Details

sample95.0ms

Algorithm

intervals

Results

43.0ms	103×	body	1280	valid
18.0ms	81×	body	640	valid
12.0ms	262×	body	80	valid
6.0ms	40×	body	320	valid
2.0ms	16×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (10.0ms)

Iter	Nodes	Cost
0	23	7
1	60	7
2	112	7
3	236	7
4	520	6
5	702	6
6	1514	6
7	2284	6
8	5001	6

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp (- im)) (exp im))
0.0b	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-sqr-sqrt` `add-cube-cbrt` `associate-r` `add-log-exp`
3×	`fma-def` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3-+` `associate-*r/` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-l` `sum-log` `*-commutative`

Counts

2 → 42

Calls

2 calls:

19.0ms	(+ (exp (- im)) (exp im))
59.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series75.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(+ (exp (- im)) (exp im))
56.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	258	374
1	1276	311
2	5002	307

prune174.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 0.5 (exp im) (/ 0.5 (exp im)))
0.0b	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
0.0b	(/ 0.5 (exp im))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

0.0ms	(fma 0.5 (exp im) (/ 0.5 (exp im)))
8.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
8.0ms	(/ 0.5 (exp im))

series111.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(fma 0.5 (exp im) (/ 0.5 (exp im)))
62.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
12.0ms	(/ 0.5 (exp im))

simplify121.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	215	417
1	712	366
2	4318	366
3	5001	364

prune243.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.5 (exp im) (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5))))
0.0b	(* (fma 0.5 (exp im) (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))) (cos re))
0.0b	(/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))
1.0b	(/ (exp im) (sqrt 0.5))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`add-cube-cbrt` `*-un-lft-identity`
144×	`sqrt-prod`
28×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`add-exp-log`
9×	`div-inv` `associate-/l*`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`frac-2neg` `clear-num`
1×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 248

Calls

4 calls:

0.0ms	(fma 0.5 (exp im) (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5))))
10.0ms	(* (fma 0.5 (exp im) (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))) (cos re))
15.0ms	(/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))
8.0ms	(/ (exp im) (sqrt 0.5))

series326.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 0.5 (exp im) (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5))))
140.0ms	(* (fma 0.5 (exp im) (/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))) (cos re))
59.0ms	(/ (sqrt 0.5) (/ (exp im) (sqrt 0.5)))
43.0ms	(/ (exp im) (sqrt 0.5))

simplify92.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	695	2898
1	3414	2537
2	5001	2501

prune739.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (- im)) (exp im))
0.0b	(+ (exp (- im)) (exp im))
0.2b	(* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im))))
0.7b	(* (* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
14×	`sqrt-div` `associate-r`
10×	`add-sqr-sqrt` `add-cube-cbrt` `associate-*r/`
9×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
8×	`sqrt-prod` `add-log-exp`
6×	`fma-def`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `associate-l` `associate-l/` `sum-log` `-commutative`

Counts

4 → 95

Calls

4 calls:

20.0ms	(+ (exp (- im)) (exp im))
18.0ms	(+ (exp (- im)) (exp im))
59.0ms	(* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im))))
153.0ms	(* (* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (exp (- im)) (exp im))
21.0ms	(+ (exp (- im)) (exp im))
77.0ms	(* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im))))
53.0ms	(* (* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))

simplify61.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	400	1151
1	2046	946
2	5001	928

prune470.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes163.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	3056×	body	1280	valid
573.0ms	2516×	body	640	valid
405.0ms	8425×	body	80	valid
191.0ms	1214×	body	320	valid
58.0ms	581×	body	160	valid