Average Error: 0.7 → 0.9
Time: 3.7s
Precision: binary64
\[ \begin{array}{c}[z, t] = \mathsf{sort}([z, t])\\ \end{array} \]
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
↓
\[1 + \frac{-1}{\frac{y - z}{x} \cdot \left(y - t\right)} \]
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))
↓
(FPCore (x y z t)
 :precision binary64
 (+ 1.0 (/ -1.0 (* (/ (- y z) x) (- y t)))))
double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}
↓
double code(double x, double y, double z, double t) {
	return 1.0 + (-1.0 / (((y - z) / x) * (y - t)));
}

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - (x / ((y - z) * (y - t)))
end function
↓
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + ((-1.0d0) / (((y - z) / x) * (y - t)))
end function

public static double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}
↓
public static double code(double x, double y, double z, double t) {
	return 1.0 + (-1.0 / (((y - z) / x) * (y - t)));
}

def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))
↓
def code(x, y, z, t):
	return 1.0 + (-1.0 / (((y - z) / x) * (y - t)))

function code(x, y, z, t)
	return Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))))
end
↓
function code(x, y, z, t)
	return Float64(1.0 + Float64(-1.0 / Float64(Float64(Float64(y - z) / x) * Float64(y - t))))
end

function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / ((y - z) * (y - t)));
end
↓
function tmp = code(x, y, z, t)
	tmp = 1.0 + (-1.0 / (((y - z) / x) * (y - t)));
end

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

1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 + \frac{-1}{\frac{y - z}{x} \cdot \left(y - t\right)}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.7

    \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]

  2. Applied egg-rr1.1

    \[\leadsto 1 - \color{blue}{\frac{x}{y - z} \cdot \frac{1}{y - t}} \]

  3. Applied egg-rr0.9

    \[\leadsto 1 - \color{blue}{\frac{1}{\frac{y - z}{x} \cdot \left(y - t\right)}} \]

  4. Final simplification0.9

    \[\leadsto 1 + \frac{-1}{\frac{y - z}{x} \cdot \left(y - t\right)} \]

Reproduce

herbie shell --seed 2022166 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))