Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

264×

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: 27.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.6b	(+ (* x.re y.re) (* x.im y.im))
26.5b	(/ (+ (* 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:

2.0ms	(+ (* y.re y.re) (* y.im y.im))
2.0ms	(+ (* x.re y.re) (* x.im y.im))
10.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series134.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* 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)))

simplify133.0ms

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

prune214.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
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))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-exp-log`
86×	`prod-exp`
57×	`div-exp`
45×	`add-cbrt-cube`
35×	`1-exp`
16×	`cbrt-unprod`
14×	`cbrt-undiv`
12×	`add-sqr-sqrt` `rec-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`associate-r` `associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
1×	`frac-times` `hypot-udef` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

0.0ms	(hypot y.re y.im)
21.0ms	(* (/ 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))

series377.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
178.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
37.0ms	(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) 1))

simplify46.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	486	1106
1	1625	820
2	5001	818

prune268.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

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))
0.5b	(fma x.re y.re (* x.im y.im))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite12.0ms

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:

0.0ms	(hypot y.re y.im)
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))

series307.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot y.re y.im)
113.0ms	(/ (/ (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))
110.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify77.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (68.0ms)

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

prune312.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.2b	(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (hypot y.re y.im)))
0.5b	(fma x.re y.re (* x.im y.im))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-exp-log` `*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`pow1` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`rec-exp` `1-exp`
1×	`frac-times` `hypot-udef` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `fma-udef`

Counts

4 → 108

Calls

4 calls:

0.0ms	(hypot y.re y.im)
16.0ms	(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (hypot y.re y.im)))
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))

series309.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot y.re y.im)
117.0ms	(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (hypot y.re y.im)))
37.0ms	(fma x.re y.re (* x.im y.im))
112.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify46.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	377	886
1	1609	773
2	5002	761

prune307.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.8b

regimes195.0ms

Accuracy

38% (7.1b remaining)

Error of 13.0b against oracle of 5.9b and baseline of 17.3b

bsearch94.0ms

Steps

Iters	Range		Point
11	5.286434132095145e+107	2.6900018818139096e+129	1.8955542797321017e+121
10	-3.4896836630642546e+148	-1.4395777107888637e+138	-6.751507617690198e+142

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

sample523.0ms

Algorithm

intervals

Results

302.0ms

8511×

body

valid