Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

274×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	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: 25.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
25.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

216×	`*-un-lft-identity`
85×	`distribute-lft-out`
82×	`associate-l`
56×	`times-frac`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`fma-def`
21×	`swap-sqr`
8×	`associate-/r*`
7×	`associate-/l*` `add-log-exp`
6×	`associate-r`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`+-commutative` `sum-log` `associate-/r/` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 151

Calls

3 calls:

16.0ms	(+ (* y.re y.re) (* y.im y.im))
13.0ms	(+ (* x.re y.re) (* x.im y.im))
34.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series140.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
80.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	301	1060
1	1238	954
2	5001	927

prune274.0ms

Filtered

160 candidates to 81 candidates (50.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	152	9	161

Merged error: 15.8b

Counts

161 → 9

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)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.3b	(fma x.re y.re (* x.im y.im))
15.5b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

536×	`associate-/r*`
527×	`add-sqr-sqrt`
388×	`times-frac`
386×	`*-un-lft-identity`
361×	`frac-times`
330×	`add-cube-cbrt`
155×	`add-exp-log`
133×	`associate-l`
131×	`associate-/l*`
124×	`associate-r`
102×	`unswap-sqr`
81×	`div-exp`
62×	`prod-exp`
45×	`add-cbrt-cube`
43×	`clear-num`
42×	`frac-2neg`
35×	`1-exp`
28×	`*-commutative`
26×	`div-inv`
19×	`associate-r/` `associate-l/`
17×	`cbrt-undiv`
13×	`associate-/r/` `cbrt-unprod`
12×	`rec-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`un-div-inv`
1×	`hypot-udef` `pow-prod-down` `fma-udef`

Counts

4 → 680

Calls

4 calls:

1.0ms	(hypot y.re y.im)
70.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
1.0ms	(fma x.re y.re (* x.im y.im))
7.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series407.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(hypot y.re y.im)
188.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
41.0ms	(fma x.re y.re (* x.im y.im))
124.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify129.0ms

Algorithm

egg-herbie

Counts

692 → 692

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	3028	7879
1	5001	6928

prune953.0ms

Filtered

692 candidates to 251 candidates (36.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	681	11	692
Fresh	7	0	7
Picked	1	0	1
Done	0	1	1
Total	689	12	701

Merged error: 5.8b

Counts

701 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ (/ (hypot y.re y.im) 1) (sqrt 1)))
0.3b	(fma x.re y.re (* x.im y.im))
15.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

3679×	`times-frac`
1572×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
549×	`sqrt-prod`
184×	`div-inv`
97×	`associate-/r*`
35×	`associate-/l*`
34×	`add-exp-log`
31×	`associate-/r/`
27×	`add-cbrt-cube`
23×	`div-exp`
18×	`associate-/l/`
16×	`cbrt-undiv`
5×	`frac-2neg` `clear-num`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`1-exp`
1×	`hypot-udef` `fma-udef`

Counts

4 → 1276

Calls

4 calls:

1.0ms	(hypot y.re y.im)
45.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ (/ (hypot y.re y.im) 1) (sqrt 1)))
1.0ms	(fma x.re y.re (* x.im y.im))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series323.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot y.re y.im)
117.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ (/ (hypot y.re y.im) 1) (sqrt 1)))
37.0ms	(fma x.re y.re (* x.im y.im))
121.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify249.0ms

Algorithm

egg-herbie

Counts

1288 → 1288

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5001	26980

prune3.8s

Filtered

1288 candidates to 801 candidates (62.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	1281	7	1288
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	1287	13	1300

Merged error: 5.7b

Counts

1300 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.2b	(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (sqrt 1))))
0.3b	(fma x.re y.re (* x.im y.im))
15.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

355×	`times-frac`
343×	`add-sqr-sqrt`
316×	`associate-/r*`
295×	`*-un-lft-identity`
282×	`add-cube-cbrt`
252×	`frac-times`
128×	`sqrt-prod`
124×	`associate-/l*`
82×	`associate-r`
51×	`add-exp-log`
42×	`clear-num`
41×	`frac-2neg`
28×	`associate-*r/`
27×	`add-cbrt-cube`
22×	`div-exp`
18×	`unswap-sqr`
16×	`div-inv`
14×	`prod-exp`
13×	`associate-l`
12×	`associate-/r/`
10×	`cbrt-undiv`
9×	`associate-*l/`
6×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv`
1×	`hypot-udef` `pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 485

Calls

4 calls:

1.0ms	(hypot y.re y.im)
47.0ms	(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (sqrt 1))))
1.0ms	(fma x.re y.re (* x.im y.im))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series340.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot y.re y.im)
120.0ms	(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (sqrt 1))))
44.0ms	(fma x.re y.re (* x.im y.im))
124.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify103.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2070	6440
1	5001	5260

prune906.0ms

Filtered

497 candidates to 218 candidates (43.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	494	3	497
Fresh	4	7	11
Picked	0	1	1
Done	0	1	1
Total	498	12	510

Merged error: 5.7b

Counts

510 → 12

regimes304.0ms

Accuracy

37.3% (7.1b remaining)

Error of 12.8b against oracle of 5.7b and baseline of 17.0b

bsearch74.0ms

Steps

Iters	Range		Point
7	3.110085981024015e+154	8.769655940674386e+155	3.997498131334168e+155
7	-1.8864815038392082e+94	-2.1159267475207395e+92	-7.863570656598141e+93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	20
1	33	20
2	34	20
3	34	20

end0.0ms

sample531.0ms

Algorithm

intervals

Results

313.0ms

8506×

body

valid