Details

sample61.0ms

Algorithm

intervals

Results

25.0ms	51×	body	1280	valid
11.0ms	35×	body	640	valid
8.0ms	135×	body	80	valid
4.0ms	20×	body	320	valid
2.0ms	15×	body	160	valid

simplify25.0ms

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: 16.6b

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)))
16.4b	(/ (* (* (/ 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)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
19.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series185.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
87.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify63.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (55.0ms)

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

prune278.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

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×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 116

Calls

3 calls:

4.0ms	(/ (sin x) (sin (* 0.5 x)))
15.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series174.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (sin x) (sin (* 0.5 x)))
86.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify79.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	550	1204
1	2727	1016
2	5001	992

prune402.0ms

Filtered

125 candidates to 94 candidates (75.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
20×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-l`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
5×	`pow1`
4×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative`

Counts

3 → 91

Calls

3 calls:

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

series197.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
86.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
44.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	433	924
1	2228	739
2	5002	723

prune288.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

157×	`times-frac`
104×	`add-sqr-sqrt`
100×	`add-exp-log`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
52×	`add-cbrt-cube`
45×	`div-exp`
44×	`associate-l`
29×	`prod-exp`
21×	`cbrt-undiv`
17×	`associate-/r*`
13×	`cbrt-unprod`
11×	`div-inv`
8×	`rec-exp` `1-exp`
7×	`pow1` `associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/r/`
2×	`associate-*l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 221

Calls

4 calls:

23.0ms	(* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0)
4.0ms	(/ (sin (* 0.5 x)) (sin x))
5.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))
13.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0))

series261.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0)
43.0ms	(/ (sin (* 0.5 x)) (sin x))
51.0ms	(/ 1 (/ (sin (* 0.5 x)) (sin x)))
94.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ 1 (/ (sin (* 0.5 x)) (sin x))) 3.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	847	2302
1	4390	1933
2	5001	1779

prune594.0ms

Filtered

233 candidates to 141 candidates (60.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes37.0ms

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	19	10
1	21	10
2	21	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

784.0ms	1562×	body	1280	valid
407.0ms	1250×	body	640	valid
275.0ms	4291×	body	80	valid
132.0ms	590×	body	320	valid
52.0ms	307×	body	160	valid