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

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(+ (* x.re y.re) (* x.im y.im))
27.7b	(/ (+ (* 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:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
2.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series133.0ms

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))
78.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify134.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

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

prune211.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.5b

localize12.0ms

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)))
0.5b	(fma x.re y.re (* x.im y.im))
13.1b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite38.0ms

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:

4.0ms	(/ 1 (* (hypot y.re y.im) 1))
24.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.0ms	(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) 1))

series373.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1 (* (hypot y.re y.im) 1))
177.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
36.0ms	(fma x.re y.re (* x.im y.im))
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 (34.0ms)

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

prune276.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.5b	(fma x.re y.re (* x.im y.im))
13.1b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite12.0ms

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:

6.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms	(fma x.re y.re (* x.im y.im))
2.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series259.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
38.0ms	(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))

simplify77.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (68.0ms)

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

prune272.0ms

Filtered

98 candidates to 76 candidates (77.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.5b	(fma x.re y.re (* x.im y.im))
13.1b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite12.0ms

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:

6.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms	(fma x.re y.re (* x.im y.im))
2.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series266.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
40.0ms	(fma x.re y.re (* x.im y.im))
114.0ms	(/ (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 (66.0ms)

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

prune272.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.3b

regimes220.0ms

Accuracy

15.4% (9.2b remaining)

Error of 14.9b against oracle of 5.7b and baseline of 16.5b

bsearch39.0ms

Steps

Iters	Range		Point
8	1.695796626129481e+71	2.2080787432878896e+74	2.1850720944349345e+74

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	22	11
2	22	11

end0.0ms

sample498.0ms

Algorithm

intervals

Results

293.0ms

8440×

body

valid