Details

sample79.0ms

Algorithm

intervals

Results

26.0ms	73×	body	1280	valid
15.0ms	76×	body	640	valid
12.0ms	251×	body	80	valid
4.0ms	28×	body	320	valid
3.0ms	28×	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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite23.0ms

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:

0.0ms	(fma a1 a1 (* a2 a2))
9.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series343.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(fma a1 a1 (* a2 a2))
109.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
202.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (28.0ms)

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

prune185.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))))
0.3b	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
4.4b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite63.0ms

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:

8.0ms	(* (cos th) (hypot a1 a2))
23.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
28.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (cos th) (hypot a1 a2))
173.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
277.0ms	(/ (* (* (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 (41.0ms)

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

prune288.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize9.0ms

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)))
0.4b	(/ (hypot a1 a2) (sqrt 2.0))

rewrite48.0ms

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:

9.0ms	(* (cos th) (hypot a1 a2))
29.0ms	(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
7.0ms	(/ (hypot a1 a2) (sqrt 2.0))

series426.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* (cos th) (hypot a1 a2))
224.0ms	(* (* (cos th) (hypot a1 a2)) (/ (hypot a1 a2) (sqrt 2.0)))
104.0ms	(/ (hypot a1 a2) (sqrt 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (47.0ms)

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

prune274.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (cos th) (hypot a1 a2))
0.3b	(* (* (cos th) (hypot a1 a2)) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
4.6b	(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `sqrt-prod`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac` `associate-r`
12×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`rem-sqrt-square` `sqrt-div` `*-commutative` `div-inv`
1×	`+-commutative` `fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

8.0ms	(+ (* a1 a1) (* a2 a2))
9.0ms	(* (cos th) (hypot a1 a2))
39.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
9.0ms	(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

series428.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* a1 a1) (* a2 a2))
96.0ms	(* (cos th) (hypot a1 a2))
234.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
68.0ms	(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	803
1	1791	697
2	5001	688

prune294.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes151.0ms

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

sample2.5s

Algorithm

intervals

Results

993.0ms	2511×	body	1280	valid
455.0ms	2182×	body	640	valid
381.0ms	7971×	body	80	valid
164.0ms	1046×	body	320	valid
62.0ms	589×	body	160	valid