Details

sample371.0ms

Algorithm

intervals

Results

53.0ms	83×	body	1280	valid
25.0ms	259×	body	80	valid
18.0ms	43×	body	640	valid
5.0ms	17×	body	320	valid
2.0ms	11×	body	160	valid
2.0ms	1×	body	2560	valid

simplify40.0ms

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: 30.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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.im)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2509	386
4	5001	386

prune354.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.6b

localize30.0ms

Local error

Found 4 expressions with local error:

27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.1b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.1b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(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)))

rewrite22.0ms

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:

3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(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)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
91.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
92.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
266.0ms	(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)))

simplify65.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (58.0ms)

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

prune452.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.5b

localize42.0ms

Local error

Found 4 expressions with local error:

27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.1b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(pow (+ (pow x.re 2) (pow x.im 2)) 1/3)
31.4b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (* (cbrt 1) (pow (+ (pow x.re 2) (pow x.im 2)) 1/3))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite135.0ms

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:

3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(pow (+ (pow x.re 2) (pow x.im 2)) 1/3)
111.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (* (cbrt 1) (pow (+ (pow x.re 2) (pow x.im 2)) 1/3))))) y.im) (* (atan2 x.im x.re) y.re)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
91.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms	(pow (+ (pow x.re 2) (pow x.im 2)) 1/3)
265.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (* (cbrt 1) (pow (+ (pow x.re 2) (pow x.im 2)) 1/3))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify114.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	286	622
1	954	543
2	3506	538
3	5002	538

prune576.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.5b

localize34.0ms

Local error

Found 4 expressions with local error:

28.1b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.1b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
28.1b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (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)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
265.0ms	(sin (+ (* (log (* (fabs (* (* (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (cbrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (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)))

simplify61.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	214	777
1	648	689
2	1928	683
3	5001	683

prune477.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.5b

regimes407.0ms

Accuracy

78% (3.1b remaining)

Error of 22.5b against oracle of 19.4b and baseline of 33.7b

bsearch132.0ms

Steps

Iters	Range		Point
8	-1.2183125014823537e-305	2.1669339449380637e-307	8.5967781878852e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2280×	body	1280	valid
710.0ms	7893×	body	80	valid
609.0ms	1436×	body	640	valid
164.0ms	578×	body	320	valid
81.0ms	52×	body	2560	valid
55.0ms	265×	body	160	valid