Details

Time bar (total: 3.6s)

sample21.0ms

Algorithm
intervals
Results
8.0ms279×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b
(+ (* x.re y.re) (* x.im y.im))
29.4b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 47
Calls
2 calls:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
34.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series98.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(+ (* x.re y.re) (* x.im y.im))
71.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify84.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune160.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.0b

localize10.0ms

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)))
0.8b
(fma x.re y.re (* x.im y.im))
18.5b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite78.0ms

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:
12.0ms
(/ 1 (* (hypot y.re y.im) 1))
51.0ms
(* (/ 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))

series336.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1 (* (hypot y.re y.im) 1))
156.0ms
(* (/ 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))
100.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify43.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
04861191
11654892
25002884

prune266.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.7b

localize9.0ms

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))
0.8b
(fma x.re y.re (* x.im y.im))
18.5b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite25.0ms

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:
14.0ms
(/ (/ (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))
7.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series241.0ms

Counts
3 → 9
Calls
3 calls:
106.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
33.0ms
(fma x.re y.re (* x.im y.im))
102.0ms
(/ (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)

IterNodesCost
0297767
11133677
23251677
35001670

prune261.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
0.2b
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
0.8b
(fma x.re y.re (* x.im y.im))
18.5b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
124×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
81×add-exp-log
50×div-exp associate-/l*
32×add-cbrt-cube
17×associate-/r*
16×cbrt-undiv
15×1-exp div-inv
14×prod-exp
8×rec-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/r/ cbrt-unprod
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 246
Calls
4 calls:
25.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
10.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
0.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
102.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
37.0ms
(fma x.re y.re (* x.im y.im))
87.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify84.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
07952590
136872260
250012098

prune502.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.6b

regimes240.0ms

Accuracy

26.8% (7.9b remaining)

Error of 13.9b against oracle of 6.0b and baseline of 16.8b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02918
13118
23118

end0.0ms

sample560.0ms

Algorithm
intervals
Results
272.0ms8493×body80valid