Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

273×

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: 28.5b

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

rewrite17.0ms

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))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
31.0ms	(+ (* x.re y.re) (* x.im y.im))
83.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify138.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (32.0ms)

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

prune192.0ms

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

localize10.0ms

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))

rewrite30.0ms

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)))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series417.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma x.re y.re (* x.im y.im))
56.0ms	(/ 1 (* (hypot y.re y.im) 1))
210.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
114.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify45.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (33.0ms)

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

prune245.0ms

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

localize9.0ms

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))
10.0ms	(/ (/ (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))

series270.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma x.re y.re (* x.im y.im))
116.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
113.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify74.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (65.0ms)

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

prune244.0ms

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)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma x.re y.re (* x.im y.im))
188.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
114.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
93.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 2 (58.0ms)

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

prune420.0ms

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

regimes169.0ms

Accuracy

27.3% (8.1b remaining)

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

bsearch58.0ms

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

sample494.0ms

Algorithm

intervals

Results

289.0ms

8502×

body

valid

Details

sample19.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite17.0ms

series144.0ms

simplify138.0ms

prune192.0ms

localize10.0ms

rewrite30.0ms

series417.0ms

simplify45.0ms

prune245.0ms

localize9.0ms

rewrite16.0ms

series270.0ms

simplify74.0ms

prune244.0ms

localize14.0ms

rewrite34.0ms

series438.0ms

simplify84.0ms

prune420.0ms

regimes169.0ms

bsearch58.0ms

simplify2.0ms

end0.0ms

sample494.0ms

Profiling