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

Average Error: 0.6 → 1.1

Time: 26.0s

Precision: binary64

Cost: 832

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

Math

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

↓

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

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

Derivation

1. Initial program 0.6

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

2. Applied egg-rr 0.7

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

3. Applied egg-rr 1.1

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

4. Final simplification 1.1

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

Alternatives

Alternative 1
Error	18.5
Cost	908

\[\begin{array}{l} t_1 := \frac{x}{y \cdot t} - -1\\ \mathbf{if}\;t \leq 1.1 \cdot 10^{-124}:\\ \;\;\;\;\frac{x}{y \cdot z} - -1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t} - -1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	18.5
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{y \cdot t} - -1\\ \mathbf{if}\;t \leq 10^{-124}:\\ \;\;\;\;\frac{x}{y \cdot z} - -1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+19}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	9.2
Cost	840

\[\begin{array}{l} t_1 := 1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t} - -1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	6.6
Cost	840

\[\begin{array}{l} t_1 := 1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-56}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	6.8
Cost	840

\[\begin{array}{l} t_1 := 1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-57}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	6.9
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-85}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 7
Error	4.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-192}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-61}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} - -1\\ \end{array} \]

Alternative 8
Error	18.1
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{y \cdot t} - -1\\ \mathbf{if}\;y \leq -1.36 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	0.6
Cost	704

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

Alternative 10
Error	1.2
Cost	704

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

Alternative 11
Error	25.1
Cost	448

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

Reproduce

herbie shell --seed 2023074 
(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)))))