Details

sample96.0ms

Algorithm

intervals

Results

40.0ms	97×	body	1280	valid
17.0ms	70×	body	640	valid
17.0ms	255×	body	80	valid
6.0ms	35×	body	320	valid
2.0ms	19×	body	160	valid

simplify76.0ms

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)

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

Merged error: 0.0b

Counts

2 → 1

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)))

rewrite17.0ms

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:

6.0ms	(+ (exp (- im)) (exp im))
10.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series86.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ (exp (- im)) (exp im))
63.0ms	(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (35.0ms)

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

prune109.0ms

Filtered

48 candidates to 35 candidates (72.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Merged error: 0b

Counts

49 → 4

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (pow im 4) 1/12 (fma im im 2))
0.0b	(* (* 0.5 (cos re)) (fma (pow im 4) 1/12 (fma im im 2)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 32

Calls

2 calls:

1.0ms	(fma (pow im 4) 1/12 (fma im im 2))
5.0ms	(* (* 0.5 (cos re)) (fma (pow im 4) 1/12 (fma im im 2)))

series169.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(fma (pow im 4) 1/12 (fma im im 2))
123.0ms	(* (* 0.5 (cos re)) (fma (pow im 4) 1/12 (fma im im 2)))

simplify33.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	182	279
1	901	232
2	5001	230

prune85.0ms

Filtered

38 candidates to 26 candidates (68.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	39	3	42

Merged error: 0b

Counts

42 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (cos re) (fma 0.5 (pow im 2) 1.0)) (* 0.041666666666666664 (* (cos re) (pow im 4))))
0.0b	(* (cos re) (fma 0.5 (pow im 2) 1.0))
0.0b	(* (cos re) (pow im 4))
0.1b	(* 0.041666666666666664 (* (cos re) (pow im 4)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
17×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
11×	`associate-r` `prod-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `unpow-prod-down` `fma-udef` `log1p-expm1-u` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-lft-in` `pow-prod-down` `pow-exp` `sqr-pow`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

4 → 86

Calls

4 calls:

4.0ms	(+ (* (cos re) (fma 0.5 (pow im 2) 1.0)) (* 0.041666666666666664 (* (cos re) (pow im 4))))
4.0ms	(* (cos re) (fma 0.5 (pow im 2) 1.0))
5.0ms	(* (cos re) (pow im 4))
6.0ms	(* 0.041666666666666664 (* (cos re) (pow im 4)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ (* (cos re) (fma 0.5 (pow im 2) 1.0)) (* 0.041666666666666664 (* (cos re) (pow im 4))))
87.0ms	(* (cos re) (fma 0.5 (pow im 2) 1.0))
91.0ms	(* (cos re) (pow im 4))
116.0ms	(* 0.041666666666666664 (* (cos re) (pow im 4)))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	351	655
1	1470	585
2	5002	571

prune235.0ms

Filtered

98 candidates to 68 candidates (69.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	98	3	101

Merged error: 0b

Counts

101 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp im) -2)
0.1b	(pow (exp im) 3)
0.1b	(pow (exp (- im)) 3)
5.3b	(- (pow (exp im) -2) 1)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
32×	`add-cube-cbrt`
24×	`unpow-prod-down`
21×	`prod-diff`
19×	`pow-pow`
16×	`exp-prod`
10×	`sqr-pow`
9×	`pow-unpow`
7×	`pow1` `fma-neg`
6×	`cube-prod` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `expm1-def` `distribute-rgt-neg-in` `difference-of-sqr-1`
2×	`cube-div` `cube-mult` `unpow3` `rem-cube-cbrt`
1×	`neg-sub0` `exp-neg` `neg-mul-1` `sub-neg` `flip3--` `exp-diff` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 142

Calls

4 calls:

3.0ms	(pow (exp im) -2)
3.0ms	(pow (exp im) 3)
5.0ms	(pow (exp (- im)) 3)
7.0ms	(- (pow (exp im) -2) 1)

series108.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (exp im) -2)
24.0ms	(pow (exp im) 3)
28.0ms	(pow (exp (- im)) 3)
37.0ms	(- (pow (exp im) -2) 1)

simplify74.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	426	734
1	1889	507
2	5002	446

prune398.0ms

Filtered

154 candidates to 86 candidates (55.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	154	3	157

Merged error: 0b

Counts

157 → 3

regimes135.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	3052×	body	1280	valid
619.0ms	2503×	body	640	valid
426.0ms	8424×	body	80	valid
197.0ms	1201×	body	320	valid
69.0ms	618×	body	160	valid