Details

sample58.0ms

Algorithm

intervals

Results

22.0ms	49×	body	1280	valid
12.0ms	39×	body	640	valid
8.0ms	131×	body	80	valid
5.0ms	26×	body	320	valid
2.0ms	11×	body	160	valid

simplify18.0ms

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: 14.6b

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)))
14.4b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite157.0ms

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:

65.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
25.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
64.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series153.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
68.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify60.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (49.0ms)

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

prune209.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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)))

rewrite77.0ms

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:

33.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
12.0ms	(/ (sin x) (sin (* 0.5 x)))
28.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
38.0ms	(/ (sin x) (sin (* 0.5 x)))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify68.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (57.0ms)

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

prune320.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize12.0ms

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)))

rewrite53.0ms

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:

12.0ms	(/ (sin (* 0.5 x)) 3.0)
23.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
14.0ms	(/ (sin x) (sin (* 0.5 x)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (sin (* 0.5 x)) 3.0)
70.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
42.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (55.0ms)

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

prune274.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.3b	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
0.4b	(pow (/ (sin x) (sin (* 0.5 x))) 3)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

116×	`times-frac`
96×	`cbrt-prod`
74×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down` `cube-prod`
38×	`associate-/r*`
18×	`add-exp-log`
15×	`add-cbrt-cube`
10×	`div-inv`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`cube-mult` `unpow3` `associate-/l*` `add-log-exp` `sqr-pow`
3×	`cube-div` `pow-unpow`
2×	`cbrt-div` `frac-2neg` `pow-exp` `prod-exp` `clear-num` `cbrt-unprod` `rem-cube-cbrt`
1×	`pow-to-exp` `pow-pow` `pow1/3` `associate-*r/` `associate-/r/` `rem-cbrt-cube` `associate-/l/`

Counts

4 → 204

Calls

4 calls:

39.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)))
12.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
12.0ms	(pow (/ (sin x) (sin (* 0.5 x))) 3)

series231.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)))
43.0ms	(/ (sin x) (sin (* 0.5 x)))
37.0ms	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
76.0ms	(pow (/ (sin x) (sin (* 0.5 x))) 3)

simplify97.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	649	2315
1	3285	2104
2	5002	2075

prune386.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

724.0ms	1496×	body	1280	valid
390.0ms	1282×	body	640	valid
264.0ms	4288×	body	80	valid
122.0ms	606×	body	320	valid
45.0ms	328×	body	160	valid