Details

sample82.0ms

Algorithm

intervals

Results

28.0ms	88×	body	1280	valid
19.0ms	89×	body	640	valid
11.0ms	245×	body	80	valid
5.0ms	35×	body	320	valid
2.0ms	21×	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: 0.6b

Counts

2 → 2

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.6b	(/ (* (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:

37.0ms	(fma a1 a1 (* a2 a2))
107.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
215.0ms	(/ (* (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

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: 0.3b

Counts

72 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
0.6b	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
10.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
4.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series344.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma a1 a1 (* a2 a2))
206.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
101.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	258	819
1	1145	718
2	5001	693

prune233.0ms

Filtered

104 candidates to 69 candidates (66.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Merged error: 0.0b

Counts

112 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))))
0.2b	(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
0.2b	(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
0.5b	(* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

240×	`sqrt-prod`
230×	`add-sqr-sqrt`
222×	`times-frac`
137×	`add-cube-cbrt` `*-un-lft-identity`
49×	`swap-sqr`
38×	`add-exp-log` `add-cbrt-cube`
34×	`associate-l`
32×	`associate-r`
18×	`associate-/r*`
17×	`unswap-sqr`
16×	`pow1`
13×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
6×	`sqrt-undiv` `hypot-udef` `div-inv` `associate-/l*`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `pow-sqr` `pow-prod-up`

Counts

4 → 293

Calls

4 calls:

15.0ms	(* (cos th) (* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))))
6.0ms	(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
5.0ms	(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
28.0ms	(* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(* (cos th) (* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))))
162.0ms	(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
162.0ms	(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
127.0ms	(* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	714	3973
1	3488	3509
2	5001	3477

prune585.0ms

Filtered

305 candidates to 164 candidates (53.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	302	3	305
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	307	6	313

Merged error: 0b

Counts

313 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
75×	`times-frac`
70×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-r`
34×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`pow1`
6×	`associate-l`
5×	`hypot-udef` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-undiv` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`associate-*r/`
2×	`frac-2neg` `sqrt-unprod` `pow-prod-down` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 185

Calls

4 calls:

14.0ms	(* (cos th) (/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))
11.0ms	(/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
15.0ms	(* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))
5.0ms	(/ (hypot a1 a2) (sqrt (sqrt 2.0)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(* (cos th) (/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))
131.0ms	(/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
181.0ms	(* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))
161.0ms	(/ (hypot a1 a2) (sqrt (sqrt 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	518	1991
1	2688	1702
2	5002	1577

prune407.0ms

Filtered

197 candidates to 120 candidates (60.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	197	6	203

Merged error: 0b

Counts

203 → 6

regimes165.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	11
1	14	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

801.0ms	2509×	body	1280	valid
446.0ms	2065×	body	640	valid
398.0ms	7918×	body	80	valid
162.0ms	1063×	body	320	valid
51.0ms	500×	body	160	valid