Details

sample18.0ms

Algorithm

intervals

Results

9.0ms

265×

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: 27.4b

Counts

2 → 1

localize12.0ms

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))
26.9b	(/ (+ (* 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)))

series132.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
77.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify136.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

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

prune193.0ms

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: 17.7b

Counts

71 → 9

localize11.0ms

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)) (/ (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))
17.2b	(/ (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:

5.0ms	(/ 1 (* (hypot y.re y.im) 1))
11.0ms	(* (/ 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))

series362.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1 (* (hypot y.re y.im) 1))
172.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
35.0ms	(fma x.re y.re (* x.im y.im))
107.0ms	(/ (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

prune266.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

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

Merged error: 7.5b

Counts

166 → 9

localize10.0ms

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))
0.3b	(fma x.re y.re (* x.im y.im))
17.2b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

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) 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))

series304.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot y.re y.im)
115.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
36.0ms	(fma x.re y.re (* x.im y.im))
108.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify80.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	308	794
1	1149	701
2	3275	701
3	5001	693

prune293.0ms

Filtered

111 candidates to 89 candidates (80.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	110	10	120

Merged error: 7.5b

Counts

120 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.1b	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.3b	(fma x.re y.re (* x.im y.im))
17.3b	(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`add-cbrt-cube`
27×	`add-sqr-sqrt`
26×	`prod-exp`
25×	`div-exp`
21×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
13×	`associate-r`
10×	`cbrt-undiv` `1-exp`
9×	`cbrt-unprod`
7×	`pow1`
5×	`rec-exp`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `associate-/l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 119

Calls

4 calls:

3.0ms	(/ 1 (hypot y.re y.im))
8.0ms	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re 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)) (/ 1 (hypot y.re y.im)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (hypot y.re y.im))
108.0ms	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
35.0ms	(fma x.re y.re (* x.im y.im))
106.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	394	872
1	1636	690
2	5001	663

prune228.0ms

Filtered

131 candidates to 72 candidates (55.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	131	10	141

Merged error: 7.5b

Counts

141 → 10

regimes161.0ms

Accuracy

36.4% (7.0b remaining)

Error of 12.9b against oracle of 6.0b and baseline of 16.9b

bsearch62.0ms

Steps

Iters	Range		Point
7	1.1965702813225714e+120	1.5789597603016236e+122	8.272314228208718e+121
8	-4.444336960874317e+114	-1.7976808176493555e+110	-4.3740717809307965e+114

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

sample489.0ms

Algorithm

intervals

Results

284.0ms

8478×

body

valid