Details

sample86.0ms

Algorithm

intervals

Results

29.0ms	80×	body	1280	valid
15.0ms	257×	body	80	valid
15.0ms	58×	body	640	valid
7.0ms	35×	body	320	valid
2.0ms	20×	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: 0.3b

Counts

2 → 2

localize16.0ms

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))

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))

series359.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma a1 a1 (* a2 a2))
105.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
217.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

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

prune175.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	1	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))) (* (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:

34.0ms	(fma a1 a1 (* a2 a2))
113.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
643.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
219.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (58.0ms)

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

prune383.0ms

Filtered

149 candidates to 103 candidates (69.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	148	8	156

Merged error: 0b

Counts

156 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
150×	`cbrt-prod`
112×	`add-exp-log`
76×	`add-sqr-sqrt`
74×	`add-cube-cbrt` `*-un-lft-identity`
61×	`add-cbrt-cube`
51×	`cbrt-undiv` `div-exp`
31×	`prod-exp` `cbrt-unprod` `div-inv`
30×	`sqrt-prod`
15×	`associate-/l*`
14×	`associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num`
2×	`fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 253

Calls

4 calls:

4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
10.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
28.0ms	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
16.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

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))))
231.0ms	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
781.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify148.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	921	7187
1	4636	6299
2	5001	6220

prune813.0ms

Filtered

265 candidates to 192 candidates (72.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	265	8	273

Merged error: 0b

Counts

273 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

559×	`times-frac`
244×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
168×	`cbrt-prod`
84×	`sqrt-prod`
43×	`div-inv`
35×	`associate-/l*`
32×	`add-exp-log`
22×	`add-cbrt-cube`
19×	`associate-/r*`
16×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate-/r/` `fma-udef` `associate-/l/`

Counts

4 → 367

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
5.0ms	(/ (cos th) (cbrt (sqrt 2.0)))
7.0ms	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (fma a1 a1 (* a2 a2)))
18.0ms	(/ (/ (cos th) (cbrt (sqrt 2.0))) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (fma a1 a1 (* a2 a2))))

series850.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(fma a1 a1 (* a2 a2))
253.0ms	(/ (cos th) (cbrt (sqrt 2.0)))
347.0ms	(/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (fma a1 a1 (* a2 a2)))
217.0ms	(/ (/ (cos th) (cbrt (sqrt 2.0))) (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (fma a1 a1 (* a2 a2))))

simplify96.0ms

Algorithm

egg-herbie

Counts

379 → 379

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1476	7727
1	5002	7304

prune1.1s

Filtered

379 candidates to 291 candidates (76.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	377	2	379
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	380	7	387

Merged error: 0b

Counts

387 → 7

regimes173.0ms

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	13
1	14	13

end0.0ms

sample2.6s

Algorithm

intervals

Results

952.0ms	2559×	body	1280	valid
555.0ms	2124×	body	640	valid
481.0ms	7995×	body	80	valid
196.0ms	1067×	body	320	valid
79.0ms	585×	body	160	valid