Details

sample56.0ms

Algorithm

intervals

Results

21.0ms	46×	body	1280	valid
11.0ms	37×	body	640	valid
8.0ms	133×	body	80	valid
5.0ms	24×	body	320	valid
2.0ms	16×	body	160	valid

simplify21.0ms

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: 17.0b

localize16.0ms

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)))
16.9b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite31.0ms

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:

9.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
11.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series184.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
87.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify61.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (52.0ms)

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

prune252.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin x)) (cbrt (sin x)))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series457.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
105.0ms	(cbrt (sin x))
115.0ms	(cbrt (sin x))
110.0ms	(cbrt (sin x))

simplify104.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	159	483
1	568	431
2	3135	398
3	5001	392

prune343.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (sin x))
5.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series436.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (sin x))
108.0ms	(cbrt (sin x))
109.0ms	(cbrt (sin x))
110.0ms	(cbrt (sin x))

simplify53.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	62	268
1	132	248
2	334	240
3	1067	240
4	5001	240

prune328.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series448.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (sin x))
110.0ms	(cbrt (sin x))
117.0ms	(cbrt (sin x))
111.0ms	(cbrt (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	62	268
1	132	248
2	334	240
3	1067	240
4	5001	240

prune273.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 0.0b

regimes76.0ms

Accuracy

0% (1.3b remaining)

Error of 1.4b against oracle of 0.1b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	16
1	20	16
2	20	16

end0.0ms

sample1.7s

Algorithm

intervals

Results

682.0ms	1514×	body	1280	valid
390.0ms	1266×	body	640	valid
285.0ms	4317×	body	80	valid
119.0ms	571×	body	320	valid
46.0ms	332×	body	160	valid