Details

Time bar (total: 3.9s)

sample19.0ms

Algorithm
intervals
Results
9.0ms269×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: 26.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
26.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

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:
3.0ms
(+ (* 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)))

series107.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* x.re y.re) (* x.im y.im))
78.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify87.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune169.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re 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)))
0.3b
(fma x.re y.re (* x.im y.im))
14.9b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite22.0ms

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

series376.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(hypot y.re y.im)
177.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
40.0ms
(fma x.re y.re (* x.im y.im))
114.0ms
(/ (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
04861106
11625820
25001818

prune271.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
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))
14.9b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite13.0ms

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)
6.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
1.0ms
(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))

series307.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot y.re y.im)
112.0ms
(/ (/ (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))
113.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify74.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0308794
11149701
23275701
35001693

prune491.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt (hypot y.re y.im)))
0.3b
(fma x.re y.re (* x.im y.im))
5.9b
(* (/ 1 (sqrt (hypot y.re y.im))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
8.9b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
106×add-sqr-sqrt
94×times-frac
66×*-un-lft-identity
60×add-cube-cbrt
53×sqrt-prod
32×add-exp-log
22×associate-*r* associate-*l*
20×add-cbrt-cube
15×unswap-sqr
12×associate-/r*
11×div-exp
8×pow1 prod-exp
6×cbrt-undiv associate-/l*
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp pow-flip 1-exp
2×frac-2neg clear-num
1×frac-times sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef inv-pow
Counts
4 → 183
Calls
4 calls:
4.0ms
(/ 1 (sqrt (hypot y.re y.im)))
1.0ms
(fma x.re y.re (* x.im y.im))
17.0ms
(* (/ 1 (sqrt (hypot y.re y.im))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ 1 (sqrt (hypot y.re y.im)))
36.0ms
(fma x.re y.re (* x.im y.im))
108.0ms
(* (/ 1 (sqrt (hypot y.re y.im))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im))))
194.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (hypot y.re y.im)))

simplify75.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05501897
127331667
250011549

prune422.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.3b

regimes280.0ms

Accuracy

36.9% (7.4b remaining)

Error of 12.9b against oracle of 5.5b and baseline of 17.2b

bsearch78.0ms

Steps
ItersRangePoint
8
3.6488667609934286e+129
1.0432818500293452e+133
9.2828111171169e+132
9
-5.0019624427725543e+172
-6.814808586201778e+164
-7.402786013663931e+164

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample498.0ms

Algorithm
intervals
Results
291.0ms8488×body80valid