Details

sample59.0ms

Algorithm

intervals

Results

20.0ms	43×	body	1280	valid
12.0ms	145×	body	80	valid
12.0ms	38×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 16.0b

Counts

2 → 1

localize10.0ms

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)))
15.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite28.0ms

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:

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

series167.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
77.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify56.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (47.0ms)

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

prune225.0ms

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

localize13.0ms

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)))

rewrite25.0ms

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

series161.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ (sin (* 0.5 x)) (sin x))
87.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify65.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (55.0ms)

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

prune274.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Merged error: 0b

Counts

124 → 10

localize11.0ms

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)))

rewrite26.0ms

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:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
4.0ms	(/ (sin (* 0.5 x)) (sin x))
15.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (sin (* 0.5 x)) 3.0)
36.0ms	(/ (sin (* 0.5 x)) (sin x))
76.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (49.0ms)

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

prune221.0ms

Filtered

108 candidates to 79 candidates (73.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Merged error: 0b

Counts

118 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
1.0ms	(expm1 (/ (sin (* 0.5 x)) 3.0))
4.0ms	(/ (sin (* 0.5 x)) (sin x))
8.0ms	(* (* 8.0 (log1p (expm1 (/ (sin (* 0.5 x)) 3.0)))) (/ (sin (* 0.5 x)) (sin x)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (sin (* 0.5 x)) 3.0)
71.0ms	(expm1 (/ (sin (* 0.5 x)) 3.0))
36.0ms	(/ (sin (* 0.5 x)) (sin x))
353.0ms	(* (* 8.0 (log1p (expm1 (/ (sin (* 0.5 x)) 3.0)))) (/ (sin (* 0.5 x)) (sin x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	428	1007
1	1934	842
2	5001	821

prune271.0ms

Filtered

116 candidates to 88 candidates (75.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	116	9	125

Merged error: 0b

Counts

125 → 9

regimes38.0ms

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	16	11
1	16	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

743.0ms	1500×	body	1280	valid
411.0ms	1281×	body	640	valid
301.0ms	4315×	body	80	valid
130.0ms	579×	body	320	valid
53.0ms	325×	body	160	valid