Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

267×

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: 25.8b

localize13.0ms

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))
25.4b	(/ (+ (* 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))
3.0ms	(+ (* 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)))

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)))

simplify130.0ms

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

prune199.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(* (/ 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))
13.3b	(/ (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))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series380.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1 (* (hypot y.re y.im) 1))
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))
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 (33.0ms)

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

prune284.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

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))
13.3b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite17.0ms

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)
10.0ms	(/ (/ (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))

series301.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot y.re y.im)
111.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
35.0ms	(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))

simplify74.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (65.0ms)

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

prune314.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.6b	(+ (* x.re y.re) (* x.im y.im))
13.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (hypot y.re y.im))

rewrite23.0ms

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`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `prod-exp` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `flip3-+` `1-exp` `clear-num` `cbrt-unprod` `flip-+`
1×	`+-commutative` `hypot-udef` `fma-def` `sum-log`

Counts

4 → 105

Calls

4 calls:

1.0ms	(hypot y.re y.im)
10.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
6.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (hypot y.re y.im))

series295.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot y.re y.im)
108.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
34.0ms	(+ (* x.re y.re) (* x.im y.im))
109.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (hypot y.re y.im))

simplify125.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	402	941
1	1518	828
2	4924	825
3	5001	825

prune285.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

regimes172.0ms

Accuracy

33.9% (7.3b remaining)

Error of 13.2b against oracle of 5.9b and baseline of 16.9b

bsearch55.0ms

Steps

Iters	Range		Point
8	8.459637994792616e+144	2.5242783012259312e+148	1.4191655951273249e+147
4	-2.274413166241503e+185	-1.4888806322782983e+185	-2.1516737078097526e+185

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	33	15
2	33	15

end0.0ms

sample555.0ms

Algorithm

intervals

Results

328.0ms

8449×

body

valid