Details

sample89.0ms

Algorithm

intervals

Results

30.0ms	80×	body	1280	valid
20.0ms	67×	body	640	valid
16.0ms	251×	body	80	valid
5.0ms	30×	body	320	valid
1.0ms	11×	body	160	valid

simplify20.0ms

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))
0.2b	(* (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))

series369.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma a1 a1 (* a2 a2))
111.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
223.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (28.0ms)

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

prune178.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Merged error: 0.0b

Counts

72 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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)))
10.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
13.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series666.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(fma a1 a1 (* a2 a2))
106.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
311.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
216.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (55.0ms)

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

prune405.0ms

Filtered

237 candidates to 110 candidates (46.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	237	8	245

Merged error: 0b

Counts

245 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite554.0ms

Algorithm

rewrite-expression-head

Rules

2253×	`sqrt-prod`
1726×	`times-frac`
1186×	`add-sqr-sqrt`
808×	`add-cube-cbrt` `*-un-lft-identity`
376×	`associate-r`
85×	`unswap-sqr`
40×	`associate-l`
37×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
33×	`associate-/r*`
30×	`div-inv`
14×	`cbrt-undiv` `div-exp`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 1077

Calls

4 calls:

7.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
23.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))
5.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
421.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
403.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))
153.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))
220.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

simplify220.0ms

Algorithm

egg-herbie

Counts

1089 → 1089

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2582	21519
1	5001	20240

prune1.7s

Filtered

1089 candidates to 380 candidates (34.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1089	0	1089
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	1089	8	1097

Merged error: 0b

Counts

1097 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
0.4b	(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

1038×	`sqrt-prod`
799×	`times-frac`
494×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
394×	`add-cube-cbrt`
379×	`associate-r`
75×	`add-exp-log`
49×	`add-cbrt-cube`
32×	`div-exp`
30×	`unswap-sqr`
22×	`prod-exp`
21×	`associate-/r*`
19×	`associate-l`
18×	`cbrt-undiv`
16×	`div-inv`
14×	`cbrt-unprod`
11×	`pow1`
5×	`pow-flip`
4×	`expm1-log1p-u` `rec-exp` `sqrt-pow1` `1-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `pow1/2` `pow-prod-down` `clear-num` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-r/` `associate-l/` `inv-pow`

Counts

4 → 583

Calls

4 calls:

4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
8.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
142.0ms	(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))

series841.0ms

Counts

4 → 10

Calls

4 calls:

109.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
511.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
220.0ms	(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify125.0ms

Algorithm

egg-herbie

Counts

593 → 593

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2262	10311
1	5002	9229

prune951.0ms

Filtered

593 candidates to 209 candidates (35.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	593	0	593
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	593	8	601

Merged error: 0b

Counts

601 → 8

regimes184.0ms

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	15	15
1	15	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

942.0ms	2507×	body	1280	valid
547.0ms	2108×	body	640	valid
490.0ms	7898×	body	80	valid
193.0ms	1051×	body	320	valid
73.0ms	535×	body	160	valid