Details

sample58.0ms

Algorithm

intervals

Results

22.0ms	50×	body	1280	valid
11.0ms	38×	body	640	valid
8.0ms	133×	body	80	valid
5.0ms	25×	body	320	valid
1.0ms	10×	body	160	valid

simplify25.0ms

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: 13.5b

Counts

2 → 1

localize12.0ms

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)))
13.3b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite33.0ms

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)))
12.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series232.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
52.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
109.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify93.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (80.0ms)

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

prune329.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	12	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 0.1b

Counts

95 → 12

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite29.0ms

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:

5.0ms	(/ (sin x) (sin (* 0.5 x)))
12.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (sin x) (sin (* 0.5 x)))
97.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify84.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (71.0ms)

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

prune651.0ms

Filtered

125 candidates to 95 candidates (76.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Merged error: 0b

Counts

137 → 9

localize16.0ms

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:

8.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
5.0ms	(/ (sin x) (sin (* 0.5 x)))
11.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

series215.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
51.0ms	(/ (sin x) (sin (* 0.5 x)))
99.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (62.0ms)

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

prune306.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 0b

Counts

109 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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:

1.0ms	(expm1 (/ (sin x) (sin (* 0.5 x))))
5.0ms	(/ (sin x) (sin (* 0.5 x)))
8.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (log1p (expm1 (/ (sin x) (sin (* 0.5 x))))) 3.0))
1.0ms	(log1p (expm1 (/ (sin x) (sin (* 0.5 x)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(expm1 (/ (sin x) (sin (* 0.5 x))))
51.0ms	(/ (sin x) (sin (* 0.5 x)))
291.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (log1p (expm1 (/ (sin x) (sin (* 0.5 x))))) 3.0))
230.0ms	(log1p (expm1 (/ (sin x) (sin (* 0.5 x)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	365	801
1	1671	653
2	5001	622

prune273.0ms

Filtered

86 candidates to 63 candidates (73.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Merged error: 0b

Counts

94 → 8

regimes38.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	17	11
1	19	11
2	19	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

699.0ms	1454×	body	1280	valid
377.0ms	1234×	body	640	valid
270.0ms	4289×	body	80	valid
173.0ms	696×	body	320	valid
53.0ms	327×	body	160	valid