Details

sample371.0ms

Algorithm

intervals

Results

39.0ms	68×	body	1280	valid
23.0ms	256×	body	80	valid
22.0ms	58×	body	640	valid
6.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (16.0ms)

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

prune13.0ms

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: 36.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
31.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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×	`cos-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)
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
140.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381

prune289.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 19.7b

Counts

69 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

7.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
93.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	280	545
1	825	486
2	2118	481
3	5001	481

prune253.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	78	8	86

Merged error: 3.4b

Counts

86 → 8

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
0.3b	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
1.7b	(* (atan2 x.im x.re) y.im)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down`
17×	`associate-/r*`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`exp-prod`
5×	`pow1` `div-exp` `div-inv` `add-log-exp`
4×	`sqr-pow`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`neg-sub0` `exp-neg` `exp-diff` `pow-exp` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `frac-2neg` `pow-prod-down` `neg-log` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 123

Calls

3 calls:

2.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
9.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
4.0ms	(* (atan2 x.im x.re) y.im)

series132.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
88.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
20.0ms	(* (atan2 x.im x.re) y.im)

simplify56.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	467	1459
1	1753	1413
2	5001	1411

prune400.0ms

Filtered

132 candidates to 101 candidates (76.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	132	8	140

Merged error: 3.4b

Counts

140 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
1.7b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.im)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
66×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down`
17×	`associate-/r*`
14×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`pow1`
9×	`associate-r` `associate-l`
5×	`div-exp` `div-inv`
4×	`add-log-exp` `sqr-pow`
3×	`pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`pow-exp` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `exp-neg` `pow-to-exp` `frac-2neg` `exp-diff` `clear-num`

Counts

4 → 142

Calls

4 calls:

12.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.im)

series140.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(* (atan2 x.im x.re) y.im)

simplify52.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	434	1519
1	1551	1458
2	5001	1455

prune579.0ms

Filtered

154 candidates to 112 candidates (72.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	154	8	162

Merged error: 3.4b

Counts

162 → 8

regimes343.0ms

Accuracy

80.1% (5.3b remaining)

Error of 9.2b against oracle of 3.9b and baseline of 30.4b

bsearch100.0ms

Steps

Iters	Range		Point
9	-5.459969929633657e-306	2.8649750194033813e-305	1.73062623171225e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	35	15
2	35	15

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1986×	body	1280	valid
660.0ms	7939×	body	80	valid
538.0ms	1432×	body	640	valid
182.0ms	679×	body	320	valid
55.0ms	314×	body	160	valid