Details

Time bar (total: 4.0s)

sample20.0ms

Algorithm
intervals
Results
9.0ms270×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: 25.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(+ (* x.re y.re) (* x.im y.im))
25.0b
(/ (+ (* 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))
4.0ms
(+ (* 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)))

series139.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* y.re y.re) (* y.im y.im))
30.0ms
(+ (* x.re y.re) (* x.im y.im))
80.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify134.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune218.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.0b
(fma x.re y.re (* x.im 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)))
16.3b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite27.0ms

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))
1.0ms
(fma x.re y.re (* x.im y.im))
11.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series401.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ 1 (* (hypot y.re y.im) 1))
37.0ms
(fma x.re y.re (* x.im y.im))
188.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
117.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify49.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04861191
11654892
25002884

prune285.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(fma x.re y.re (* x.im y.im))
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
16.3b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite14.0ms

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)
1.0ms
(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)) (* (hypot y.re y.im) 1))
3.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series322.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(hypot y.re y.im)
37.0ms
(fma x.re y.re (* x.im y.im))
122.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
114.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify80.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0308794
11149701
23275701
35001693

prune320.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
0.2b
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
16.4b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
249×add-exp-log
159×times-frac
120×div-exp
112×prod-exp
105×add-sqr-sqrt
93×*-un-lft-identity
91×add-cube-cbrt
64×1-exp
47×add-cbrt-cube
44×associate-*r*
43×rec-exp
19×cbrt-undiv
16×associate-/r*
12×pow1 cbrt-unprod
11×div-inv
7×associate-*l*
6×associate-/l*
5×pow-flip pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×inv-pow
2×frac-2neg clear-num associate-/r/
1×frac-times associate-*r/ associate-*l/ un-div-inv *-commutative fma-udef
Counts
4 → 270
Calls
4 calls:
1.0ms
(fma x.re y.re (* x.im y.im))
22.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
6.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
6.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(fma x.re y.re (* x.im y.im))
192.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
169.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
92.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
010202692
139752350
250012153

prune512.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.8b

regimes240.0ms

Accuracy

36.5% (7.1b remaining)

Error of 13.0b against oracle of 5.9b and baseline of 17.1b

bsearch51.0ms

Steps
ItersRangePoint
4
5.897233584531583e+145
1.1753371349242699e+146
6.674460111187106e+145
7
-1.0216026790269869e+141
-5.828232727961281e+138
-4.632748065302152e+140

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03016
13316
23316

end0.0ms

sample517.0ms

Algorithm
intervals
Results
306.0ms8464×body80valid