Details

sample361.0ms

Algorithm

intervals

Results

49.0ms	78×	body	1280	valid
22.0ms	259×	body	80	valid
14.0ms	34×	body	640	valid
4.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.re)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
162.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	194	427
1	496	390
2	1117	386
3	2398	386
4	5002	386

prune336.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

localize30.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
36.2b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sin-sum`

Counts

4 → 49

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
92.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
270.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	226	599
1	690	543
2	2010	539
3	5002	538

prune423.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.8b

localize47.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(pow (+ (pow x.re 2) (pow x.im 2)) 1/3)
36.0b	(sin (+ (* (log (* (fabs (* (cbrt 1) (pow (+ (pow x.re 2) (pow x.im 2)) 1/3))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`unpow-prod-down`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `sqrt-prod`
2×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow1/3` `sin-sum` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(pow (+ (pow x.re 2) (pow x.im 2)) 1/3)
11.0ms	(sin (+ (* (log (* (fabs (* (cbrt 1) (pow (+ (pow x.re 2) (pow x.im 2)) 1/3))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms	(pow (+ (pow x.re 2) (pow x.im 2)) 1/3)
270.0ms	(sin (+ (* (log (* (fabs (* (cbrt 1) (pow (+ (pow x.re 2) (pow x.im 2)) 1/3))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify109.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	286	622
1	957	543
2	3526	538
3	5001	538

prune515.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.7b

localize51.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(pow (+ (pow x.re 2) (pow x.im 2)) (* (cbrt 1/3) (cbrt 1/3)))
35.8b	(sin (+ (* (log (* (fabs (* (cbrt 1) (pow (pow (+ (pow x.re 2) (pow x.im 2)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `unpow-prod-down`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `sqrt-prod`
2×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2` `sin-sum` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(pow (+ (pow x.re 2) (pow x.im 2)) (* (cbrt 1/3) (cbrt 1/3)))
10.0ms	(sin (+ (* (log (* (fabs (* (cbrt 1) (pow (pow (+ (pow x.re 2) (pow x.im 2)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series957.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms	(pow (+ (pow x.re 2) (pow x.im 2)) (* (cbrt 1/3) (cbrt 1/3)))
603.0ms	(sin (+ (* (log (* (fabs (* (cbrt 1) (pow (pow (+ (pow x.re 2) (pow x.im 2)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify120.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	329	757
1	1103	684
2	4084	671
3	5002	671

prune554.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.7b

regimes420.0ms

Accuracy

77.7% (3.0b remaining)

Error of 22.8b against oracle of 19.7b and baseline of 33.4b

bsearch155.0ms

Steps

Iters	Range		Point
10	-1.2633929192945347e-304	1.928209425921678e-301	1.4488852536328e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	36
1	45	36

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	2211×	body	1280	valid
684.0ms	7893×	body	80	valid
584.0ms	1412×	body	640	valid
155.0ms	551×	body	320	valid
105.0ms	68×	body	2560	valid
48.0ms	241×	body	160	valid