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

Average Error: 0.6 → 0.6

Time: 8.6s

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	12.1
Cost	978

\[\begin{array}{l} \mathbf{if}\;y \leq -2020000000000 \lor \neg \left(y \leq 2.8 \cdot 10^{-115} \lor \neg \left(y \leq 8.8 \cdot 10^{-79}\right) \land y \leq 7.8 \cdot 10^{-27}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 2
Error	12.1
Cost	977

\[\begin{array}{l} t_1 := 1 - \frac{x}{y \cdot y}\\ \mathbf{if}\;y \leq -2400000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-115}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-79} \lor \neg \left(y \leq 7 \cdot 10^{-27}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 3
Error	12.1
Cost	977

\[\begin{array}{l} \mathbf{if}\;y \leq -1550000:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-115}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-79} \lor \neg \left(y \leq 7.5 \cdot 10^{-27}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 4
Error	9.0
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-94} \lor \neg \left(y \leq 1.02 \cdot 10^{-150}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 5
Error	7.2
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-57} \lor \neg \left(y \leq 8.5 \cdot 10^{-131}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \end{array} \]

Alternative 6
Error	7.0
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-84} \lor \neg \left(y \leq 2.8 \cdot 10^{-115}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \end{array} \]

Alternative 7
Error	18.7
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2200000000000 \lor \neg \left(y \leq 1.05 \cdot 10^{+124}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 8
Error	25.6
Cost	448

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

Reproduce

herbie shell --seed 2023031 
(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)))))