Details

analyze1.5s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample150.0ms

Algorithm

intervals

Results

62.0ms	79×	body	1280	invalid
28.0ms	243×	body	80	valid
20.0ms	41×	body	640	invalid
9.0ms	26×	body	320	invalid
3.0ms	6×	body	640	valid
3.0ms	11×	body	160	invalid
2.0ms	3×	body	1280	valid
1.0ms	6×	body	80	invalid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify488.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	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: 35.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.re)
32.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

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)))
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify43.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5098	677

prune126.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 18.8b

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)
1.6b	(* (atan2 x.im x.re) y.im)
32.0b	(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` `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 → 65

Calls

4 calls:

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

series76.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
23.0ms	(* (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)))

simplify51.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4931	892
1	4931	892

prune119.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	76	6	82

Merged error: 3.3b

Counts

82 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
2.1b	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
32.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4966	744
1	4966	744

prune123.0ms

Filtered

61 candidates to 82 candidates (-34.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	82	6	88

Merged error: 3.3b

Counts

88 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log (neg x.re)) y.re)
1.6b	(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`pow1`
7×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
6×	`associate-r`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 48

Calls

3 calls:

4.0ms	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(* (log (neg x.re)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series41.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(- (* (log (neg x.re)) y.re) (* (atan2 x.im x.re) y.im))
11.0ms	(* (log (neg x.re)) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

simplify73.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	6389	492

prune52.0ms

Filtered

36 candidates to 57 candidates (-58.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	57	6	63

Merged error: 3.3b

Counts

63 → 6

regimes437.0ms

Accuracy

82.7% (5.5b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 35.2b

bsearch203.0ms

Steps

Iters	Range		Point
9	9.176971540993956e-47	2.6776788610594255e-38	2.0538964275531915e-46
7	6.244224889483291e-113	3.0290628435590816e-111	1.3420662967240638e-111
8	-1.860806577041847e-305	4.3133035984950444e-308	-2.8978419282618e-311

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	119	94
1	119	94

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1823×	body	1280	invalid
816.0ms	7537×	body	80	valid
637.0ms	1339×	body	640	invalid
187.0ms	564×	body	320	invalid
98.0ms	138×	body	1280	valid
70.0ms	148×	body	640	valid
56.0ms	251×	body	160	invalid
43.0ms	382×	body	80	invalid
38.0ms	114×	body	320	valid
17.0ms	63×	body	160	valid

Details

analyze1.5s

sample150.0ms

simplify488.0ms

prune15.0ms

localize24.0ms

rewrite37.0ms

series86.0ms

simplify43.0ms

prune126.0ms

localize16.0ms

rewrite18.0ms

series76.0ms

simplify51.0ms

prune119.0ms

localize17.0ms

rewrite18.0ms

series43.0ms

simplify54.0ms

prune123.0ms

localize12.0ms

rewrite12.0ms

series41.0ms

simplify73.0ms

prune52.0ms

regimes437.0ms

bsearch203.0ms

simplify3.0ms

end0.0ms

sample3.6s

Profiling