Details

sample86.0ms

Algorithm

intervals

Results

27.0ms	84×	body	1280	valid
21.0ms	78×	body	640	valid
14.0ms	272×	body	80	valid
5.0ms	33×	body	320	valid
2.0ms	14×	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

prune8.0ms

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

localize11.0ms

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))

series362.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(fma a1 a1 (* a2 a2))
112.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
216.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

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

prune174.0ms

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

localize14.0ms

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))
7.1b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite23.0ms

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

series820.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
303.0ms	(* (cos th) (hypot a1 a2))
291.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
48.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	305	785
1	1700	625
2	5001	573

prune259.0ms

Filtered

102 candidates to 72 candidates (70.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 0b

Counts

109 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos th) (hypot a1 a2))
0.3b	(/ (* (cos th) (hypot a1 a2)) (/ (sqrt 2.0) (hypot a1 a2)))
0.4b	(/ (sqrt 2.0) (hypot a1 a2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 128

Calls

3 calls:

4.0ms	(* (cos th) (hypot a1 a2))
8.0ms	(/ (* (cos th) (hypot a1 a2)) (/ (sqrt 2.0) (hypot a1 a2)))
7.0ms	(/ (sqrt 2.0) (hypot a1 a2))

series419.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(* (cos th) (hypot a1 a2))
233.0ms	(/ (* (cos th) (hypot a1 a2)) (/ (sqrt 2.0) (hypot a1 a2)))
83.0ms	(/ (sqrt 2.0) (hypot a1 a2))

simplify59.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	419	1120
1	2035	1024
2	5001	1007

prune286.0ms

Filtered

137 candidates to 94 candidates (68.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	137	8	145

Merged error: 0b

Counts

145 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos th) (hypot a1 a2))
0.2b	(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
0.5b	(/ (hypot a1 a2) (sqrt 2.0))

rewrite24.0ms

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))
12.0ms	(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
4.0ms	(/ (hypot a1 a2) (sqrt 2.0))

series446.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(* (cos th) (hypot a1 a2))
240.0ms	(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
103.0ms	(/ (hypot a1 a2) (sqrt 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (46.0ms)

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

prune216.0ms

Filtered

115 candidates to 78 candidates (67.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	115	8	123

Merged error: 0b

Counts

123 → 8

regimes192.0ms

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	11	7
1	11	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

822.0ms	2502×	body	1280	valid
457.0ms	2059×	body	640	valid
401.0ms	8035×	body	80	valid
171.0ms	1042×	body	320	valid
58.0ms	536×	body	160	valid