0ms	(/ 1 (/ 3.0 (sin (* 0.5 x))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 3.0 (sin (* 0.5 x)))
76.0ms	(/ (* 8.0 (/ 1 (/ 3.0 (sin (* 0.5 x))))) (/ (sin x) (sin (* 0.5 x))))
42.0ms	(/ (sin x) (sin (* 0.5 x)))
36.0ms	(/ 1 (/ 3.0 (sin (* 0.5 x))))

simplify102.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	826	2064
1	4222	1751
2	5001	1643

prune365.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes38.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

792.0ms	1495×	body	1280	valid
445.0ms	1267×	body	640	valid
340.0ms	4278×	body	80	valid
151.0ms	606×	body	320	valid
60.0ms	354×	body	160	valid