Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

270×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 24.3b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
23.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (* x.im y.re) (* x.re y.im))
84.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	270	481
1	1012	432
2	3842	422
3	5001	421

prune136.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	50	6	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	6	57

Merged error: 9.7b

Counts

57 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.3b	(- (* x.im y.re) (* x.re y.im))
12.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`prod-exp`
26×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`rec-exp`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 110

Calls

3 calls:

12.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series329.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
35.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify59.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	537	1095
1	2236	907
2	5002	905

prune241.0ms

Filtered

119 candidates to 78 candidates (65.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	7	119
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Merged error: 4.0b

Counts

125 → 8

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
12.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 121

Calls

3 calls:

7.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series268.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
39.0ms	(- (* x.im y.re) (* x.re y.im))
113.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	451	1408
1	1659	1307
2	5001	1298

prune289.0ms

Filtered

130 candidates to 99 candidates (76.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	128	10	138

Merged error: 4.0b

Counts

138 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
0.3b	(- (* x.im y.re) (* x.re y.im))
13.0b	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

528×	`times-frac`
255×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
56×	`associate-/l*`
39×	`associate-/r/`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
21×	`associate-/r*`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `associate-/l/` `inv-pow`

Counts

4 → 359

Calls

4 calls:

16.0ms	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
8.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
4.0ms	(- (* x.im y.re) (* x.re y.im))
5.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
115.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
40.0ms	(- (* x.im y.re) (* x.re y.im))
91.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1296	5404
1	5002	4894

prune681.0ms

Filtered

371 candidates to 229 candidates (61.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	371	0	371
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	371	10	381

Merged error: 4.0b

Counts

381 → 10

regimes166.0ms

Accuracy

31.9% (8.2b remaining)

Error of 12.7b against oracle of 4.5b and baseline of 16.6b

bsearch72.0ms

Steps

Iters	Range		Point
7	3.1837334327695434e+155	6.857760642350757e+156	9.341472830619268e+155
9	-6.544231823169852e+220	-2.0003023358733455e+215	-2.0310852147485622e+215

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	25	12
2	25	12

end0.0ms

sample604.0ms

Algorithm

intervals

Results

386.0ms

8441×

body

valid