Details

sample382.0ms

Algorithm

intervals

Results

39.0ms	56×	body	1280	valid
33.0ms	48×	body	640	valid
29.0ms	250×	body	80	valid
6.0ms	18×	body	320	valid
3.0ms	13×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17

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

localize23.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

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)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (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)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	205	456
1	546	415
2	1264	411
3	2748	411
4	5001	411

prune351.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 21.4b

Counts

80 → 6

localize20.0ms

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)))

rewrite19.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `exp-sum` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `prod-diff` `flip-+` `hypot-def`

Counts

4 → 79

Calls

4 calls:

4.0ms	(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)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
90.0ms	(* (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)))

simplify65.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	308	585
1	921	522
2	2504	484
3	5002	467

prune307.0ms

Filtered

91 candidates to 74 candidates (81.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	88	9	97

Merged error: 4.2b

Counts

97 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (pow (hypot x.re x.im) y.re))
0.0b	(log (pow (exp (pow (hypot x.re x.im) y.re)) (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)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `exp-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log` `log-prod` `add-log-exp`
6×	`pow1` `unpow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rem-log-exp` `associate-r` `associate-l` `rem-exp-log`
2×	`sqr-pow`
1×	`neg-sub0` `distribute-lft-neg-in` `exp-neg` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `exp-diff` `pow-prod-down` `neg-log` `pow-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

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

series319.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(exp (pow (hypot x.re x.im) y.re))
149.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
23.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)

simplify135.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	294	551
1	994	487
2	4741	467
3	5001	467

prune320.0ms

Filtered

88 candidates to 68 candidates (77.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 4.2b

Counts

97 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (exp (* (atan2 x.im x.re) y.im)))
0.0b	(log (pow (exp (pow (hypot x.re x.im) y.re)) (/ 1 (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)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `log-prod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-flip` `rem-log-exp` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`exp-prod` `exp-to-pow` `div-exp`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `rem-exp-log` `inv-pow` `unswap-sqr` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

4.0ms	(/ 1 (exp (* (atan2 x.im x.re) y.im)))
3.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (/ 1 (exp (* (atan2 x.im x.re) y.im)))))
2.0ms	(exp (* (atan2 x.im x.re) y.im))
4.0ms	(* (atan2 x.im x.re) y.im)

series224.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (exp (* (atan2 x.im x.re) y.im)))
153.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (/ 1 (exp (* (atan2 x.im x.re) y.im)))))
20.0ms	(exp (* (atan2 x.im x.re) y.im))
19.0ms	(* (atan2 x.im x.re) y.im)

simplify39.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	287	659
1	1103	577
2	5002	553

prune263.0ms

Filtered

99 candidates to 64 candidates (64.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 4.2b

Counts

109 → 10

regimes231.0ms

Accuracy

0% (0.6b remaining)

Error of 4.1b against oracle of 3.5b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	20
1	25	20
2	25	20

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2002×	body	1280	valid
843.0ms	7955×	body	80	valid
690.0ms	1452×	body	640	valid
213.0ms	637×	body	320	valid
67.0ms	304×	body	160	valid