Details

sample89.0ms

Algorithm

intervals

Results

31.0ms	83×	body	1280	valid
17.0ms	66×	body	640	valid
16.0ms	254×	body	80	valid
6.0ms	35×	body	320	valid
3.0ms	21×	body	160	valid

simplify21.0ms

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

prune9.0ms

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: 0.3b

Counts

2 → 2

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
6.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series358.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma a1 a1 (* a2 a2))
108.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
211.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	205	467
1	1002	399
2	5001	393

prune165.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Merged error: 0.0b

Counts

72 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b	(/ (* (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)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
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))))
12.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma a1 a1 (* a2 a2))
109.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
658.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
218.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	491	2250
1	2535	1935
2	5001	1905

prune366.0ms

Filtered

149 candidates to 103 candidates (69.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	150	6	156

Merged error: 0b

Counts

156 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

234×	`sqrt-prod`
216×	`times-frac`
96×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
14×	`associate-/l*`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 225

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
6.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
12.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma a1 a1 (* a2 a2))
108.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
313.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
217.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	626	3262
1	2999	2821
2	5001	2813

prune398.0ms

Filtered

237 candidates to 112 candidates (47.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	237	6	243

Merged error: 0b

Counts

243 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 155

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
8.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
14.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

series1.7s

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma a1 a1 (* a2 a2))
114.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
570.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
935.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (fabs (cbrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (sqrt (cbrt (sqrt 2.0))))

simplify98.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	618	3150
1	3360	2859
2	5003	2841

prune480.0ms

Filtered

167 candidates to 108 candidates (64.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	167	6	173

Merged error: 0b

Counts

173 → 6

regimes147.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

990.0ms	2655×	body	1280	valid
523.0ms	2006×	body	640	valid
493.0ms	7931×	body	80	valid
198.0ms	1056×	body	320	valid
67.0ms	507×	body	160	valid