Details

sample76.0ms

Algorithm

intervals

Results

26.0ms	82×	body	1280	valid
16.0ms	76×	body	640	valid
11.0ms	235×	body	80	valid
5.0ms	34×	body	320	valid
2.0ms	23×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	7
1	57	6
2	87	6
3	114	6
4	132	6
5	151	6
6	171	6
7	173	6
8	173	6

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.4b

Counts

2 → 2

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `associate-/r*` `sqrt-prod`
4×	`pow1`
3×	`associate-r` `associate-l`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

2 → 51

Calls

2 calls:

4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
6.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series315.0ms

Counts

2 → 6

Calls

2 calls:

106.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
209.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	202	424
1	995	365
2	5001	359

prune156.0ms

Filtered

57 candidates to 39 candidates (68.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	49	8	57
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	50	9	59

Merged error: 0.0b

Counts

59 → 9

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b

(* (cos th) (fma a1 a1 (* a2 a2)))

0.3b

(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

0.3b

(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
36×	`cbrt-prod`
35×	`add-exp-log` `add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
18×	`sqrt-prod`
13×	`cbrt-undiv` `div-exp`
12×	`div-inv`
10×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

3 → 127

Calls

3 calls:

4.0ms

(* (cos th) (fma a1 a1 (* a2 a2)))

9.0ms

(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

13.0ms

(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series969.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms

(* (cos th) (fma a1 a1 (* a2 a2)))

646.0ms

(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

217.0ms

(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	488	2207
1	2528	1901
2	5001	1871

prune570.0ms

Filtered

136 candidates to 93 candidates (68.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	6	1	7
Picked	1	0	1
Done	1	0	1
Total	139	6	145

Merged error: 0b

Counts

145 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (hypot a1 a2))
0.3b	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
0.3b	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
5.1b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log` `times-frac`
38×	`add-sqr-sqrt`
37×	`add-cbrt-cube`
36×	`cbrt-prod`
35×	`add-cube-cbrt` `*-un-lft-identity`
21×	`sqrt-prod`
19×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
12×	`div-inv`
10×	`associate-/r*`
7×	`pow1`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative` `fma-udef` `hypot-def` `associate-/l/` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

4.0ms	(* (cos th) (hypot a1 a2))
15.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
11.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (cos th) (hypot a1 a2))
283.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
686.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
45.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify84.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	565	2803
1	2979	2283
2	5002	2194

prune486.0ms

Filtered

161 candidates to 111 candidates (68.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	162	5	167

Merged error: 0b

Counts

167 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))
0.2b	(* (cos th) (hypot a1 a2))
0.3b	(/ (/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))) (cbrt (sqrt 2.0)))
0.3b	(/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

224×	`times-frac`
83×	`add-sqr-sqrt`
81×	`add-cube-cbrt` `*-un-lft-identity`
78×	`cbrt-prod`
61×	`add-exp-log`
44×	`add-cbrt-cube`
39×	`sqrt-prod`
29×	`cbrt-undiv` `div-exp`
25×	`div-inv`
19×	`associate-/r*`
14×	`associate-/l*`
12×	`prod-exp` `cbrt-unprod`
11×	`associate-/r/`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num`
1×	`pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 239

Calls

4 calls:

7.0ms	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))
4.0ms	(* (cos th) (hypot a1 a2))
15.0ms	(/ (/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))) (cbrt (sqrt 2.0)))
10.0ms	(/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

288.0ms	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))
100.0ms	(* (cos th) (hypot a1 a2))
238.0ms	(/ (/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2))) (cbrt (sqrt 2.0)))
648.0ms	(/ (* (cos th) (hypot a1 a2)) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (hypot a1 a2)))

simplify131.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	889	4532
1	4690	4102
2	5001	4056

prune731.0ms

Filtered

251 candidates to 184 candidates (73.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	251	5	256

Merged error: 0b

Counts

256 → 5

regimes148.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	14
1	14	14

end0.0ms

sample2.2s

Algorithm

intervals

Results

766.0ms	2428×	body	1280	valid
474.0ms	2116×	body	640	valid
403.0ms	8197×	body	80	valid
152.0ms	1021×	body	320	valid
57.0ms	528×	body	160	valid