Average Error: 0.0 → 0.0
Time: 11.7s
Precision: binary64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(a + \left(z + x\right)\right) - \left(y \cdot z + t \cdot a\right)\right) \]
(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))
↓
(FPCore (x y z t a b)
 :precision binary64
 (fma (- (+ y t) 2.0) b (- (+ a (+ z x)) (+ (* y z) (* t a)))))
double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return fma(((y + t) - 2.0), b, ((a + (z + x)) - ((y * z) + (t * a))));
}

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end
↓
function code(x, y, z, t, a, b)
	return fma(Float64(Float64(y + t) - 2.0), b, Float64(Float64(a + Float64(z + x)) - Float64(Float64(y * z) + Float64(t * a))))
end

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(N[(a + N[(z + x), $MachinePrecision]), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(a + \left(z + x\right)\right) - \left(y \cdot z + t \cdot a\right)\right)

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 0.0

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)} \]

  3. Applied add-cube-cbrt_binary641.0

    \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)} \cdot \sqrt[3]{\mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)}}\right) \]

  4. Taylor expanded in z around 0 0.0

    \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, \color{blue}{\left(a + \left(z + x\right)\right) - \left(y \cdot z + a \cdot t\right)}\right) \]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, \left(a + \left(z + x\right)\right) - \left(y \cdot z + t \cdot a\right)\right) \]

Reproduce

herbie shell --seed 2022131 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))