Details

sample75.0ms

Algorithm

intervals

Results

31.0ms	55×	body	1280	valid
14.0ms	36×	body	640	valid
13.0ms	138×	body	80	valid
7.0ms	23×	body	320	valid
1.0ms	4×	body	160	valid

simplify20.0ms

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: 12.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite61.0ms

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)))
16.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
21.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series195.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
90.0ms	(/ (* (* (/ 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

prune269.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (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)))

rewrite45.0ms

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:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
22.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin (* 0.5 x)) (sin x))
84.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify72.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (56.0ms)

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

prune518.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
27×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-l` `associate-l/` `-commutative`

Counts

3 → 99

Calls

3 calls:

3.0ms	(/ (sin (* 0.5 x)) 3.0)
4.0ms	(/ (sin (* 0.5 x)) (sin x))
17.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (sin (* 0.5 x)) 3.0)
40.0ms	(/ (sin (* 0.5 x)) (sin x))
81.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	437	968
1	2144	808
2	5001	786

prune281.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(log1p (expm1 (/ (sin (* 0.5 x)) (sin x))))
0.2b	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (log1p (expm1 (/ (sin (* 0.5 x)) (sin x)))))
0.2b	(expm1 (/ (sin (* 0.5 x)) (sin x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
0.0ms	(log1p (expm1 (/ (sin (* 0.5 x)) (sin x))))
13.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (log1p (expm1 (/ (sin (* 0.5 x)) (sin x)))))
0.0ms	(expm1 (/ (sin (* 0.5 x)) (sin x)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (sin (* 0.5 x)) (sin x))
186.0ms	(log1p (expm1 (/ (sin (* 0.5 x)) (sin x))))
265.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (log1p (expm1 (/ (sin (* 0.5 x)) (sin x)))))
93.0ms	(expm1 (/ (sin (* 0.5 x)) (sin x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	348	766
1	1481	629
2	5002	614

prune228.0ms

Pruning

10 alts after pruning (8 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

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	9
1	14	9

end0.0ms

sample2.2s

Algorithm

intervals

Results

900.0ms	1541×	body	1280	valid
479.0ms	1205×	body	640	valid
425.0ms	4308×	body	80	valid
181.0ms	621×	body	320	valid
66.0ms	325×	body	160	valid