Details

sample80.0ms

Algorithm

intervals

Results

25.0ms	77×	body	1280	valid
15.0ms	67×	body	640	valid
14.0ms	264×	body	80	valid
7.0ms	44×	body	320	valid
1.0ms	13×	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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.3b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite10.0ms

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:

0.0ms	(fma a1 a1 (* a2 a2))
3.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series359.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma a1 a1 (* a2 a2))
106.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
219.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

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

prune187.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

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

rewrite33.0ms

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:

0.0ms	(fma a1 a1 (* a2 a2))
12.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))

series673.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma a1 a1 (* a2 a2))
217.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
304.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
111.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))

simplify81.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	626	3262
1	2999	2821
2	5002	2819

prune485.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.2b	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt (sqrt 2.0)))
7.8b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

240×	`sqrt-prod`
216×	`times-frac`
96×	`add-sqr-sqrt`
95×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
14×	`associate-/l*`
12×	`div-inv`
10×	`pow1` `cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `fma-udef` `hypot-def` `associate-/l/`

Counts

4 → 236

Calls

4 calls:

8.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
17.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
10.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt (sqrt 2.0)))
1.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series914.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
308.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
375.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt (sqrt 2.0)))
49.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify98.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	704	4083
1	4120	3432
2	5001	3314

prune549.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (cos th) (hypot a1 a2)) (hypot a1 a2))
0.2b	(/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0))))
0.2b	(/ (/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
0.2b	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

804×	`sqrt-prod`
623×	`times-frac`
348×	`add-sqr-sqrt`
249×	`*-un-lft-identity`
233×	`add-cube-cbrt`
151×	`associate-r`
117×	`add-exp-log`
77×	`add-cbrt-cube`
48×	`div-exp`
41×	`associate-l` `prod-exp`
36×	`unswap-sqr`
29×	`cbrt-undiv`
25×	`cbrt-unprod`
23×	`div-inv`
21×	`associate-/r*`
17×	`associate-/l*`
11×	`pow1`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `associate-l/` `associate-/l/`

Counts

4 → 521

Calls

4 calls:

7.0ms	(* (* (cos th) (hypot a1 a2)) (hypot a1 a2))
11.0ms	(/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0))))
21.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
146.0ms	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))

series1.9s

Counts

4 → 12

Calls

4 calls:

335.0ms	(* (* (cos th) (hypot a1 a2)) (hypot a1 a2))
536.0ms	(/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0))))
771.0ms	(/ (/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
249.0ms	(* (/ 1 (sqrt (sqrt (sqrt 2.0)))) (/ (/ (* (* (cos th) (hypot a1 a2)) (hypot a1 a2)) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))

simplify108.0ms

Algorithm

egg-herbie

Counts

533 → 533

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1617	10185
1	5001	8944

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes142.0ms

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	21	17
1	21	17

end0.0ms

sample2.3s

Algorithm

intervals

Results

848.0ms	2511×	body	1280	valid
458.0ms	2041×	body	640	valid
438.0ms	8164×	body	80	valid
178.0ms	1027×	body	320	valid
59.0ms	537×	body	160	valid