Details

sample76.0ms

Algorithm

intervals

Results

28.0ms	84×	body	1280	valid
13.0ms	57×	body	640	valid
12.0ms	250×	body	80	valid
5.0ms	30×	body	320	valid
2.0ms	17×	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))

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))

series351.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(fma a1 a1 (* a2 a2))
108.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
211.0ms	(/ (* (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

prune178.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Merged error: 0b

Counts

72 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.1b	(* (cos th) (hypot a1 a2))
0.4b	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
6.4b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `sqrt-prod`
9×	`associate-r`
7×	`prod-exp` `cbrt-unprod`
6×	`times-frac` `associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `fma-udef` `hypot-def` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

6.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
4.0ms	(* (cos th) (hypot a1 a2))
9.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
106.0ms	(* (cos th) (hypot a1 a2))
288.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
43.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	305	786
1	1700	625
2	5001	573

prune263.0ms

Filtered

102 candidates to 72 candidates (70.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	103	7	110

Merged error: 0b

Counts

110 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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:

32.0ms	(fma a1 a1 (* a2 a2))
113.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
646.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
220.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify77.0ms

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 104 candidates (69.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	149	7	156

Merged error: 0b

Counts

156 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos th) (hypot a1 a2))
0.3b	(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
0.5b	(/ (hypot a1 a2) (sqrt 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-r`
21×	`sqrt-prod`
19×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r*`
4×	`associate-l` `pow-prod-down`
3×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`*-commutative` `div-inv`
1×	`sqrt-undiv` `hypot-udef` `frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`

Counts

3 → 106

Calls

3 calls:

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

series452.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(* (cos th) (hypot a1 a2))
245.0ms	(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
103.0ms	(/ (hypot a1 a2) (sqrt 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	358	850
1	2005	753
2	5001	735

prune239.0ms

Filtered

115 candidates to 78 candidates (67.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	115	7	122

Merged error: 0b

Counts

122 → 7

regimes182.0ms

Accuracy

0% (0.3b 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	16	9
1	16	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

824.0ms	2491×	body	1280	valid
453.0ms	2075×	body	640	valid
406.0ms	8009×	body	80	valid
171.0ms	1063×	body	320	valid
58.0ms	505×	body	160	valid