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

Average Accuracy: 99.0% → 99.0%

Time: 12.0s

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 99.0%

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

2. Final simplification 99.0%

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

Alternatives

Alternative 1
Accuracy	81.6%
Cost	977

\[\begin{array}{l} t_1 := 1 - \frac{x}{y \cdot y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+14}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-6} \lor \neg \left(y \leq 4.3 \cdot 10^{-14}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 2
Accuracy	81.5%
Cost	976

\[\begin{array}{l} t_1 := 1 - \frac{x}{y \cdot y}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+17}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-6}:\\ \;\;\;\;1 + \frac{x}{y} \cdot \frac{-1}{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	86.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-70} \lor \neg \left(y \leq 1.3 \cdot 10^{-66}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 4
Accuracy	91.9%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-10} \lor \neg \left(z \leq 7.6 \cdot 10^{-90}\right):\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 5
Accuracy	92.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1700000 \lor \neg \left(z \leq 1.25 \cdot 10^{-89}\right):\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 6
Accuracy	86.7%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-70}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-67}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 7
Accuracy	91.8%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -7800:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-123}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 8
Accuracy	86.9%
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-85}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-35}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9
Accuracy	70.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+32} \lor \neg \left(y \leq 30000000000\right):\\ \;\;\;\;1 - \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 10
Accuracy	82.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-6} \lor \neg \left(y \leq 1.35 \cdot 10^{-13}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 11
Accuracy	59.9%
Cost	448

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

Reproduce

herbie shell --seed 2023147 
(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)))))