Average Error: 0.3 → 0.2
Time: 3.1s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
↓
\[\left(6 \cdot \left(y \cdot z\right) + x\right) - 6 \cdot \left(z \cdot x\right) \]
(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))
↓
(FPCore (x y z) :precision binary64 (- (+ (* 6.0 (* y z)) x) (* 6.0 (* z x))))
double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}
↓
double code(double x, double y, double z) {
	return ((6.0 * (y * z)) + x) - (6.0 * (z * x));
}

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function
↓
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((6.0d0 * (y * z)) + x) - (6.0d0 * (z * x))
end function

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}
↓
public static double code(double x, double y, double z) {
	return ((6.0 * (y * z)) + x) - (6.0 * (z * x));
}

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)
↓
def code(x, y, z):
	return ((6.0 * (y * z)) + x) - (6.0 * (z * x))

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end
↓
function code(x, y, z)
	return Float64(Float64(Float64(6.0 * Float64(y * z)) + x) - Float64(6.0 * Float64(z * x)))
end

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end
↓
function tmp = code(x, y, z)
	tmp = ((6.0 * (y * z)) + x) - (6.0 * (z * x));
end

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(N[(N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - N[(6.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\left(6 \cdot \left(y \cdot z\right) + x\right) - 6 \cdot \left(z \cdot x\right)

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right) \]

Derivation

  1. Initial program 0.3

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

  2. Simplified0.3

    \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, z, x\right)} \]

  3. Taylor expanded in y around 0 0.2

    \[\leadsto \color{blue}{\left(6 \cdot \left(y \cdot z\right) + x\right) - 6 \cdot \left(z \cdot x\right)} \]

  4. Final simplification0.2

    \[\leadsto \left(6 \cdot \left(y \cdot z\right) + x\right) - 6 \cdot \left(z \cdot x\right) \]

Reproduce

herbie shell --seed 2022134 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))