Details

sample94.0ms

Algorithm

intervals

Results

40.0ms	105×	body	1280	valid
17.0ms	83×	body	640	valid
12.0ms	290×	body	80	valid
9.0ms	46×	body	320	valid
2.0ms	17×	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

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite8.0ms

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)))
3.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
3.0ms	(/ 0.5 (exp im))

series120.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(fma 0.5 (exp im) (/ 0.5 (exp im)))
67.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
12.0ms	(/ 0.5 (exp im))

simplify124.0ms

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

prune165.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`add-cbrt-cube`
13×	`add-exp-log`
12×	`associate-l`
11×	`pow1`
7×	`sqrt-prod`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

13.0ms	(* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (cos re)))
5.0ms	(* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (cos re))
3.0ms	(/ 0.5 (exp im))
3.0ms	(/ 0.5 (exp im))

series190.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (cos re)))
97.0ms	(* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (cos re))
13.0ms	(/ 0.5 (exp im))
13.0ms	(/ 0.5 (exp im))

simplify146.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	276	882
1	1007	758
2	4823	758
3	5001	756

prune337.0ms

Filtered

117 candidates to 86 candidates (73.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ 0.5 (exp im)))
0.0b	(/ 0.5 (exp im))
0.0b	(/ 0.5 (exp im))
0.0b	(log (exp (/ 0.5 (exp im))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
26×	`exp-prod`
14×	`log-pow`
8×	`add-cbrt-cube`
6×	`add-exp-log` `associate-/r` `associate-/l`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`log-prod`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 108

Calls

4 calls:

4.0ms	(exp (/ 0.5 (exp im)))
2.0ms	(/ 0.5 (exp im))
3.0ms	(/ 0.5 (exp im))
5.0ms	(log (exp (/ 0.5 (exp im))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp (/ 0.5 (exp im)))
12.0ms	(/ 0.5 (exp im))
15.0ms	(/ 0.5 (exp im))
13.0ms	(log (exp (/ 0.5 (exp im))))

simplify54.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	183	541
1	480	499
2	1655	495
3	5001	492

prune448.0ms

Filtered

120 candidates to 96 candidates (80.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	3042×	body	1280	valid
521.0ms	2496×	body	640	valid
372.0ms	8745×	body	80	valid
156.0ms	1144×	body	320	valid
62.0ms	621×	body	160	valid