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

Average Error: 0.7 → 0.7

Time: 11.4s

Precision: binary64

Cost: 832

Math

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

↓

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

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 (/ (/ -1.0 (- y t)) (- y z)))))

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 * ((-1.0 / (y - t)) / (y - z)));
}

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 * (((-1.0d0) / (y - t)) / (y - z)))
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 * ((-1.0 / (y - t)) / (y - z)));
}

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 * ((-1.0 / (y - t)) / (y - z)))

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

Derivation

1. Initial program 0.7

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

2. Simplified 1.0

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

   [Start] 0.7	\[ 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   associate-/r* [=>] 1.0	\[ 1 - \color{blue}{\frac{\frac{x}{y - z}}{y - t}} \]

3. Applied egg-rr 0.7

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

4. Final simplification 0.7

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

Alternatives

Alternative 1
Error	8.1
Cost	1104

\[\begin{array}{l} t_1 := 1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{if}\;z \leq -1550000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-46}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-168}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	7.7
Cost	1104

\[\begin{array}{l} t_1 := 1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{if}\;z \leq -1550000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-45}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-168}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	8.0
Cost	1104

\[\begin{array}{l} t_1 := 1 + x \cdot \frac{\frac{1}{y - t}}{z}\\ \mathbf{if}\;z \leq -1550000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-45}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-168}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	8.1
Cost	1104

\[\begin{array}{l} t_1 := 1 + x \cdot \frac{\frac{1}{y - t}}{z}\\ \mathbf{if}\;z \leq -2300000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-45}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{y}}{y - t}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-171}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	11.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-30}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{-71}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	8.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-26}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-47}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z - y}\\ \end{array} \]

Alternative 7
Error	9.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-115}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	0.7
Cost	704

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

Alternative 9
Error	13.0
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023039 
(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)))))