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

Average Accuracy: 98.9% → 98.6%

Time: 11.9s

Precision: binary64

Cost: 832

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

Math

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

↓

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

FPCore

(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))))

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 + ((-1.0 / (y - z)) / ((y - t) / x));
}

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 + (((-1.0d0) / (y - z)) / ((y - t) / x))
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 + ((-1.0 / (y - z)) / ((y - t) / x));
}

Python

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))

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

Derivation

1. Initial program 98.9%

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

2. Applied egg-rr 98.8%

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

   [Start] 98.9	\[ 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   clear-num [=>] 98.9	\[ 1 - \color{blue}{\frac{1}{\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}}} \]
   associate-/r/ [=>] 98.8	\[ 1 - \color{blue}{\frac{1}{\left(y - z\right) \cdot \left(y - t\right)} \cdot x} \]
   associate-/r* [=>] 98.8	\[ 1 - \color{blue}{\frac{\frac{1}{y - z}}{y - t}} \cdot x \]

3. Applied egg-rr 98.6%

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

   [Start] 98.8	\[ 1 - \frac{\frac{1}{y - z}}{y - t} \cdot x \]
   associate-*l/ [=>] 98.4	\[ 1 - \color{blue}{\frac{\frac{1}{y - z} \cdot x}{y - t}} \]
   associate-/l* [=>] 98.6	\[ 1 - \color{blue}{\frac{\frac{1}{y - z}}{\frac{y - t}{x}}} \]

4. Final simplification 98.6%

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

Alternatives

Alternative 1
Accuracy	86.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-33} \lor \neg \left(y \leq 6.6 \cdot 10^{-93}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 2
Accuracy	87.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+90} \lor \neg \left(y \leq 8 \cdot 10^{-93}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \end{array} \]

Alternative 3
Accuracy	91.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-129} \lor \neg \left(z \leq 3.5 \cdot 10^{-144}\right):\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 4
Accuracy	91.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-128} \lor \neg \left(z \leq 1.8 \cdot 10^{-144}\right):\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \]

Alternative 5
Accuracy	91.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{-127} \lor \neg \left(z \leq 3.5 \cdot 10^{-144}\right):\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 6
Accuracy	71.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+40} \lor \neg \left(y \leq 3.9 \cdot 10^{+23}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 7
Accuracy	81.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+38} \lor \neg \left(y \leq 2.85 \cdot 10^{-62}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 8
Accuracy	98.9%
Cost	704

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

Alternative 9
Accuracy	98.5%
Cost	704

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

Alternative 10
Accuracy	60.6%
Cost	448

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

Reproduce

herbie shell --seed 2023151 
(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)))))