Details

sample94.0ms

Algorithm

intervals

Results

34.0ms	88×	body	1280	valid
18.0ms	69×	body	640	valid
16.0ms	260×	body	80	valid
6.0ms	29×	body	320	valid
3.0ms	23×	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

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

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `associate-/r*` `sqrt-prod`
4×	`pow1`
3×	`associate-r` `associate-l`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

2 → 51

Calls

2 calls:

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

series341.0ms

Counts

2 → 6

Calls

2 calls:

113.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
227.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	202	424
1	995	365
2	5001	359

prune165.0ms

Filtered

57 candidates to 39 candidates (68.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	48	9	57
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	50	9	59

Merged error: 0.0b

Counts

59 → 9

localize15.0ms

Local error

Found 3 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 (sqrt 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
36×	`cbrt-prod`
35×	`add-exp-log` `add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
18×	`sqrt-prod`
13×	`cbrt-undiv` `div-exp`
12×	`div-inv`
10×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

3 → 127

Calls

3 calls:

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))))

13.0ms

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

series1.0s

Counts

3 → 9

Calls

3 calls:

120.0ms

(* (cos th) (fma a1 a1 (* a2 a2)))

692.0ms

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

234.0ms

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

simplify75.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	488	2207
1	2528	1901
2	5001	1871

prune374.0ms

Filtered

136 candidates to 94 candidates (69.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	136	9	145

Merged error: 0b

Counts

145 → 9

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 85

Calls

2 calls:

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

series336.0ms

Counts

2 → 6

Calls

2 calls:

223.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
113.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	253	776
1	1117	684
2	5001	659

prune213.0ms

Filtered

91 candidates to 58 candidates (63.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	92	8	100

Merged error: 0b

Counts

100 → 8

localize15.0ms

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))
6.0b	(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:

7.0ms	(* (* (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)))

series660.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
109.0ms	(* (cos th) (hypot a1 a2))
308.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
50.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune262.0ms

Filtered

102 candidates to 72 candidates (70.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	102	8	110

Merged error: 0b

Counts

110 → 8

regimes392.0ms

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	13
1	14	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.0s	2527×	body	1280	valid
579.0ms	2150×	body	640	valid
528.0ms	8184×	body	80	valid
204.0ms	1012×	body	320	valid
67.0ms	505×	body	160	valid