Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 24.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(+ (* x.re y.re) (* x.im y.im))
23.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite66.0ms

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:

15.0ms	(+ (* y.re y.re) (* y.im y.im))
15.0ms	(+ (* x.re y.re) (* x.im y.im))
28.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
99.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify139.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	289	1060
1	1169	954
2	4795	929
3	5001	929

prune203.0ms

Filtered

160 candidates to 81 candidates (50.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	149	11	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	11	161

Merged error: 14.7b

Counts

161 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(/ 1 (/ (hypot y.re y.im) 1))
0.3b	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
14.4b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

571×	`add-sqr-sqrt`
552×	`associate-/r*`
463×	`times-frac`
431×	`*-un-lft-identity`
374×	`add-cube-cbrt`
361×	`frac-times`
170×	`add-exp-log`
138×	`associate-/l*`
133×	`associate-l`
124×	`associate-r`
102×	`unswap-sqr`
93×	`div-exp`
62×	`prod-exp`
50×	`add-cbrt-cube`
46×	`clear-num`
44×	`frac-2neg`
41×	`1-exp`
31×	`div-inv`
28×	`*-commutative`
22×	`associate-/r/`
20×	`cbrt-undiv`
19×	`associate-r/` `associate-l/`
15×	`rec-exp`
13×	`cbrt-unprod`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`un-div-inv` `remove-double-div`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 761

Calls

4 calls:

1.0ms	(hypot y.re y.im)
7.0ms	(/ 1 (/ (hypot y.re y.im) 1))
56.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
7.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series415.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
58.0ms	(/ 1 (/ (hypot y.re y.im) 1))
188.0ms	(* (/ 1 (/ (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
121.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify152.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	3095	8391
1	5001	7362

prune904.0ms

Filtered

773 candidates to 283 candidates (36.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	765	8	773
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	774	10	784

Merged error: 4.7b

Counts

784 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
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))
14.4b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*` `associate-/l/`
6×	`div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`hypot-udef`

Counts

4 → 129

Calls

4 calls:

1.0ms	(hypot y.re y.im)
1.0ms	(hypot y.re y.im)
7.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series338.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot y.re y.im)
49.0ms	(hypot y.re y.im)
122.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
117.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify88.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	342	1225
1	1055	1137
2	3997	1120
3	5001	1115

prune292.0ms

Filtered

141 candidates to 112 candidates (79.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	140	11	151

Merged error: 4.6b

Counts

151 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(/ 1 (hypot y.re y.im))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
14.4b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
81×	`frac-times`
77×	`*-un-lft-identity`
74×	`add-cube-cbrt`
67×	`associate-/l*`
66×	`associate-/r*`
43×	`times-frac`
32×	`add-exp-log`
23×	`clear-num`
22×	`frac-2neg`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
9×	`associate-r/` `associate-l/`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`un-div-inv`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 228

Calls

4 calls:

1.0ms	(hypot y.re y.im)
3.0ms	(/ 1 (hypot y.re y.im))
14.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series424.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot y.re y.im)
57.0ms	(/ 1 (hypot y.re y.im))
200.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
120.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify106.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	722	1934
1	3650	1720
2	5001	1634

prune308.0ms

Filtered

240 candidates to 125 candidates (52.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	239	1	240
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	241	10	251

Merged error: 4.6b

Counts

251 → 10

regimes163.0ms

Accuracy

35.2% (6.8b remaining)

Error of 12.7b against oracle of 5.9b and baseline of 16.5b

bsearch73.0ms

Steps

Iters	Range		Point
8	2.108882011704695e+145	3.055944189201881e+149	3.3012917942497675e+146
7	-1.9994462549967526e+205	-3.459071203583835e+203	-1.674096505949315e+204

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	14
1	29	14
2	32	14
3	32	14

end0.0ms

sample505.0ms

Algorithm

intervals

Results

297.0ms

8505×

body

valid