?

Average Accuracy: 26.8% → 99.9%
Time: 1.5min
Precision: binary64

?

\[i > 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1} \]
↓
\[\begin{array}{l} t_0 := \frac{i}{i} \cdot \frac{i}{2}\\ \frac{t_0}{\mathsf{fma}\left(i, 2, 1\right)} \cdot \frac{t_0}{\mathsf{fma}\left(i, 2, -1\right)} \end{array} \]
(FPCore (i)
 :precision binary64
 (/
  (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i)))
  (- (* (* 2.0 i) (* 2.0 i)) 1.0)))
↓
(FPCore (i)
 :precision binary64
 (let* ((t_0 (* (/ i i) (/ i 2.0))))
   (* (/ t_0 (fma i 2.0 1.0)) (/ t_0 (fma i 2.0 -1.0)))))
double code(double i) {
	return (((i * i) * (i * i)) / ((2.0 * i) * (2.0 * i))) / (((2.0 * i) * (2.0 * i)) - 1.0);
}
↓
double code(double i) {
	double t_0 = (i / i) * (i / 2.0);
	return (t_0 / fma(i, 2.0, 1.0)) * (t_0 / fma(i, 2.0, -1.0));
}

function code(i)
	return Float64(Float64(Float64(Float64(i * i) * Float64(i * i)) / Float64(Float64(2.0 * i) * Float64(2.0 * i))) / Float64(Float64(Float64(2.0 * i) * Float64(2.0 * i)) - 1.0))
end
↓
function code(i)
	t_0 = Float64(Float64(i / i) * Float64(i / 2.0))
	return Float64(Float64(t_0 / fma(i, 2.0, 1.0)) * Float64(t_0 / fma(i, 2.0, -1.0)))
end

code[i_] := N[(N[(N[(N[(i * i), $MachinePrecision] * N[(i * i), $MachinePrecision]), $MachinePrecision] / N[(N[(2.0 * i), $MachinePrecision] * N[(2.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(2.0 * i), $MachinePrecision] * N[(2.0 * i), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]
↓
code[i_] := Block[{t$95$0 = N[(N[(i / i), $MachinePrecision] * N[(i / 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(t$95$0 / N[(i * 2.0 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / N[(i * 2.0 + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}
↓
\begin{array}{l}
t_0 := \frac{i}{i} \cdot \frac{i}{2}\\
\frac{t_0}{\mathsf{fma}\left(i, 2, 1\right)} \cdot \frac{t_0}{\mathsf{fma}\left(i, 2, -1\right)}
\end{array}

Error?

Derivation?

  1. Initial program 26.8%

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1} \]

  2. Applied egg-rr99.9%

    \[\leadsto \color{blue}{\frac{\frac{i}{i} \cdot \frac{i}{2}}{\mathsf{fma}\left(i, 2, 1\right)} \cdot \frac{\frac{i}{i} \cdot \frac{i}{2}}{\mathsf{fma}\left(i, 2, -1\right)}} \]

Reproduce?

herbie shell --seed 2023237 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (> i 0.0)
  (/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0)))