Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify13.0ms

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 (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: 24.9b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
24.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

340×	`*-un-lft-identity`
276×	`add-sqr-sqrt`
170×	`associate-l`
144×	`prod-diff`
104×	`add-cube-cbrt`
88×	`times-frac`
78×	`associate-r`
66×	`unswap-sqr`
65×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares`
29×	`swap-sqr`
26×	`*-commutative`
15×	`fma-def`
12×	`fma-neg`
11×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 337

Calls

3 calls:

19.0ms	(+ (* y.re y.re) (* y.im y.im))
16.0ms	(- (* x.im y.re) (* x.re y.im))
39.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(- (* 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)))

simplify102.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	810	4080
1	2677	3154
2	5001	2993

prune386.0ms

Filtered

346 candidates to 112 candidates (32.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	337	9	346
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	337	10	347

Merged error: 11.0b

Counts

347 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.2b	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1)))
0.7b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

1404×	`add-sqr-sqrt`
997×	`*-un-lft-identity`
686×	`times-frac`
666×	`associate-/r*`
551×	`frac-times`
533×	`add-cube-cbrt`
452×	`associate-l`
351×	`associate-r` `unswap-sqr`
333×	`associate-/l*`
196×	`distribute-lft-out--`
192×	`difference-of-squares`
155×	`add-exp-log`
144×	`prod-diff`
81×	`div-exp`
69×	`*-commutative`
62×	`prod-exp`
53×	`clear-num`
52×	`frac-2neg`
45×	`add-cbrt-cube`
42×	`associate-/l/`
36×	`div-inv`
35×	`1-exp`
29×	`associate-*r/`
22×	`flip3--` `flip--`
19×	`associate-*l/`
17×	`cbrt-undiv`
13×	`associate-/r/` `cbrt-unprod`
12×	`rec-exp` `fma-neg`
6×	`pow1` `un-div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
1×	`sub-neg` `hypot-udef` `diff-log` `div-sub` `pow-prod-down`

Counts

4 → 1271

Calls

4 calls:

1.0ms	(hypot y.re y.im)
140.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1)))
16.0ms	(- (* x.im y.re) (* x.re y.im))
32.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

series388.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
181.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1)))
35.0ms	(- (* x.im y.re) (* x.re y.im))
124.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

simplify217.0ms

Algorithm

egg-herbie

Counts

1283 → 1283

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5001	16624

prune2.2s

Filtered

1283 candidates to 538 candidates (41.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1279	4	1283
Fresh	7	1	8
Picked	1	0	1
Done	0	1	1
Total	1287	6	1293

Merged error: 0.1b

Counts

1293 → 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)))
0.2b	(* (/ 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))))
2.4b	(/ x.im (/ (hypot y.re y.im) y.re))
3.6b	(/ 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:

177.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
532.0ms	(* (/ 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))

series628.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
302.0ms	(* (/ 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))))
68.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
70.0ms	(/ x.re (/ (hypot y.re y.im) y.im))

simplify6.2s

Algorithm

egg-herbie

Counts

16111 → 16111

Iterations

Useful iterations: 0 (238.0ms)

Iter	Nodes	Cost
0	19802	642879

prune1.1m

Filtered

16111 candidates to 12204 candidates (75.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	16107	4	16111
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	16111	6	16117

Merged error: 0b

Counts

16117 → 6

localize16.0ms

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)))
0.1b	(/ (* (/ 1 (/ 1 (sqrt 1))) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))) (/ (hypot y.re y.im) (sqrt 1)))
2.4b	(/ x.im (/ (hypot y.re y.im) y.re))
3.6b	(/ x.re (/ (hypot y.re y.im) y.im))

rewrite4.9s

Algorithm

rewrite-expression-head

Rules

32884×	`times-frac`
23341×	`associate-/r*`
23119×	`add-sqr-sqrt`
22229×	`*-un-lft-identity`
21358×	`add-cube-cbrt`
10830×	`frac-sub`
10555×	`associate-/l/`
10164×	`frac-times`
5242×	`sqrt-prod`
5031×	`associate-/l*`
2704×	`prod-diff`
2196×	`div-inv`
1886×	`associate-l`
1638×	`frac-2neg` `clear-num`
1251×	`associate-/r/`
414×	`associate-r`
363×	`associate-*r/`
345×	`unswap-sqr`
216×	`difference-of-squares`
144×	`distribute-lft-out--`
124×	`add-exp-log`
76×	`div-exp`
52×	`fma-neg`
46×	`add-cbrt-cube`
30×	`flip3--` `flip--`
28×	`associate-*l/`
26×	`prod-exp`
24×	`cbrt-undiv`
23×	`*-commutative`
14×	`rec-exp` `1-exp`
6×	`cbrt-unprod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`sub-neg` `diff-log`

Counts

4 → 16703

Calls

4 calls:

201.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
1.4s	(/ (* (/ 1 (/ 1 (sqrt 1))) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))) (/ (hypot y.re y.im) (sqrt 1)))
7.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
7.0ms	(/ x.re (/ (hypot y.re y.im) y.im))

series581.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))
252.0ms	(/ (* (/ 1 (/ 1 (sqrt 1))) (- (/ x.im (/ (hypot y.re y.im) y.re)) (/ x.re (/ (hypot y.re y.im) y.im)))) (/ (hypot y.re y.im) (sqrt 1)))
74.0ms	(/ x.im (/ (hypot y.re y.im) y.re))
69.0ms	(/ x.re (/ (hypot y.re y.im) y.im))

simplify3.7s

Algorithm

egg-herbie

Counts

16715 → 16715

Iterations

Useful iterations: 0 (227.0ms)

Iter	Nodes	Cost
0	17166	375358

prune1.2m

Filtered

16715 candidates to 12404 candidates (74.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	16714	1	16715
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	16716	5	16721

Merged error: 0b

Counts

16721 → 5

regimes128.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	15
1	20	15

end0.0ms

sample531.0ms

Algorithm

intervals

Results

316.0ms

8500×

body

valid