Details

sample376.0ms

Algorithm

intervals

Results

39.0ms	67×	body	1280	valid
24.0ms	263×	body	80	valid
23.0ms	59×	body	640	valid
6.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid

simplify42.0ms

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

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: 35.1b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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

series243.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
154.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	422
1	501	385
2	1134	381
3	2496	381
4	5001	381

prune295.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Merged error: 19.4b

Counts

69 → 3

localize17.0ms

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)
31.8b	(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)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
89.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

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

prune249.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	77	7	84

Merged error: 4.4b

Counts

84 → 7

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)

rewrite22.0ms

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:

3.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
10.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
4.0ms	(* (atan2 x.im x.re) y.im)

series133.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
89.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
16.0ms	(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (41.0ms)

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

prune424.0ms

Filtered

132 candidates to 101 candidates (76.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	132	7	139

Merged error: 4.4b

Counts

139 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-prod`
26×	`add-sqr-sqrt` `unpow-prod-down`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-r` `associate-l` `div-inv` `associate-/l*`
2×	`cbrt-undiv` `pow1/3` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `sqr-pow`
1×	`neg-sub0` `exp-neg` `frac-2neg` `exp-diff` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

4.0ms	(cbrt (pow (/ -1 x.re) y.re))
4.0ms	(cbrt (pow (/ -1 x.re) y.re))
16.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (* (cbrt (pow (/ -1 x.re) y.re)) (cbrt (pow (/ -1 x.re) y.re))))
4.0ms	(* (atan2 x.im x.re) y.im)

series369.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (pow (/ -1 x.re) y.re))
92.0ms	(cbrt (pow (/ -1 x.re) y.re))
165.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (* (cbrt (pow (/ -1 x.re) y.re)) (cbrt (pow (/ -1 x.re) y.re))))
19.0ms	(* (atan2 x.im x.re) y.im)

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	457	922
1	1510	827
2	5001	794

prune378.0ms

Filtered

103 candidates to 80 candidates (77.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	103	7	110

Merged error: 4.4b

Counts

110 → 7

regimes234.0ms

Accuracy

65.9% (5.5b remaining)

Error of 9.1b against oracle of 3.7b and baseline of 19.7b

bsearch128.0ms

Steps

Iters	Range		Point
11	-3.161620283751132e-295	9.444972038939536e-299	-8.3696575552804e-311

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

sample3.1s

Algorithm

intervals

Results

1.2s	2008×	body	1280	valid
667.0ms	7998×	body	80	valid
579.0ms	1506×	body	640	valid
184.0ms	677×	body	320	valid
57.0ms	308×	body	160	valid