Average Error: 0.0 → 0.0
Time: 5.9s
Precision: binary64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
↓
\[\mathsf{fma}\left(a, 1 - t, x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(y, b - z, z\right)\right)\right) \]
(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 a (- 1.0 t) (+ x (fma b (+ t -2.0) (fma y (- b z) z)))))
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(a, (1.0 - t), (x + fma(b, (t + -2.0), fma(y, (b - z), z))));
}

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(a, Float64(1.0 - t), Float64(x + fma(b, Float64(t + -2.0), fma(y, Float64(b - z), z))))
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[(a * N[(1.0 - t), $MachinePrecision] + N[(x + N[(b * N[(t + -2.0), $MachinePrecision] + N[(y * N[(b - z), $MachinePrecision] + z), $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(a, 1 - t, x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(y, b - z, z\right)\right)\right)

Error

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

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

  3. Taylor expanded in y around 0 0.0

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

  4. Simplified0.0

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

  5. Taylor expanded in z around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2022192 
(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)))