Details

sample58.0ms

Algorithm

intervals

Results

18.0ms	41×	body	1280	valid
12.0ms	142×	body	80	valid
12.0ms	40×	body	640	valid
4.0ms	21×	body	320	valid
2.0ms	12×	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: 13.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
13.1b	(/ (* (* (/ 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))

series177.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
81.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (50.0ms)

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

prune256.0ms

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

localize14.0ms

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

rewrite29.0ms

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)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (sin (* 0.5 x)) (sin x))
80.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify68.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (58.0ms)

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

prune329.0ms

Filtered

113 candidates to 80 candidates (70.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Merged error: 0b

Counts

125 → 12

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 100

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) (sin x))
5.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
12.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

series167.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (sin (* 0.5 x)) (sin x))
37.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
85.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	469	1030
1	2437	847
2	5001	823

prune325.0ms

Filtered

109 candidates to 81 candidates (74.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 0b

Counts

121 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

5.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
1.0ms	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))
1.0ms	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
7.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* 0.5 x)) (sin x)))

series660.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
193.0ms	(log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0)))
73.0ms	(expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))
348.0ms	(* (log1p (expm1 (/ (* 8.0 (sin (* x 0.5))) 3.0))) (/ (sin (* 0.5 x)) (sin x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	398	807
1	1773	676
2	5001	676

prune292.0ms

Filtered

91 candidates to 72 candidates (79.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	91	11	102

Merged error: 0b

Counts

102 → 11

regimes48.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.9s

Algorithm

intervals

Results

674.0ms	1444×	body	1280	valid
609.0ms	1262×	body	640	valid
291.0ms	4379×	body	80	valid
132.0ms	595×	body	320	valid
52.0ms	320×	body	160	valid