Details

sample57.0ms

Algorithm

intervals

Results

23.0ms	47×	body	1280	valid
11.0ms	36×	body	640	valid
10.0ms	149×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	5×	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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.3b

Counts

2 → 1

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)))
16.1b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite37.0ms

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:

10.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
16.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series185.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
85.0ms	(/ (* (* (/ 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 (51.0ms)

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

prune256.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.1b

Counts

95 → 13

localize20.0ms

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)))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series462.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
108.0ms	(cbrt (sin x))
110.0ms	(cbrt (sin x))
110.0ms	(cbrt (sin x))

simplify105.0ms

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

prune334.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	91	15	106

Merged error: 0.1b

Counts

106 → 15

localize21.0ms

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))

rewrite16.0ms

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:

9.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series471.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
113.0ms	(cbrt (sin x))
109.0ms	(cbrt (sin x))
105.0ms	(cbrt (sin x))

simplify108.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (94.0ms)

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

prune375.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	93	15	108

Merged error: 0.1b

Counts

108 → 15

localize32.0ms

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))

series440.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (sin x))
107.0ms	(cbrt (sin x))
108.0ms	(cbrt (sin x))
113.0ms	(cbrt (sin x))

simplify53.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (9.0ms)

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

prune270.0ms

Filtered

64 candidates to 52 candidates (81.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	64	15	79

Merged error: 0.1b

Counts

79 → 15

regimes142.0ms

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	20	18
1	22	18
2	22	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

773.0ms	1559×	body	1280	valid
386.0ms	1233×	body	640	valid
309.0ms	4281×	body	80	valid
139.0ms	649×	body	320	valid
42.0ms	278×	body	160	valid