Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

272×

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 (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: 26.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.1b	(- (* x.im y.re) (* x.re y.im))
26.0b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite96.0ms

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:

16.0ms	(+ (* y.re y.re) (* y.im y.im))
20.0ms	(- (* x.im y.re) (* x.re y.im))
40.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series168.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
43.0ms	(- (* x.im y.re) (* x.re y.im))
95.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify104.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	798	4080
1	2578	3154
2	5001	2994

prune288.0ms

Filtered

346 candidates to 112 candidates (32.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	338	8	346
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	339	8	347

Merged error: 10.3b

Counts

347 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (hypot y.re y.im) 1))
0.2b	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1)))
1.1b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

rewrite308.0ms

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:

10.0ms	(/ 1 (/ (hypot y.re y.im) 1))
145.0ms	(* (/ 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))
33.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

series442.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1 (/ (hypot y.re y.im) 1))
211.0ms	(* (/ 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))
133.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (hypot y.re y.im) 1))

simplify404.0ms

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 (42.7%)

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	0	0	0
Total	1366	6	1372

Merged error: 0.1b

Counts

1372 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (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))))
2.1b	(/ x.re (/ (hypot y.re y.im) y.im))
3.4b	(/ x.im (/ (hypot y.re y.im) y.re))

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

24113×	`times-frac`
16885×	`add-sqr-sqrt`
16853×	`*-un-lft-identity`
16828×	`add-cube-cbrt`
15274×	`associate-/r*`
7220×	`frac-sub`
6897×	`frac-times`
5408×	`prod-diff`
4015×	`associate-/l*`
2706×	`distribute-rgt-in` `distribute-lft-in`
1973×	`div-inv`
1900×	`associate-/r/`
1338×	`frac-2neg` `clear-num`
363×	`associate-*r/`
52×	`associate-l`
42×	`add-exp-log`
25×	`add-cbrt-cube`
20×	`flip3--` `flip--`
19×	`div-exp` `associate-*l/`
18×	`associate-r`
10×	`cbrt-undiv` `prod-exp`
9×	`difference-of-squares`
8×	`unswap-sqr`
6×	`pow1` `1-exp` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `cbrt-unprod`
2×	`sub-neg`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 12982

Calls

4 calls:

13.0ms	(/ (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.re (/ (hypot y.re y.im) y.im))
7.0ms	(/ x.im (/ (hypot y.re y.im) y.re))

series545.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (hypot y.re y.im) y.im)
319.0ms	(* (/ 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.re (/ (hypot y.re y.im) y.im))
77.0ms	(/ x.im (/ (hypot y.re y.im) y.re))

simplify4.6s

Algorithm

egg-herbie

Counts

12994 → 12994

Iterations

Useful iterations: 0 (241.0ms)

Iter	Nodes	Cost
0	19792	518829

prune56.6s

Filtered

12994 candidates to 11703 candidates (90.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	12989	5	12994
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	12993	7	13000

Merged error: 0b

Counts

13000 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (hypot y.re y.im) y.im)
0.1b	(/ (* (- 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)))
2.1b	(/ x.re (/ (hypot y.re y.im) y.im))
3.4b	(/ x.im (/ (hypot y.re y.im) y.re))

rewrite711.0ms

Algorithm

rewrite-expression-head

Rules

3205×	`times-frac`
2326×	`add-sqr-sqrt`
1768×	`*-un-lft-identity`
1148×	`add-cube-cbrt`
562×	`associate-/r*`
558×	`associate-r`
548×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
363×	`associate-*r/` `associate-/l/`
361×	`frac-sub`
310×	`associate-l`
279×	`difference-of-squares`
186×	`distribute-lft-out--`
182×	`div-inv`
166×	`associate-/l*`
66×	`neg-mul-1`
45×	`frac-2neg` `clear-num`
31×	`*-commutative` `unswap-sqr`
27×	`associate-/r/`
21×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp` `distribute-neg-frac`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-lft-neg-out` `flip3--` `distribute-frac-neg` `prod-exp` `flip--` `cbrt-unprod`

Counts

4 → 1662

Calls

4 calls:

3.0ms	(/ (hypot y.re y.im) y.im)
511.0ms	(/ (* (- 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)))
7.0ms	(/ x.re (/ (hypot y.re y.im) y.im))
7.0ms	(/ x.im (/ (hypot y.re y.im) y.re))

series498.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (hypot y.re y.im) y.im)
258.0ms	(/ (* (- 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)))
73.0ms	(/ x.re (/ (hypot y.re y.im) y.im))
84.0ms	(/ x.im (/ (hypot y.re y.im) y.re))

simplify328.0ms

Algorithm

egg-herbie

Counts

1674 → 1674

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5001	32051

prune4.4s

Filtered

1674 candidates to 1193 candidates (71.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1673	1	1674
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	1674	7	1681

Merged error: 0b

Counts

1681 → 7

regimes147.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	13
1	32	11
2	40	11
3	40	11

end0.0ms

sample565.0ms

Algorithm

intervals

Results

331.0ms

8490×

body

valid