Details

sample56.0ms

Algorithm

intervals

Results

18.0ms	38×	body	1280	valid
10.0ms	160×	body	80	valid
9.0ms	29×	body	640	valid
7.0ms	16×	body	320	valid
2.0ms	13×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize10.0ms

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)))
19.4b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite54.0ms

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:

21.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
20.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series192.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
47.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
86.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (52.0ms)

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

prune257.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.1b	(/ (sin x) (sin (* 0.5 x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite30.0ms

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:

11.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series192.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
70.0ms	(/ (sin x) (sin (* 0.5 x)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (60.0ms)

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

prune367.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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

series185.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
40.0ms	(/ (sin x) (sin (* 0.5 x)))
80.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	433	924
1	2247	743
2	5001	724

prune282.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (expm1 (/ (sin x) (sin (* 0.5 x)))))
0.1b	(expm1 (/ (sin x) (sin (* 0.5 x))))
0.1b	(/ (sin x) (sin (* 0.5 x)))
0.1b	(/ (* 8.0 (sin (* x 0.5))) (* (log1p (expm1 (/ (sin x) (sin (* 0.5 x))))) 3.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`times-frac`
5×	`cbrt-undiv` `div-exp` `log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `add-log-exp`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 74

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (sin x) (sin (* 0.5 x)))))
0.0ms	(expm1 (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
6.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (log1p (expm1 (/ (sin x) (sin (* 0.5 x))))) 3.0))

series597.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(log1p (expm1 (/ (sin x) (sin (* 0.5 x)))))
99.0ms	(expm1 (/ (sin x) (sin (* 0.5 x))))
42.0ms	(/ (sin x) (sin (* 0.5 x)))
253.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (log1p (expm1 (/ (sin x) (sin (* 0.5 x))))) 3.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	365	801
1	1701	653
2	5001	620

prune255.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes39.0ms

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

sample1.7s

Algorithm

intervals

Results

724.0ms	1477×	body	1280	valid
378.0ms	1201×	body	640	valid
284.0ms	4338×	body	80	valid
147.0ms	648×	body	320	valid
52.0ms	336×	body	160	valid