Details

Time bar (total: 4.1s)

sample24.0ms

Algorithm
intervals
Results
11.0ms266×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: 23.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(+ (* x.re y.re) (* x.im y.im))
22.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

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:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
10.0ms
(+ (* x.re y.re) (* x.im y.im))
32.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series127.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(+ (* y.re y.re) (* y.im y.im))
31.0ms
(+ (* x.re y.re) (* x.im y.im))
72.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify133.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune191.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

localize11.0ms

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))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
12.3b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
155×add-exp-log
86×prod-exp
57×div-exp
45×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×add-sqr-sqrt rec-exp
10×add-cube-cbrt *-un-lft-identity
9×times-frac
7×associate-*r* associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv associate-/l*
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative fma-udef unswap-sqr
Counts
4 → 122
Calls
4 calls:
0.0ms
(hypot y.re y.im)
0.0ms
(fma x.re y.re (* x.im y.im))
50.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
8.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series358.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(hypot y.re y.im)
35.0ms
(fma x.re y.re (* x.im y.im))
169.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
108.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify45.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04861114
11626820
25001818

prune268.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

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))
12.3b
(/ (fma 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
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:
0.0ms
(hypot y.re y.im)
0.0ms
(fma x.re y.re (* x.im y.im))
14.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series300.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(hypot y.re y.im)
34.0ms
(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)) (* (hypot y.re y.im) 1))
109.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify81.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0308794
11149701
23275701
35001693

prune324.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
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))))
12.5b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite55.0ms

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:
0.0ms
(fma x.re y.re (* x.im y.im))
25.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
13.0ms
(/ 1 (/ (hypot y.re y.im) (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)))

series410.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(fma x.re y.re (* x.im y.im))
173.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
108.0ms
(/ 1 (/ (hypot y.re y.im) (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)))

simplify83.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
07952590
136872260
250012098

prune488.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.5b

regimes195.0ms

Accuracy

33.5% (7.5b remaining)

Error of 13.0b against oracle of 5.4b and baseline of 16.7b

bsearch69.0ms

Steps
ItersRangePoint
9
5.298754271440407e+215
1.7144382061264391e+223
5.258979463944342e+219
7
-1.6689308349593681e+136
-7.115247008094498e+134
-2.760768008240295e+135

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample766.0ms

Algorithm
intervals
Results
482.0ms8491×body80valid