Details

sample372.0ms

Algorithm

intervals

Results

38.0ms	56×	body	1280	valid
28.0ms	250×	body	80	valid
22.0ms	48×	body	640	valid
6.0ms	18×	body	320	valid
3.0ms	13×	body	160	valid

simplify39.0ms

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

prune16.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 35.7b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
32.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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×	`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.re)
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)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
143.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	189	422
1	491	385
2	1112	381
3	2393	381
4	5001	381

prune290.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 21.4b

Counts

70 → 6

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)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.0b	(* (atan2 x.im x.re) y.im)
32.4b	(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:

5.0ms	(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)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
92.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify59.0ms

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

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Merged error: 4.3b

Counts

87 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
1.0b	(* (atan2 x.im x.re) y.im)

rewrite24.0ms

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*`
11×	`add-exp-log`
8×	`div-exp`
7×	`add-cbrt-cube`
6×	`exp-prod`
5×	`pow1` `div-inv` `add-log-exp`
4×	`pow-exp` `sqr-pow`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`neg-sub0` `exp-neg` `exp-diff` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `1-exp` `pow-prod-down` `neg-log` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 125

Calls

3 calls:

12.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
2.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
4.0ms	(* (atan2 x.im x.re) y.im)

series119.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
24.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify53.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	447	1462
1	1665	1379
2	5001	1369

prune345.0ms

Filtered

134 candidates to 86 candidates (64.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	133	10	143

Merged error: 4.3b

Counts

143 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
1.0b	(* (atan2 x.im x.re) y.im)
1.0b	(* (atan2 x.im x.re) y.im)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`exp-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-r` `associate-l`
4×	`rem-exp-log`
2×	`neg-sub0` `distribute-lft-neg-in` `exp-neg` `neg-mul-1` `distribute-rgt-neg-in` `exp-diff` `pow-prod-down` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

3.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
3.0ms	(exp (- (* (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)

series85.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
24.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
17.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify59.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	119	326
1	468	294
2	2163	294
3	5001	292

prune242.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	82	10	92

Merged error: 4.3b

Counts

92 → 10

regimes343.0ms

Accuracy

76.4% (6.7b remaining)

Error of 10.6b against oracle of 3.9b and baseline of 32.2b

bsearch136.0ms

Steps

Iters	Range		Point
10	-1.2302628846532179e-300	1.3380757040254623e-304	2.5143911341178e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	26
1	43	26
2	43	26

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	2002×	body	1280	valid
807.0ms	7955×	body	80	valid
669.0ms	1452×	body	640	valid
208.0ms	637×	body	320	valid
66.0ms	304×	body	160	valid