Average Error: 7.6 → 2.3
Time: 4.3s
Precision: binary64
\[ \begin{array}{c}[y, t] = \mathsf{sort}([y, t])\\ \end{array} \]
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
↓
\[\frac{\frac{x}{z - y}}{z - t} \]
(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))
↓
(FPCore (x y z t) :precision binary64 (/ (/ x (- z y)) (- z t)))
double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}
↓
double code(double x, double y, double z, double t) {
	return (x / (z - y)) / (z - 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 = x / ((y - z) * (t - z))
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 = (x / (z - y)) / (z - t)
end function

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

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

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

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

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

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

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

Target

Original7.6
Target8.5
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Derivation

  1. Initial program 7.6

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

  2. Simplified2.3

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

  3. Final simplification2.3

    \[\leadsto \frac{\frac{x}{z - y}}{z - t} \]

Reproduce

herbie shell --seed 2022153 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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