Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

273×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune3.0ms

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: 28.5b

Counts

2 → 1

localize11.0ms

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))
28.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 61

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
82.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify144.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462

prune194.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	9	71

Merged error: 14.8b

Counts

71 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
14.6b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

1.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ 1 (* (hypot y.re y.im) 1))
12.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series374.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma x.re y.re (* x.im y.im))
53.0ms	(/ 1 (* (hypot y.re y.im) 1))
176.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
109.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify46.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884

prune239.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	148	9	157
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	156	10	166

Merged error: 5.3b

Counts

166 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
14.6b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`prod-exp` `associate-/r*` `div-inv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

1.0ms	(fma x.re y.re (* x.im y.im))
9.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
3.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series258.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(fma x.re y.re (* x.im y.im))
110.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
109.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify76.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670

prune221.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	98	10	108

Merged error: 5.3b

Counts

108 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
0.1b	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
0.2b	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
14.6b	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

260×	`times-frac`
124×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
81×	`add-exp-log`
50×	`div-exp` `associate-/l*`
32×	`add-cbrt-cube`
17×	`associate-/r*`
16×	`cbrt-undiv`
15×	`1-exp` `div-inv`
14×	`prod-exp`
8×	`rec-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/r/` `cbrt-unprod`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 246

Calls

4 calls:

1.0ms	(fma x.re y.re (* x.im y.im))
13.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
6.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
3.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma x.re y.re (* x.im y.im))
180.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
110.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
90.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	795	2590
1	3687	2260
2	5001	2098

prune406.0ms

Filtered

258 candidates to 141 candidates (54.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	258	10	268

Merged error: 5.3b

Counts

268 → 10

regimes166.0ms

Accuracy

27.3% (8.1b remaining)

Error of 13.9b against oracle of 5.8b and baseline of 17.0b

bsearch57.0ms

Steps

Iters	Range		Point
6	4.658876118741473e+38	5.280048301872741e+39	5.204112956458818e+39
6	-7.241639392966628e+175	-7.6320301140404966e+174	-8.741080840408781e+174

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	30	14
2	30	14

end0.0ms

sample574.0ms

Algorithm

intervals

Results

363.0ms

8502×

body

valid