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

Percentage Accurate: 99.1% → 99.1%

Time: 6.9s

Precision: binary64

Cost: 704

• Unsound rule application detected in e-graph. Results may not be sound.

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 99.6%

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

2. Final simplification 99.6%

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

Alternatives

Alternative 1
Accuracy	99.1%
Cost	704

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

Alternative 2
Accuracy	84.5%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-142} \lor \neg \left(y \leq 3.55 \cdot 10^{-178}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 3
Accuracy	88.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -4.4 \lor \neg \left(z \leq 8.5 \cdot 10^{-230}\right):\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 4
Accuracy	86.6%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-101}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Accuracy	86.2%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-234}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 6
Accuracy	83.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-142}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Accuracy	82.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-142}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Accuracy	74.8%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023165 
(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)))))