Details

Time bar (total: 3.6s)

sample20.0ms

Algorithm
intervals
Results
9.0ms273×body80valid

simplify6.0ms

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: 27.4b

localize14.0ms

Local error

Found 2 expressions with local error:

1.0b
(+ (* x.re y.re) (* x.im y.im))
26.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

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:
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)))

series109.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* x.re y.re) (* x.im y.im))
79.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify85.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune153.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.7b

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)))
0.8b
(fma x.re y.re (* x.im y.im))
16.4b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite37.0ms

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))
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))

series382.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 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))
111.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify48.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04861191
11654892
25002884

prune272.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (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))
16.4b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite11.0ms

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:
111.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
36.0ms
(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))

simplify74.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune253.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 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))
16.5b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite36.0ms

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:
17.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
5.0ms
(/ 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))
2.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
110.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
36.0ms
(fma x.re y.re (* x.im y.im))
88.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify82.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
07952590
136872260
250012098

prune476.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 4.0b

regimes208.0ms

Accuracy

30.4% (7.6b remaining)

Error of 13.3b against oracle of 5.6b and baseline of 16.6b

bsearch72.0ms

Steps
ItersRangePoint
7
3.122797533042294e+104
1.1473462442572691e+106
8.751544458807778e+105
9
-1.410000206868618e+208
-3.3815517682069295e+202
-9.727239627244697e+203

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample514.0ms

Algorithm
intervals
Results
299.0ms8480×body80valid