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

Average Accuracy: 88.5% → 97.8%

Time: 20.9s

Precision: binary64

Cost: 1864

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 0.0)
     (/ (/ x (- t z)) (- y z))
     (if (<= t_1 5e+225) t_1 (/ (/ x (- y z)) (- t z))))))

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 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x / (t - z)) / (y - z);
	} else if (t_1 <= 5e+225) {
		tmp = t_1;
	} else {
		tmp = (x / (y - z)) / (t - z);
	}
	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 = x / ((y - z) * (t - z))
    if (t_1 <= 0.0d0) then
        tmp = (x / (t - z)) / (y - z)
    else if (t_1 <= 5d+225) then
        tmp = t_1
    else
        tmp = (x / (y - z)) / (t - z)
    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 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x / (t - z)) / (y - z);
	} else if (t_1 <= 5e+225) {
		tmp = t_1;
	} else {
		tmp = (x / (y - z)) / (t - z);
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= 0.0:
		tmp = (x / (t - z)) / (y - z)
	elif t_1 <= 5e+225:
		tmp = t_1
	else:
		tmp = (x / (y - z)) / (t - z)
	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(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	elseif (t_1 <= 5e+225)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	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 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = (x / (t - z)) / (y - z);
	elseif (t_1 <= 5e+225)
		tmp = t_1;
	else
		tmp = (x / (y - z)) / (t - z);
	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[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+225], t$95$1, N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	88.5%
Target	86.8%
Herbie	97.8%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < 0.0

   1. Initial program 85.5%

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

   2. Simplified 97.8%

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

      [Start] 85.5	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      associate-/l/ [<=] 97.8	\[ \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   if 0.0 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < 4.99999999999999981e225

   1. Initial program 99.5%

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

   if 4.99999999999999981e225 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 78.3%

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

   2. Simplified 80.6%

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

      [Start] 78.3	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      associate-/r* [=>] 80.6	\[ \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 5 \cdot 10^{+225}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.0%
Cost	1865

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq 0 \lor \neg \left(t_1 \leq 10^{+260}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	92.8%
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y - z} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3
Accuracy	92.8%
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{y - z}}{\frac{z}{x}}\\ \end{array} \]

Alternative 4
Accuracy	71.4%
Cost	1372

\[\begin{array}{l} t_1 := \frac{\frac{x}{t}}{y - z}\\ t_2 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -68000000000:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 29000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \end{array} \]

Alternative 5
Accuracy	56.9%
Cost	1308

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ t_3 := \frac{-x}{y \cdot z}\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -90000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-236}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	57.0%
Cost	1308

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ t_3 := \frac{-x}{y \cdot z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{+201}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -470000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-237}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 0.0016:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	56.9%
Cost	1308

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+199}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+50}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -75000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-238}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 0.0013:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	57.3%
Cost	1308

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+176}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -80000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-237}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 0.00125:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	57.4%
Cost	1308

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+176}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -10500:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-237}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;y \leq 0.002:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	73.6%
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;y \leq -1.72 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-237}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11
Accuracy	60.7%
Cost	850

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-30} \lor \neg \left(z \leq 1.6 \cdot 10^{-32} \lor \neg \left(z \leq 820000000\right) \land z \leq 1.95 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 12
Accuracy	64.7%
Cost	848

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 55000000:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	68.7%
Cost	780

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-236}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;y \leq 0.0054:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 14
Accuracy	79.4%
Cost	776

\[\begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-136}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-48}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 15
Accuracy	81.8%
Cost	776

\[\begin{array}{l} \mathbf{if}\;y \leq -13600:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 16
Accuracy	72.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 17
Accuracy	72.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 18
Accuracy	73.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -110000:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-236}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 19
Accuracy	73.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -95000:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-237}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]

Alternative 20
Accuracy	44.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+90} \lor \neg \left(z \leq 1.35 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 21
Accuracy	60.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-30} \lor \neg \left(z \leq 7.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 22
Accuracy	61.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-28} \lor \neg \left(z \leq 5.6 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 23
Accuracy	20.9%
Cost	320

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

Reproduce

herbie shell --seed 2023151 
(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))))