Details

sample55.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
13.0ms	46×	body	640	valid
8.0ms	141×	body	80	valid
3.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid

simplify22.0ms

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: 15.4b

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)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite30.0ms

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:

56.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
86.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify64.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (55.0ms)

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

prune250.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	11	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.1b

Counts

95 → 11

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite26.0ms

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:

10.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series169.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
42.0ms	(/ (sin x) (sin (* 0.5 x)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify79.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (63.0ms)

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

prune333.0ms

Filtered

125 candidates to 96 candidates (76.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	125	11	136

Merged error: 0b

Counts

136 → 11

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

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:

7.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
7.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

series186.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
41.0ms	(/ (sin x) (sin (* 0.5 x)))
82.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (53.0ms)

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

prune251.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	100	11	111

Merged error: 0b

Counts

111 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(cbrt (pow (/ (sin x) (sin (* x 0.5))) 3))
0.4b	(pow (/ (sin x) (sin (* x 0.5))) 3)
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `times-frac`
50×	`add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-l`
7×	`pow1`
6×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-r` `associate-/r` `associate-/l`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `rem-cbrt-cube`

Counts

4 → 155

Calls

4 calls:

5.0ms	(/ (sin x) (sin (* x 0.5)))
6.0ms	(cbrt (pow (/ (sin x) (sin (* x 0.5))) 3))
6.0ms	(pow (/ (sin x) (sin (* x 0.5))) 3)
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (sin x) (sin (* x 0.5)))
45.0ms	(cbrt (pow (/ (sin x) (sin (* x 0.5))) 3))
87.0ms	(pow (/ (sin x) (sin (* x 0.5))) 3)
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify75.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	541	1314
1	2355	1210
2	5002	1199

prune325.0ms

Filtered

167 candidates to 100 candidates (59.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	167	11	178

Merged error: 0b

Counts

178 → 11

regimes44.0ms

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

sample1.6s

Algorithm

intervals

Results

666.0ms	1466×	body	1280	valid
377.0ms	1264×	body	640	valid
283.0ms	4354×	body	80	valid
124.0ms	599×	body	320	valid
48.0ms	317×	body	160	valid