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

Average Error: 0.6 → 0.6

Time: 12.5s

Precision: binary64

Cost: 704

Math

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

↓

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

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

Derivation

1. Initial program 0.6

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

2. Final simplification 0.6

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

Alternatives

Alternative 1
Error	10.8
Cost	1104

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1706683326237428 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-149}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 1.0132973802072265 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8779568980174104 \cdot 10^{+80}:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	11.1
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1706683326237428 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-149}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq 1.0132973802072265 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8779568980174104 \cdot 10^{+80}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	10.8
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1706683326237428 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-149}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 1.0132973802072265 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8779568980174104 \cdot 10^{+80}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	9.1
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \leq -1.8341197108874627 \cdot 10^{-74}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-160}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 4.0288274834137 \cdot 10^{-64}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \end{array} \]

Alternative 5
Error	9.1
Cost	840

\[\begin{array}{l} t_1 := 1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{if}\;y \leq -1.8341197108874627 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-160}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	9.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.8341197108874627 \cdot 10^{-74}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-160}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 7
Error	13.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq 1.344813327940926 \cdot 10^{-263}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4.969678022137834 \cdot 10^{-30}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	10.8
Cost	708

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7241451209207663 \cdot 10^{-109}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 9
Error	1.1
Cost	704

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

Alternative 10
Error	13.1
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022308 
(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)))))