Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

263×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune2.0ms

Filtered

1 candidates to 0 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: 24.3b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (* x.im y.re) (* x.re y.im))
23.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

322×	`*-un-lft-identity`
268×	`add-sqr-sqrt`
163×	`associate-l`
144×	`prod-diff`
98×	`add-cube-cbrt`
88×	`times-frac`
75×	`associate-r`
65×	`unswap-sqr`
60×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares`
25×	`*-commutative`
24×	`swap-sqr`
12×	`fma-neg`
11×	`associate-/l*`
8×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 304

Calls

2 calls:

16.0ms	(- (* x.im y.re) (* x.re y.im))
41.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- (* x.im y.re) (* x.re y.im))
87.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	752	3996
1	2226	3080
2	5002	2923

prune233.0ms

Filtered

310 candidates to 86 candidates (72.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	302	8	310
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	302	9	311

Merged error: 10.0b

Counts

311 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (hypot y.re y.im) 1))
0.3b	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1)))
1.0b	(- (* x.im y.re) (* x.re y.im))
15.6b	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

1448×	`add-sqr-sqrt`
1042×	`*-un-lft-identity`
761×	`times-frac`
682×	`associate-/r*`
577×	`add-cube-cbrt`
551×	`frac-times`
452×	`associate-l`
351×	`associate-r` `unswap-sqr`
340×	`associate-/l*`
196×	`distribute-lft-out--`
192×	`difference-of-squares`
170×	`add-exp-log`
144×	`prod-diff`
93×	`div-exp`
69×	`*-commutative`
62×	`prod-exp`
56×	`clear-num`
54×	`frac-2neg`
50×	`add-cbrt-cube`
42×	`associate-/l/`
41×	`1-exp` `div-inv`
29×	`associate-*r/`
22×	`flip3--` `associate-/r/` `flip--`
20×	`cbrt-undiv`
19×	`associate-*l/`
15×	`rec-exp`
13×	`cbrt-unprod`
12×	`fma-neg`
7×	`pow1`
6×	`un-div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`remove-double-div`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `pow-prod-down` `inv-pow`

Counts

4 → 1352

Calls

4 calls:

7.0ms	(/ 1 (/ (hypot y.re y.im) 1))
143.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1)))
17.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

series416.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (/ (hypot y.re y.im) 1))
196.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1)))
39.0ms	(- (* x.im y.re) (* x.re y.im))
126.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

simplify211.0ms

Algorithm

egg-herbie

Counts

1364 → 1364

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5001	17154

prune1.8s

Filtered

1364 candidates to 583 candidates (57.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1359	5	1364
Fresh	6	1	7
Picked	1	0	1
Done	1	0	1
Total	1367	6	1373

Merged error: 0.1b

Counts

1373 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
0.3b	(* (/ 1 (/ (hypot y.re y.im) 1)) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im))))
2.3b	(/ x.im (/ (hypot y.re y.im) y.re))
4.3b	(/ x.re (/ (hypot y.re y.im) y.im))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

31410×	`times-frac`
21104×	`add-sqr-sqrt`
21056×	`*-un-lft-identity`
21011×	`add-cube-cbrt`
16080×	`associate-/r*`
8112×	`prod-diff`
7581×	`frac-sub`
6897×	`frac-times`
4441×	`associate-/l*`
2845×	`associate-/r/`
2706×	`distribute-rgt-in` `distribute-lft-in`
2432×	`div-inv`
1480×	`frac-2neg` `clear-num`
363×	`associate-*r/`
52×	`fma-neg` `associate-l`
40×	`add-exp-log`
23×	`add-cbrt-cube`
21×	`flip3--` `flip--`
19×	`associate-*l/`
18×	`div-exp` `associate-r` `difference-of-squares`
12×	`distribute-lft-out--`
10×	`prod-exp`
9×	`cbrt-undiv`
8×	`unswap-sqr`
6×	`pow1` `1-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `rec-exp` `cbrt-unprod`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 16099

Calls

4 calls:

175.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
540.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im))))
6.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
6.0ms	(/ x.re (/ (hypot y.re y.im) y.im))

series658.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
315.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im))))
73.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
75.0ms	(/ x.re (/ (hypot y.re y.im) y.im))

simplify6.2s

Algorithm

egg-herbie

Counts

16111 → 16111

Iterations

Useful iterations: 0 (294.0ms)

Iter	Nodes	Cost
0	19802	642879

prune58.6s

Filtered

16111 candidates to 12204 candidates (24.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	16106	5	16111
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	16111	6	16117

Merged error: 0b

Counts

16117 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
0.0b	(/ (* 1 (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))) (/ (/ (hypot y.re y.im) 1) 1))
2.3b	(/ x.im (/ (hypot y.re y.im) y.re))
4.3b	(/ x.re (/ (hypot y.re y.im) y.im))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

12421×	`times-frac`
7584×	`add-sqr-sqrt`
6776×	`*-un-lft-identity`
5832×	`add-cube-cbrt`
2704×	`prod-diff`
1384×	`associate-/r*`
991×	`associate-/r/`
792×	`associate-r`
722×	`frac-sub`
714×	`div-inv`
599×	`associate-/l*`
405×	`difference-of-squares`
372×	`associate-/l/`
363×	`associate-*r/`
270×	`distribute-lft-out--`
188×	`frac-2neg` `clear-num`
132×	`associate-l`
88×	`unswap-sqr`
78×	`add-exp-log`
57×	`div-exp`
52×	`fma-neg`
44×	`*-commutative`
35×	`add-cbrt-cube`
22×	`1-exp`
18×	`cbrt-undiv`
14×	`prod-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 5011

Calls

4 calls:

179.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
521.0ms	(/ (* 1 (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))) (/ (/ (hypot y.re y.im) 1) 1))
7.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
7.0ms	(/ x.re (/ (hypot y.re y.im) y.im))

series638.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
262.0ms	(/ (* 1 (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))) (/ (/ (hypot y.re y.im) 1) 1))
77.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
79.0ms	(/ x.re (/ (hypot y.re y.im) y.im))

simplify1.6s

Algorithm

egg-herbie

Counts

5023 → 5023

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	6659	170308

prune19.0s

Filtered

5023 candidates to 4055 candidates (19.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	5022	1	5023
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	5024	5	5029

Merged error: 0b

Counts

5029 → 5

regimes121.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	23
1	35	23
2	43	23
3	43	23

end0.0ms

sample505.0ms

Algorithm

intervals

Results

294.0ms

8440×

body

valid