Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A

Average Accuracy: 98.9% → 98.3%

Time: 12.0s

Precision: binary64

Cost: 704

\[ \begin{array}{c}[z, t] = \mathsf{sort}([z, t])\\ \end{array} \]

Math

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

↓

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

FPCore

(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))

↓

(FPCore (x y z t) :precision binary64 (- 1.0 (/ (/ x (- y z)) (- y t))))

C

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

Fortran

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 - ((x / (y - z)) / (y - t))
end function

Java

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

Python

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

↓

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

Julia

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(x / Float64(y - z)) / Float64(y - t)))
end

MATLAB

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 - ((x / (y - z)) / (y - t));
end

Wolfram

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

Derivation

1. Initial program 98.9%

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

2. Simplified 98.3%

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

   [Start] 98.9	\[ 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   associate-/r* [=>] 98.3	\[ 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

3. Final simplification 98.3%

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

Alternatives

Alternative 1
Accuracy	86.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-79} \lor \neg \left(y \leq 6.2 \cdot 10^{-58}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 2
Accuracy	86.5%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-79}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-110}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 3
Accuracy	86.5%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-79}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 4
Accuracy	92.1%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-53}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-70}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 5
Accuracy	83.8%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -500000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-157}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Accuracy	83.8%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-16}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-157}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Accuracy	83.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-15}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Accuracy	98.9%
Cost	704

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

Alternative 9
Accuracy	79.7%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023135 
(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)))))