Details

sample93.0ms

Algorithm

intervals

Results

39.0ms	105×	body	1280	valid
17.0ms	83×	body	640	valid
12.0ms	290×	body	80	valid
10.0ms	46×	body	320	valid
2.0ms	17×	body	160	valid

simplify73.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

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))

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)))
4.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
3.0ms	(/ 0.5 (exp im))

series127.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma 0.5 (exp im) (/ 0.5 (exp im)))
71.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
13.0ms	(/ 0.5 (exp im))

simplify123.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (117.0ms)

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

prune176.0ms

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))

rewrite25.0ms

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:

12.0ms	(* (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))

series204.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (cos re)))
104.0ms	(* (sqrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (cos re))
13.0ms	(/ 0.5 (exp im))
16.0ms	(/ 0.5 (exp im))

simplify151.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (141.0ms)

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

prune354.0ms

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	(/ (* (cbrt 0.5) (cbrt 0.5)) (/ (exp im) (cbrt 0.5)))
0.0b	(/ 0.5 (exp im))
1.0b	(/ (exp im) (cbrt 0.5))
1.0b	(* (cbrt 0.5) (cbrt 0.5))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
69×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
46×	`cbrt-prod`
31×	`associate-/r*`
18×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`pow1`
8×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `associate-/r/` `*-commutative`

Counts

4 → 178

Calls

4 calls:

9.0ms	(/ (* (cbrt 0.5) (cbrt 0.5)) (/ (exp im) (cbrt 0.5)))
3.0ms	(/ 0.5 (exp im))
4.0ms	(/ (exp im) (cbrt 0.5))
6.0ms	(* (cbrt 0.5) (cbrt 0.5))

series139.0ms

Counts

4 → 10

Calls

4 calls:

70.0ms	(/ (* (cbrt 0.5) (cbrt 0.5)) (/ (exp im) (cbrt 0.5)))
13.0ms	(/ 0.5 (exp im))
56.0ms	(/ (exp im) (cbrt 0.5))
0.0ms	(* (cbrt 0.5) (cbrt 0.5))

simplify74.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	471	1326
1	2518	1224
2	5001	1105

prune667.0ms

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	18	18
1	18	18

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3042×	body	1280	valid
532.0ms	2496×	body	640	valid
366.0ms	8745×	body	80	valid
152.0ms	1144×	body	320	valid
56.0ms	621×	body	160	valid