Details

sample306.0ms

Algorithm

intervals

Results

22.0ms	52×	body	1280	valid
11.0ms	43×	body	640	valid
8.0ms	140×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	16×	body	320	valid
1.0ms	5×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	6
1	20	5
2	23	5
3	24	5
4	24	5

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
0.1b	(* e (cos v))
0.1b	(* e (sin v))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`associate-r` `associate-l`
3×	`expm1-log1p-u` `times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l*`

Counts

3 → 65

Calls

3 calls:

6.0ms	(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
4.0ms	(* e (cos v))
7.0ms	(* e (sin v))

series187.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
36.0ms	(* e (cos v))
58.0ms	(* e (sin v))

simplify43.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	303	422
1	1415	368
2	5001	362

prune185.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sin v) (- 1.0 (* e (cos v))))
0.1b	(* e (cos v))
0.1b	(* e (cos v))
0.2b	(* (/ e (fma (cos v) e 1.0)) (/ (sin v) (- 1.0 (* e (cos v)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
31×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log` `add-cbrt-cube`
21×	`associate-r`
19×	`associate-l`
10×	`pow1`
6×	`prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative` `div-inv` `associate-/l*`
2×	`flip3--` `flip--`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 125

Calls

4 calls:

6.0ms	(/ (sin v) (- 1.0 (* e (cos v))))
4.0ms	(* e (cos v))
4.0ms	(* e (cos v))
12.0ms	(* (/ e (fma (cos v) e 1.0)) (/ (sin v) (- 1.0 (* e (cos v)))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (sin v) (- 1.0 (* e (cos v))))
36.0ms	(* e (cos v))
38.0ms	(* e (cos v))
181.0ms	(* (/ e (fma (cos v) e 1.0)) (/ (sin v) (- 1.0 (* e (cos v)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	553	1194
1	2627	1075
2	5001	1070

prune399.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* e (cos v))
0.1b	(/ (+ 1.0 (* e (cos v))) (sin v))
0.3b	(/ e (/ (+ 1.0 (* e (cos v))) (sin v)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
12×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`flip3-+` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 123

Calls

3 calls:

7.0ms	(* e (cos v))
6.0ms	(/ (+ 1.0 (* e (cos v))) (sin v))
7.0ms	(/ e (/ (+ 1.0 (* e (cos v))) (sin v)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* e (cos v))
67.0ms	(/ (+ 1.0 (* e (cos v))) (sin v))
89.0ms	(/ e (/ (+ 1.0 (* e (cos v))) (sin v)))

simplify65.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	530	1326
1	2377	1222
2	5001	1212

prune360.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (fma (cos v) e 1.0) (sqrt e))
0.3b	(/ (/ (fma (cos v) e 1.0) (sqrt e)) (sin v))
0.3b	(/ (sqrt e) (/ (/ (fma (cos v) e 1.0) (sqrt e)) (sin v)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

1416×	`times-frac`
669×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
450×	`sqrt-prod`
79×	`associate-/r*`
35×	`div-inv`
31×	`associate-/l*`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `associate-/l/`

Counts

3 → 664

Calls

3 calls:

4.0ms	(/ (fma (cos v) e 1.0) (sqrt e))
9.0ms	(/ (/ (fma (cos v) e 1.0) (sqrt e)) (sin v))
24.0ms	(/ (sqrt e) (/ (/ (fma (cos v) e 1.0) (sqrt e)) (sin v)))

series292.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (fma (cos v) e 1.0) (sqrt e))
104.0ms	(/ (/ (fma (cos v) e 1.0) (sqrt e)) (sin v))
108.0ms	(/ (sqrt e) (/ (/ (fma (cos v) e 1.0) (sqrt e)) (sin v)))

simplify143.0ms

Algorithm

egg-herbie

Counts

673 → 673

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2270	12285
1	5001	11838

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	13
1	15	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

650.0ms	1544×	body	1280	valid
317.0ms	1218×	body	640	valid
236.0ms	4343×	body	80	valid
130.0ms	8000×	pre	80	true
102.0ms	574×	body	320	valid
40.0ms	321×	body	160	valid