Details

Time bar (total: 3.6s)

sample19.0ms

Algorithm
intervals
Results
9.0ms266×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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))
0.9b
(+ (* 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)))

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:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
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)))

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)))

simplify131.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune182.0ms

Filtered
70 candidates to 57 candidates (81.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.6b

localize12.0ms

Local error

Found 3 expressions with local error:

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))
16.2b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
154×add-exp-log
86×prod-exp
57×div-exp
44×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×rec-exp
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity times-frac
7×associate-*r* associate-*l*
5×pow1
3×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative fma-udef unswap-sqr
Counts
3 → 112
Calls
3 calls:
20.0ms
(* (/ 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))

series337.0ms

Counts
3 → 9
Calls
3 calls:
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))
115.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify46.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04721079
11607796
25001794

prune212.0ms

Filtered
121 candidates to 59 candidates (48.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

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))
0.3b
(fma x.re y.re (* x.im y.im))
16.2b
(/ (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))

series265.0ms

Counts
3 → 9
Calls
3 calls:
116.0ms
(/ (/ (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))
109.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify78.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune271.0ms

Filtered
98 candidates to 75 candidates (76.5%)
Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.9b

localize11.0ms

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

rewrite38.0ms

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:
18.0ms
(/ (/ 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)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
111.0ms
(/ 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))
91.0ms
(/ (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 (58.0ms)

IterNodesCost
07952590
136872260
250012098

prune506.0ms

Filtered
258 candidates to 141 candidates (54.7%)
Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.9b

regimes229.0ms

Accuracy

30.4% (7.7b remaining)

Error of 13.6b against oracle of 6.0b and baseline of 17.0b

bsearch79.0ms

Steps
ItersRangePoint
8
9.608178827202541e+116
5.152353921655058e+119
5.095160020306219e+119
9
-1.0719231849388273e+91
-8.904352624570248e+85
-7.21703912221376e+90

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample507.0ms

Algorithm
intervals
Results
295.0ms8455×body80valid