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

Average Accuracy: 88.6% → 98.8%

Time: 20.1s

Precision: binary64

Cost: 1609

\[ \begin{array}{c}[y, t] = \mathsf{sort}([y, t])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+186} \lor \neg \left(t_1 \leq 4 \cdot 10^{+282}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1}\\ \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (or (<= t_1 -1e+186) (not (<= t_1 4e+282)))
     (/ (/ x (- t z)) (- y z))
     (/ x t_1))))

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

↓

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((t_1 <= -1e+186) || !(t_1 <= 4e+282)) {
		tmp = (x / (t - z)) / (y - z);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

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 = x / ((y - z) * (t - z))
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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((t_1 <= (-1d+186)) .or. (.not. (t_1 <= 4d+282))) then
        tmp = (x / (t - z)) / (y - z)
    else
        tmp = x / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((t_1 <= -1e+186) || !(t_1 <= 4e+282)) {
		tmp = (x / (t - z)) / (y - z);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	return x / ((y - z) * (t - z))

↓

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (t_1 <= -1e+186) or not (t_1 <= 4e+282):
		tmp = (x / (t - z)) / (y - z)
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(y - z) * Float64(t - z)))
end

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if ((t_1 <= -1e+186) || !(t_1 <= 4e+282))
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((y - z) * (t - z));
end

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((t_1 <= -1e+186) || ~((t_1 <= 4e+282)))
		tmp = (x / (t - z)) / (y - z);
	else
		tmp = x / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+186], N[Not[LessEqual[t$95$1, 4e+282]], $MachinePrecision]], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]

Target

Original	88.6%
Target	87.6%
Herbie	98.8%

\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -9.9999999999999998e185 or 4.00000000000000013e282 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 78.8%

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

   2. Simplified 99.6%

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

      [Start] 78.8	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      associate-/l/ [<=] 99.6	\[ \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   if -9.9999999999999998e185 < (*.f64 (-.f64 y z) (-.f64 t z)) < 4.00000000000000013e282

   1. Initial program 97.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -1 \cdot 10^{+186} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \leq 4 \cdot 10^{+282}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	74.2%
Cost	1240

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+47}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-216}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 2
Accuracy	82.5%
Cost	1172

\[\begin{array}{l} t_1 := \frac{-x}{z}\\ t_2 := \frac{\frac{x}{t - z}}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -4900000000000:\\ \;\;\;\;\frac{t_1}{y - z}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3
Accuracy	82.6%
Cost	1172

\[\begin{array}{l} t_1 := \frac{\frac{x}{t - z}}{y}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -7600000000000:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 4
Accuracy	71.5%
Cost	1108

\[\begin{array}{l} t_1 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;t \leq -2.85 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-272}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 5
Accuracy	73.4%
Cost	1108

\[\begin{array}{l} t_1 := \frac{x}{y \cdot \left(t - z\right)}\\ t_2 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 6
Accuracy	74.3%
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-207}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 7
Accuracy	90.2%
Cost	972

\[\begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-283}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+165}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 8
Accuracy	83.1%
Cost	908

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+179}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9
Accuracy	62.5%
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-193}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	81.0%
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+177}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11
Accuracy	72.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+49}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 12
Accuracy	44.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+93} \lor \neg \left(z \leq 14.5\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 13
Accuracy	60.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+46} \lor \neg \left(z \leq 3.7 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14
Accuracy	62.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+49} \lor \neg \left(z \leq 1.12 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 15
Accuracy	66.3%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+46} \lor \neg \left(z \leq 4.3 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 16
Accuracy	66.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 17
Accuracy	66.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+46}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 18
Accuracy	66.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+46}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 19
Accuracy	37.3%
Cost	320

\[\frac{x}{y \cdot t} \]

Reproduce

herbie shell --seed 2023147 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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