Average Error: 9.9 → 0.0
Time: 4.5s
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z} \]
↓
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}} \]
(FPCore (x y z) :precision binary64 (/ (+ x (* y (- z x))) z))
↓
(FPCore (x y z) :precision binary64 (- (+ y (/ x z)) (/ y (/ z x))))
double code(double x, double y, double z) {
	return (x + (y * (z - x))) / z;
}
↓
double code(double x, double y, double z) {
	return (y + (x / z)) - (y / (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 * (z - x))) / 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 = (y + (x / z)) - (y / (z / x))
end function

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

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

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

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

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

\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}

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

Original9.9
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}} \]

Derivation

  1. Initial program 9.9

    \[\frac{x + y \cdot \left(z - x\right)}{z} \]

  2. Simplified9.9

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

  3. Taylor expanded in y around 0 3.3

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

  4. Applied egg-rr12.2

    \[\leadsto \left(y + \frac{x}{z}\right) - \color{blue}{\sqrt[3]{y \cdot y} \cdot \left(\sqrt[3]{y} \cdot \frac{x}{z}\right)} \]

  5. Applied egg-rr0.0

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

  6. Final simplification0.0

    \[\leadsto \left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}} \]

Reproduce

herbie shell --seed 2022133 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

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