Details

sample359.0ms

Algorithm

intervals

Results

39.0ms	66×	body	1280	valid
24.0ms	259×	body	80	valid
20.0ms	52×	body	640	valid
9.0ms	33×	body	320	valid
1.0ms	8×	body	160	valid

simplify51.0ms

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: 32.0b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`sqrt-div` `swap-sqr` `add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	188	482
1	483	443
2	1078	443
3	2703	443
4	5003	443

prune264.0ms

Filtered

79 candidates to 54 candidates (68.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	76	5	81

Merged error: 18.6b

Counts

81 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)
2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
20×	`associate-l`
13×	`pow1` `exp-prod`
10×	`add-cube-cbrt`
8×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r` `distribute-lft-out--` `unswap-sqr`
5×	`log-pow` `distribute-lft-out`
4×	`difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `swap-sqr` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 84

Calls

4 calls:

19.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
6.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
96.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	297	616
1	839	557
2	2126	553
3	5001	552

prune251.0ms

Filtered

96 candidates to 63 candidates (65.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 3.4b

Counts

101 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
8×	`sqrt-prod`
6×	`add-sqr-sqrt` `cos-sum`
5×	`pow1` `add-cube-cbrt` `distribute-lft-out`
4×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
3×	`+-commutative`
2×	`sqrt-div` `swap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 47

Calls

4 calls:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
145.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
140.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
147.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	134	623
1	273	557
2	570	557
3	1724	557
4	5001	557

prune291.0ms

Filtered

59 candidates to 48 candidates (81.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	58	9	67

Merged error: 3.4b

Counts

67 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cos-sum`
4×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

22.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
141.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
144.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	60	672
1	81	588
2	117	588
3	268	588
4	549	588
5	5001	588

prune257.0ms

Filtered

48 candidates to 44 candidates (91.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	48	9	57

Merged error: 3.4b

Counts

57 → 9

regimes289.0ms

Accuracy

58.7% (6.8b remaining)

Error of 10.3b against oracle of 3.6b and baseline of 20.0b

bsearch176.0ms

Steps

Iters	Range		Point
7	2.286423798219875e-14	1.373000774999114e-12	2.270578291458994e-13
8	-4.4379159581928395e-61	-3.086922346161015e-65	-1.819198211225745e-62

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	52	26
2	52	26

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2074×	body	1280	valid
684.0ms	7957×	body	80	valid
576.0ms	1463×	body	640	valid
177.0ms	653×	body	320	valid
60.0ms	339×	body	160	valid