Details

sample92.0ms

Algorithm

intervals

Results

36.0ms	95×	body	1280	valid
20.0ms	89×	body	640	valid
11.0ms	255×	body	80	valid
7.0ms	43×	body	320	valid
3.0ms	27×	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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 2

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))

rewrite14.0ms

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:

1.0ms	(fma 0.5 (exp im) (/ 0.5 (exp im)))
8.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
4.0ms	(/ 0.5 (exp im))

series133.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(fma 0.5 (exp im) (/ 0.5 (exp im)))
70.0ms	(* (fma 0.5 (exp im) (/ 0.5 (exp im))) (cos re))
14.0ms	(/ 0.5 (exp im))

simplify119.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (114.0ms)

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

prune169.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0b

Counts

70 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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:

5.0ms	(+ (exp (- im)) (exp im))
10.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series85.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (exp (- im)) (exp im))
62.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (34.0ms)

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

prune117.0ms

Filtered

48 candidates to 35 candidates (72.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	48	3	51

Merged error: 0b

Counts

51 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 0.5 (exp im) (cbrt (pow (/ 0.5 (exp im)) 3))) (cos re))
0.0b	(/ 0.5 (exp im))
0.0b	(pow (/ 0.5 (exp im)) 3)
1.0b	(cbrt (pow (/ 0.5 (exp im)) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
45×	`times-frac`
44×	`add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube`
9×	`add-exp-log`
7×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

4.0ms	(* (fma 0.5 (exp im) (cbrt (pow (/ 0.5 (exp im)) 3))) (cos re))
4.0ms	(/ 0.5 (exp im))
6.0ms	(pow (/ 0.5 (exp im)) 3)
8.0ms	(cbrt (pow (/ 0.5 (exp im)) 3))

series136.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (fma 0.5 (exp im) (cbrt (pow (/ 0.5 (exp im)) 3))) (cos re))
17.0ms	(/ 0.5 (exp im))
39.0ms	(pow (/ 0.5 (exp im)) 3)
13.0ms	(cbrt (pow (/ 0.5 (exp im)) 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	447	951
1	1966	828
2	5001	816

prune527.0ms

Filtered

153 candidates to 92 candidates (60.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	153	3	156

Merged error: 0b

Counts

156 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
16×	`cbrt-prod`
11×	`pow1`
10×	`add-cbrt-cube`
9×	`add-exp-log` `associate-/r` `associate-/l`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 129

Calls

4 calls:

5.0ms	(* (cbrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (cbrt (fma 0.5 (exp im) (/ 0.5 (exp im)))))
4.0ms	(/ 0.5 (exp im))
4.0ms	(/ 0.5 (exp im))
4.0ms	(/ 0.5 (exp im))

series222.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (cbrt (fma 0.5 (exp im) (/ 0.5 (exp im)))) (cbrt (fma 0.5 (exp im) (/ 0.5 (exp im)))))
13.0ms	(/ 0.5 (exp im))
13.0ms	(/ 0.5 (exp im))
13.0ms	(/ 0.5 (exp im))

simplify126.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	229	1000
1	810	913
2	3870	857
3	5001	845

prune442.0ms

Filtered

141 candidates to 103 candidates (73.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	141	3	144

Merged error: 0b

Counts

144 → 3

regimes115.0ms

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	13	7
1	13	7

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	2873×	body	1280	valid
528.0ms	2380×	body	640	valid
399.0ms	8458×	body	80	valid
176.0ms	1188×	body	320	valid
59.0ms	596×	body	160	valid