Details

sample90.0ms

Algorithm

intervals

Results

33.0ms	92×	body	1280	valid
16.0ms	64×	body	640	valid
15.0ms	253×	body	80	valid
7.0ms	36×	body	320	valid
2.0ms	14×	body	160	valid

simplify21.0ms

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

prune13.0ms

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))
0.2b	(* (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))

series368.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma a1 a1 (* a2 a2))
111.0ms	(* (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

prune393.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 0b

Counts

72 → 9

localize14.0ms

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))
6.8b	(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)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (cos th) (hypot a1 a2))
179.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
287.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
48.0ms	(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

prune248.0ms

Filtered

102 candidates to 72 candidates (70.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	105	6	111

Merged error: 0b

Counts

111 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot a1 a2)
0.1b	(* (cos th) (hypot a1 a2))
0.2b	(/ (* (cos th) (hypot a1 a2)) (/ (sqrt 2.0) (hypot a1 a2)))
0.4b	(/ (sqrt 2.0) (hypot a1 a2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

1.0ms	(hypot a1 a2)
4.0ms	(* (cos th) (hypot a1 a2))
8.0ms	(/ (* (cos th) (hypot a1 a2)) (/ (sqrt 2.0) (hypot a1 a2)))
4.0ms	(/ (sqrt 2.0) (hypot a1 a2))

series485.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot a1 a2)
107.0ms	(* (cos th) (hypot a1 a2))
242.0ms	(/ (* (cos th) (hypot a1 a2)) (/ (sqrt 2.0) (hypot a1 a2)))
84.0ms	(/ (sqrt 2.0) (hypot a1 a2))

simplify61.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	424	1147
1	2038	1048
2	5002	1031

prune327.0ms

Filtered

150 candidates to 107 candidates (71.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	150	6	156

Merged error: 0b

Counts

156 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot a1 a2)
0.1b	(* (cos th) (/ (hypot a1 a2) (/ (sqrt 2.0) (hypot a1 a2))))
0.2b	(/ (hypot a1 a2) (/ (sqrt 2.0) (hypot a1 a2)))
0.4b	(/ (sqrt 2.0) (hypot a1 a2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

281×	`times-frac`
170×	`add-sqr-sqrt`
157×	`add-cube-cbrt` `*-un-lft-identity`
76×	`sqrt-prod`
71×	`associate-r`
25×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
9×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `hypot-udef` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`sqrt-undiv` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 257

Calls

4 calls:

1.0ms	(hypot a1 a2)
24.0ms	(* (cos th) (/ (hypot a1 a2) (/ (sqrt 2.0) (hypot a1 a2))))
8.0ms	(/ (hypot a1 a2) (/ (sqrt 2.0) (hypot a1 a2)))
4.0ms	(/ (sqrt 2.0) (hypot a1 a2))

series506.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot a1 a2)
246.0ms	(* (cos th) (/ (hypot a1 a2) (/ (sqrt 2.0) (hypot a1 a2))))
126.0ms	(/ (hypot a1 a2) (/ (sqrt 2.0) (hypot a1 a2)))
88.0ms	(/ (sqrt 2.0) (hypot a1 a2))

simplify113.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	728	2584
1	3983	2366
2	5002	2361

prune525.0ms

Filtered

269 candidates to 176 candidates (65.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	269	6	275

Merged error: 0b

Counts

275 → 6

regimes157.0ms

Accuracy

0% (0.4b 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	11	7
1	11	7

end0.0ms

sample2.6s

Algorithm

intervals

Results

952.0ms	2465×	body	1280	valid
534.0ms	2077×	body	640	valid
483.0ms	8047×	body	80	valid
194.0ms	1060×	body	320	valid
72.0ms	568×	body	160	valid