Details

sample75.0ms

Algorithm

intervals

Results

27.0ms	83×	body	1280	valid
12.0ms	242×	body	80	valid
12.0ms	54×	body	640	valid
6.0ms	36×	body	320	valid
2.0ms	19×	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: 0.4b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite16.0ms

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))
8.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
6.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series362.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma a1 a1 (* a2 a2))
110.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
216.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

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

prune186.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	65	7	72

Merged error: 0.0b

Counts

72 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

rewrite36.0ms

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)))
12.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
7.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series672.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma a1 a1 (* a2 a2))
107.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
217.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
308.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	626	3262
1	2999	2821
2	5001	2819

prune469.0ms

Filtered

237 candidates to 113 candidates (47.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	233	4	237
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	238	6	244

Merged error: 0b

Counts

244 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (sqrt (sqrt 2.0)))
0.3b	(* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1))))
1.0b	(/ 1 (sqrt 2.0))
1.0b	(sqrt (/ 1 (sqrt 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
74×	`add-sqr-sqrt`
71×	`times-frac`
57×	`*-un-lft-identity`
53×	`add-cube-cbrt`
25×	`associate-l`
15×	`add-exp-log` `associate-/r*`
13×	`add-cbrt-cube`
11×	`pow1`
7×	`sqrt-pow1` `sqrt-div`
6×	`pow-flip` `unswap-sqr`
5×	`rem-sqrt-square` `associate-/l/`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-r/` `div-exp` `associate-r` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `pow1/2`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `inv-pow`
1×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp` `pow-prod-down` `*-commutative` `distribute-lft-out`

Counts

4 → 185

Calls

4 calls:

17.0ms	(/ (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (sqrt (sqrt 2.0)))
15.0ms	(* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1))))
5.0ms	(/ 1 (sqrt 2.0))
5.0ms	(sqrt (/ 1 (sqrt 2.0)))

series548.0ms

Counts

4 → 8

Calls

4 calls:

226.0ms	(/ (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (sqrt (sqrt 2.0)))
322.0ms	(* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1))))
0.0ms	(/ 1 (sqrt 2.0))
0.0ms	(sqrt (/ 1 (sqrt 2.0)))

simplify90.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	599	1968
1	3066	1670
2	5001	1589

prune550.0ms

Filtered

193 candidates to 115 candidates (59.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	194	5	199

Merged error: 0b

Counts

199 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (/ 1 (sqrt (sqrt 2.0))))
1.0b	(/ 1 (sqrt 2.0))
1.0b	(sqrt (/ 1 (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

108×	`sqrt-prod`
94×	`times-frac`
80×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
73×	`add-cube-cbrt`
34×	`add-exp-log`
31×	`associate-r`
20×	`add-cbrt-cube`
17×	`pow1`
15×	`associate-/r*`
12×	`prod-exp`
11×	`pow-flip` `sqrt-pow1`
9×	`frac-times`
8×	`div-exp`
7×	`sqrt-div` `associate-*l/`
6×	`cbrt-unprod` `associate-/l*`
5×	`rem-sqrt-square` `pow1/2` `associate-*r/`
4×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `flip3-+` `1-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-prod-down` `inv-pow`
2×	`frac-2neg` `clear-num`
1×	`associate-l` `un-div-inv` `*-commutative`

Counts

4 → 219

Calls

4 calls:

23.0ms	(* (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (/ 1 (sqrt (sqrt 2.0))))
4.0ms	(/ 1 (sqrt 2.0))
5.0ms	(sqrt (/ 1 (sqrt 2.0)))
6.0ms	(/ 1 (sqrt (sqrt 2.0)))

series229.0ms

Counts

4 → 6

Calls

4 calls:

229.0ms	(* (* (sqrt (/ 1 (sqrt 2.0))) (+ (* (cos th) (* a2 a2)) (* (cos th) (* a1 a1)))) (/ 1 (sqrt (sqrt 2.0))))
0.0ms	(/ 1 (sqrt 2.0))
0.0ms	(sqrt (/ 1 (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	668	2085
1	4234	1704
2	5001	1692

prune572.0ms

Filtered

225 candidates to 122 candidates (54.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	225	5	230

Merged error: 0b

Counts

230 → 5

regimes178.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	15
1	25	15

end0.0ms

sample2.3s

Algorithm

intervals

Results

818.0ms	2477×	body	1280	valid
469.0ms	2118×	body	640	valid
408.0ms	7983×	body	80	valid
168.0ms	1072×	body	320	valid
56.0ms	524×	body	160	valid