Details

sample327.0ms

Algorithm

intervals

Results

234.0ms	64×	body	1280	valid
27.0ms	249×	body	80	valid
22.0ms	46×	body	640	valid
11.0ms	25×	body	320	valid
3.0ms	13×	body	160	valid

simplify526.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4996	36
1	4996	36

prune15.0ms

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: 33.3b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b	(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.im)
3.0ms	(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)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
75.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4988	677
1	4988	677

prune116.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	5	69

Merged error: 17.9b

Counts

69 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
1.8b	(* (atan2 x.im x.re) y.im)
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
7.0ms	(* (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)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
22.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4952	898
1	4952	898

prune111.0ms

Filtered

57 candidates to 78 candidates (-36.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	76	7	83

Merged error: 4.4b

Counts

83 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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.im)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4988	677
1	4988	677

prune135.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	68	7	75

Merged error: 4.4b

Counts

75 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

29.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cos-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (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)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
50.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4918	815
1	4918	815

prune101.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	50	8	58

Merged error: 4.4b

Counts

58 → 8

regimes502.0ms

Accuracy

65.8% (5.5b remaining)

Error of 9.1b against oracle of 3.6b and baseline of 19.7b

bsearch248.0ms

Steps

Iters	Range	Point
10	-3.357329548787188e-303	1.7437112035406946e-301	1.49108249314653e-310
7	-7.839359884529182e-156	-4.027331699395915e-157	-7.134776568351581e-156
8	-4.166907913142383e+59	-1.365703734364491e+56	-1.4326246729683051e+56

Iters

Range

Point

-3.357329548787188e-303

1.7437112035406946e-301

1.49108249314653e-310

-7.839359884529182e-156

-4.027331699395915e-157

-7.134776568351581e-156

-4.166907913142383e+59

-1.365703734364491e+56

-1.4326246729683051e+56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	65
1	45	65

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	2057×	body	1280	valid
863.0ms	7999×	body	80	valid
682.0ms	1436×	body	640	valid
222.0ms	675×	body	320	valid
65.0ms	285×	body	160	valid

Details

sample327.0ms

simplify526.0ms

prune15.0ms

localize25.0ms

rewrite22.0ms

series93.0ms

simplify60.0ms

prune116.0ms

localize16.0ms

rewrite19.0ms

series70.0ms

simplify45.0ms

prune111.0ms

localize28.0ms

rewrite18.0ms

series70.0ms

simplify59.0ms

prune135.0ms

localize31.0ms

rewrite25.0ms

series159.0ms

simplify59.0ms

prune101.0ms

regimes502.0ms

bsearch248.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling