Details

sample358.0ms

Algorithm

intervals

Results

38.0ms	63×	body	1280	valid
26.0ms	257×	body	80	valid
22.0ms	58×	body	640	valid
5.0ms	17×	body	320	valid
2.0ms	9×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (17.0ms)

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 (0.0%)

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: 34.9b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
30.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite65.0ms

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:

3.0ms	(* (atan2 x.im x.re) y.im)
23.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
144.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify79.0ms

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

prune273.0ms

Filtered

79 candidates to 54 candidates (31.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	75	6	81

Merged error: 19.5b

Counts

81 → 6

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)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.9b	(* (atan2 x.im x.re) y.im)
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite44.0ms

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:

17.0ms	(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)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
95.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (53.0ms)

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

prune288.0ms

Filtered

96 candidates to 63 candidates (34.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	93	9	102

Merged error: 3.8b

Counts

102 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
0.2b	(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (- (* (atan2 x.im x.re) y.im))))
1.9b	(* (atan2 x.im x.re) y.im)
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
32×	`add-sqr-sqrt` `associate-l`
28×	`exp-prod`
18×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log` `unpow-prod-down`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-r`
10×	`distribute-lft-out`
9×	`pow1`
8×	`add-cbrt-cube`
7×	`prod-exp` `unswap-sqr`
6×	`add-log-exp`
4×	`swap-sqr` `*-commutative`
3×	`exp-neg`
2×	`neg-sub0` `pow-to-exp` `exp-diff` `sqrt-div` `associate-*r/` `pow-prod-down` `pow-exp` `cbrt-unprod` `rem-exp-log` `sqr-pow`
1×	`neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `un-div-inv` `flip-+`

Counts

4 → 118

Calls

4 calls:

10.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
43.0ms	(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (- (* (atan2 x.im x.re) y.im))))
3.0ms	(* (atan2 x.im x.re) y.im)
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
113.0ms	(* (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (- (* (atan2 x.im x.re) y.im))))
16.0ms	(* (atan2 x.im x.re) y.im)
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	395	890
1	1404	834
2	5001	830

prune319.0ms

Filtered

130 candidates to 84 candidates (35.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	129	10	139

Merged error: 3.8b

Counts

139 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ 1 x.re) (* -1 y.re))
0.0b	(exp (* (atan2 x.im x.re) y.im))
0.3b	(/ (pow (/ 1 x.re) (* -1 y.re)) (exp (* (atan2 x.im x.re) y.im)))
1.9b	(* (atan2 x.im x.re) y.im)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
75×	`add-sqr-sqrt`
69×	`add-cube-cbrt` `*-un-lft-identity`
65×	`unpow-prod-down`
29×	`add-exp-log`
18×	`div-exp`
17×	`associate-/l*`
12×	`pow-unpow` `exp-prod` `pow-exp`
9×	`associate-r` `associate-l`
8×	`pow1` `add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`sqr-pow`
3×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `associate-/r` `-commutative` `unswap-sqr`
2×	`pow-neg` `mul-1-neg`
1×	`cbrt-undiv` `exp-to-pow` `pow-flip` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `rem-exp-log` `associate-/l/` `inv-pow`

Counts

4 → 176

Calls

4 calls:

6.0ms	(pow (/ 1 x.re) (* -1 y.re))
4.0ms	(exp (* (atan2 x.im x.re) y.im))
20.0ms	(/ (pow (/ 1 x.re) (* -1 y.re)) (exp (* (atan2 x.im x.re) y.im)))
3.0ms	(* (atan2 x.im x.re) y.im)

series166.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (/ 1 x.re) (* -1 y.re))
21.0ms	(exp (* (atan2 x.im x.re) y.im))
78.0ms	(/ (pow (/ 1 x.re) (* -1 y.re)) (exp (* (atan2 x.im x.re) y.im)))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify66.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	578	1726
1	2256	1589
2	5001	1521

prune383.0ms

Filtered

188 candidates to 119 candidates (36.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	1	6	7
Picked	1	0	1
Done	1	1	2
Total	187	11	198

Merged error: 3.8b

Counts

198 → 11

regimes371.0ms

Accuracy

69.3% (5.1b remaining)

Error of 8.8b against oracle of 3.7b and baseline of 20.4b

bsearch144.0ms

Steps

Iters	Range		Point
11	-3.0295251196676372e-294	2.480952709492434e-302	-6.97109659623231e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	43	18
2	43	18

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2076×	body	1280	valid
691.0ms	7973×	body	80	valid
610.0ms	1549×	body	640	valid
174.0ms	644×	body	320	valid
58.0ms	307×	body	160	valid