Details

sample437.0ms

Algorithm

intervals

Results

47.0ms	68×	body	1280	valid
43.0ms	256×	body	80	valid
18.0ms	39×	body	640	valid
10.0ms	30×	body	320	valid
3.0ms	13×	body	160	valid

simplify54.0ms

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

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 31.9b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(cos (+ (* (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×	`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)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify71.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	189	422
1	491	385
2	1112	381
3	2385	381
4	5001	381

prune393.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 19.5b

Counts

69 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re x.re) (* x.im x.im))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.8b	(* (atan2 x.im x.re) y.im)
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

4.0ms	(+ (* x.re x.re) (* x.im x.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* x.re x.re) (* x.im x.im))
102.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	265	435
1	1023	385
2	3343	382
3	5001	382

prune537.0ms

Filtered

77 candidates to 55 candidates (28.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	73	7	80

Merged error: 3.2b

Counts

80 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.8b	(* (atan2 x.im x.re) y.im)
3.4b	(log (exp (* (atan2 x.im x.re) y.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
18.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify102.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	247	426
1	716	377
2	1692	374
3	3924	374
4	5001	374

prune502.0ms

Filtered

80 candidates to 56 candidates (30.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	81	6	87

Merged error: 3.2b

Counts

87 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (atan2 x.im x.re) y.im))
0.2b	(* (log x.re) y.re)
0.8b	(* (atan2 x.im x.re) y.im)
3.4b	(log (exp (* (atan2 x.im x.re) y.im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l` `add-log-exp`
6×	`associate-r`
4×	`log-pow`
3×	`log-prod`
2×	`exp-prod` `exp-to-pow` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

2.0ms	(exp (* (atan2 x.im x.re) y.im))
4.0ms	(* (log x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(log (exp (* (atan2 x.im x.re) y.im)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (* (atan2 x.im x.re) y.im))
71.0ms	(* (log x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(log (exp (* (atan2 x.im x.re) y.im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	185	272
1	648	239
2	2526	234
3	5002	234

prune299.0ms

Filtered

73 candidates to 46 candidates (37.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	73	6	79

Merged error: 3.2b

Counts

79 → 6

regimes523.0ms

Accuracy

59.5% (6.6b remaining)

Error of 10.1b against oracle of 3.5b and baseline of 19.9b

bsearch368.0ms

Steps

Iters	Range	Point
8	-1.1433292428005646e-306	7.32008218467031e-307	-3.87382222655497e-310
9	-2.0633252129481594e-247	-1.8094312987938748e-255	-1.9191176685539453e-248
10	-8.242753446919823e+102	-4.869990785594588e+88	-5.531726628269177e+88

Iters

Range

Point

-1.1433292428005646e-306

7.32008218467031e-307

-3.87382222655497e-310

-2.0633252129481594e-247

-1.8094312987938748e-255

-1.9191176685539453e-248

-8.242753446919823e+102

-4.869990785594588e+88

-5.531726628269177e+88

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	38
1	60	38
2	60	38

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	2067×	body	1280	valid
809.0ms	8004×	body	80	valid
673.0ms	1463×	body	640	valid
213.0ms	665×	body	320	valid
75.0ms	343×	body	160	valid

Details

sample437.0ms

simplify54.0ms

prune18.0ms

localize32.0ms

rewrite22.0ms

series263.0ms

simplify71.0ms

prune393.0ms

localize16.0ms

rewrite18.0ms

series197.0ms

simplify80.0ms

prune537.0ms

localize18.0ms

rewrite15.0ms

series186.0ms

simplify102.0ms

prune502.0ms

localize13.0ms

rewrite12.0ms

series127.0ms

simplify70.0ms

prune299.0ms

regimes523.0ms

bsearch368.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling