Average Error: 0.7 → 1.0
Time: 10.1s
Precision: binary64
Cost: 832
\[ \begin{array}{c}[z, t] = \mathsf{sort}([z, t])\\ \end{array} \]
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
↓
\[1 + \frac{\frac{-1}{y - z}}{\frac{y - t}{x}} \]
(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)) (/ (- y t) x))))
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)) / ((y - t) / x));
}

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)) / ((y - t) / x))
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)) / ((y - t) / x));
}

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)) / ((y - t) / x))

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(Float64(-1.0 / Float64(y - z)) / Float64(Float64(y - t) / x)))
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)) / ((y - t) / x));
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[(N[(-1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error

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. Simplified1.1

    \[\leadsto \color{blue}{1 - \frac{\frac{x}{y - z}}{y - t}} \]
    Proof
    (-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))): 0 points increase in error, 0 points decrease in error
    (-.f64 1 (Rewrite<= associate-/r*_binary64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))): 11 points increase in error, 13 points decrease in error

  3. Applied egg-rr1.1

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

  4. Applied egg-rr1.0

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

  5. Final simplification1.0

    \[\leadsto 1 + \frac{\frac{-1}{y - z}}{\frac{y - t}{x}} \]

Alternatives

Alternative 1
Error6.8
Cost968
\[\begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-36}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-60}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{y - t}}{y}\\ \end{array} \]
Alternative 2
Error9.3
Cost841
\[\begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-50} \lor \neg \left(y \leq 7.6 \cdot 10^{-100}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{t} \cdot \frac{-1}{z}\\ \end{array} \]
Alternative 3
Error10.2
Cost840
\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-121}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;1 + \frac{x}{t} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 4
Error9.0
Cost840
\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-86}:\\ \;\;\;\;1 + \frac{x}{t} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]
Alternative 5
Error9.1
Cost840
\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-86}:\\ \;\;\;\;1 + \frac{x}{t} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \]
Alternative 6
Error6.9
Cost840
\[\begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-36}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-62}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \]
Alternative 7
Error1.1
Cost832
\[1 + \frac{x}{y - t} \cdot \frac{-1}{y - z} \]
Alternative 8
Error9.9
Cost712
\[\begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-121}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-113}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 9
Error10.2
Cost712
\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-121}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-114}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 10
Error0.7
Cost704
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
Alternative 11
Error13.9
Cost580
\[\begin{array}{l} \mathbf{if}\;z \leq 2.9 \cdot 10^{-307}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
Alternative 12
Error13.3
Cost64
\[1 \]

Error

Reproduce

herbie shell --seed 2022326 
(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)))))