Details

sample78.0ms

Algorithm

intervals

Results

28.0ms	76×	body	1280	valid
16.0ms	74×	body	640	valid
13.0ms	276×	body	80	valid
3.0ms	22×	body	320	valid
2.0ms	18×	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: 0.4b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (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))

series335.0ms

Counts

2 → 6

Calls

2 calls:

110.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
225.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (29.0ms)

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

prune151.0ms

Filtered

57 candidates to 39 candidates (68.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	50	7	57
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	52	7	59

Merged error: 0.0b

Counts

59 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (hypot a1 a2))
0.1b	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.4b	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
5.5b	(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:

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

series826.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cos th) (hypot a1 a2))
374.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
304.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
44.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune255.0ms

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	1	5	6
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Merged error: 0b

Counts

109 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

234×	`sqrt-prod`
216×	`times-frac`
95×	`add-sqr-sqrt`
93×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
14×	`associate-/l*`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-exp` `cbrt-unprod` `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 → 215

Calls

3 calls:

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

series623.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
301.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
215.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	623	3219
1	2992	2787
2	5002	2779

prune357.0ms

Filtered

224 candidates to 101 candidates (45.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	224	7	231

Merged error: 0b

Counts

231 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b

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

0.3b

(/ (* (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)))

rewrite33.0ms

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))))

16.0ms

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

series981.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms

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

655.0ms

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

218.0ms

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

simplify73.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (55.0ms)

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

prune318.0ms

Filtered

136 candidates to 93 candidates (68.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	136	7	143

Merged error: 0b

Counts

143 → 7

regimes160.0ms

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	13	10
1	13	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

812.0ms	2517×	body	1280	valid
449.0ms	2069×	body	640	valid
401.0ms	7900×	body	80	valid
169.0ms	1080×	body	320	valid
52.0ms	499×	body	160	valid