Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

280×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize9.0ms

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))
26.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

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:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(+ (* x.re y.re) (* x.im y.im))
33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
32.0ms	(+ (* 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)))

simplify129.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (28.0ms)

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

prune193.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.7b

localize13.0ms

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))
16.3b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite73.0ms

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:

11.0ms	(/ 1 (* (hypot y.re y.im) 1))
48.0ms	(* (/ 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))
8.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series393.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (* (hypot y.re y.im) 1))
182.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
39.0ms	(fma x.re y.re (* x.im y.im))
117.0ms	(/ (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

prune266.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize10.0ms

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))
0.3b	(fma x.re y.re (* x.im y.im))
16.3b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite24.0ms

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:

16.0ms	(/ (/ (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))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series282.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
39.0ms	(fma x.re y.re (* x.im y.im))
119.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify80.0ms

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

prune257.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(* (* 1 (/ 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))
16.3b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

366×	`add-exp-log`
262×	`prod-exp`
120×	`div-exp`
116×	`1-exp`
68×	`add-cbrt-cube`
30×	`cbrt-unprod`
27×	`rec-exp`
18×	`cbrt-undiv`
12×	`pow1`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`associate-r`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `div-inv`
2×	`frac-times` `pow-flip` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `un-div-inv`
1×	`associate-l` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 188

Calls

4 calls:

11.0ms	(/ 1 (* (hypot y.re y.im) 1))
91.0ms	(* (* 1 (/ 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))
10.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series399.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (* (hypot y.re y.im) 1))
183.0ms	(* (* 1 (/ 1 (* (hypot y.re y.im) 1))) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
40.0ms	(fma x.re y.re (* x.im y.im))
120.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify48.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	791	1674
1	1879	1235
2	5002	1224

prune234.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.2b

regimes185.0ms

Accuracy

33.6% (7.5b remaining)

Error of 13.4b against oracle of 5.9b and baseline of 17.1b

bsearch63.0ms

Steps

Iters	Range		Point
6	1.4211719871959458e+151	1.5804785112129858e+152	4.355931456769411e+151
10	-9.74529748598903e+204	-2.833408922216708e+192	-3.9421165304259007e+195

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample567.0ms

Algorithm

intervals

Results

269.0ms

8450×

body

valid