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

Average Error: 8.0 → 1.6

Time: 16.5s

Precision: binary64

Cost: 2120

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+140}:\\ \;\;\;\;\frac{1}{\frac{z - y}{x}} \cdot \frac{1}{z - t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-305}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t - z \cdot \left(y - z\right)}\\ \end{array} \]

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 -2e+140)
     (* (/ 1.0 (/ (- z y) x)) (/ 1.0 (- z t)))
     (if (<= t_1 2e-305)
       (/ (/ x (- z t)) (- z y))
       (/ x (- (* (- y z) t) (* z (- y 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 <= -2e+140) {
		tmp = (1.0 / ((z - y) / x)) * (1.0 / (z - t));
	} else if (t_1 <= 2e-305) {
		tmp = (x / (z - t)) / (z - y);
	} else {
		tmp = x / (((y - z) * t) - (z * (y - 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 <= (-2d+140)) then
        tmp = (1.0d0 / ((z - y) / x)) * (1.0d0 / (z - t))
    else if (t_1 <= 2d-305) then
        tmp = (x / (z - t)) / (z - y)
    else
        tmp = x / (((y - z) * t) - (z * (y - 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 <= -2e+140) {
		tmp = (1.0 / ((z - y) / x)) * (1.0 / (z - t));
	} else if (t_1 <= 2e-305) {
		tmp = (x / (z - t)) / (z - y);
	} else {
		tmp = x / (((y - z) * t) - (z * (y - 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 <= -2e+140:
		tmp = (1.0 / ((z - y) / x)) * (1.0 / (z - t))
	elif t_1 <= 2e-305:
		tmp = (x / (z - t)) / (z - y)
	else:
		tmp = x / (((y - z) * t) - (z * (y - 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 <= -2e+140)
		tmp = Float64(Float64(1.0 / Float64(Float64(z - y) / x)) * Float64(1.0 / Float64(z - t)));
	elseif (t_1 <= 2e-305)
		tmp = Float64(Float64(x / Float64(z - t)) / Float64(z - y));
	else
		tmp = Float64(x / Float64(Float64(Float64(y - z) * t) - Float64(z * Float64(y - 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 <= -2e+140)
		tmp = (1.0 / ((z - y) / x)) * (1.0 / (z - t));
	elseif (t_1 <= 2e-305)
		tmp = (x / (z - t)) / (z - y);
	else
		tmp = x / (((y - z) * t) - (z * (y - 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, -2e+140], N[(N[(1.0 / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-305], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] - N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	8.0
Target	8.8
Herbie	1.6

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -2.00000000000000012e140

   1. Initial program 7.5

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

   2. Simplified 6.6

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

      [Start] 7.5	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 7.5	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 7.5	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 7.5	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 7.5	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 7.5	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 7.5	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 7.5	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 7.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 7.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 7.5	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 7.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 7.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]
      associate-/l/ [<=] 6.6	\[ \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]

   3. Applied egg-rr 8.8

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

   if -2.00000000000000012e140 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < 1.99999999999999999e-305

   1. Initial program 10.1

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

   2. Simplified 1.1

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

      [Start] 10.1	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 10.1	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 10.1	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 10.1	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 10.1	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 10.1	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 10.1	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 10.1	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 10.1	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 10.1	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 10.1	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 10.1	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 10.1	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]
      associate-/l/ [<=] 1.1	\[ \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]

   if 1.99999999999999999e-305 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 1.5

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

   2. Simplified 1.5

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

      [Start] 1.5	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 1.5	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 1.5	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 1.5	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 1.5	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 1.5	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 1.5	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 1.5	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 1.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 1.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 1.5	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 1.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 1.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]

   3. Applied egg-rr 1.5

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

   4. Taylor expanded in x around 0 1.5

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

   5. Simplified 1.5

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

      [Start] 1.5	\[ \frac{x}{-1 \cdot \left(\left(z - y\right) \cdot t\right) + \left(z - y\right) \cdot z} \]
      +-commutative [=>] 1.5	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot z + -1 \cdot \left(\left(z - y\right) \cdot t\right)}} \]
      *-commutative [<=] 1.5	\[ \frac{x}{\color{blue}{z \cdot \left(z - y\right)} + -1 \cdot \left(\left(z - y\right) \cdot t\right)} \]
      mul-1-neg [=>] 1.5	\[ \frac{x}{z \cdot \left(z - y\right) + \color{blue}{\left(-\left(z - y\right) \cdot t\right)}} \]
      sub-neg [<=] 1.5	\[ \frac{x}{\color{blue}{z \cdot \left(z - y\right) - \left(z - y\right) \cdot t}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq -2 \cdot 10^{+140}:\\ \;\;\;\;\frac{1}{\frac{z - y}{x}} \cdot \frac{1}{z - t}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 2 \cdot 10^{-305}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t - z \cdot \left(y - z\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	1.6
Cost	1864

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+140}:\\ \;\;\;\;\frac{1}{\frac{z - y}{x}} \cdot \frac{1}{z - t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-305}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	4.6
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \]

Alternative 3
Error	1.9
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \end{array} \]

Alternative 4
Error	27.8
Cost	1108

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -7.1 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-219}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 1.96 \cdot 10^{-94}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \end{array} \]

Alternative 5
Error	27.8
Cost	1108

\[\begin{array}{l} t_1 := \frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-83}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	27.8
Cost	1044

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -7.1 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+92}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-95}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 7
Error	27.8
Cost	1044

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-94}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 8
Error	20.1
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-255}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 9
Error	18.2
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;t \leq 4.5 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 10
Error	12.2
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+170}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-217}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y - z}\\ \end{array} \]

Alternative 11
Error	12.2
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+170}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-217}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(y - z\right) \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 12
Error	14.3
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 13
Error	11.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+169}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-148}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 14
Error	12.2
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+169}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-217}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 15
Error	15.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 16
Error	15.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 17
Error	36.0
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -125 \lor \neg \left(z \leq 4 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 18
Error	25.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -55000000 \lor \neg \left(z \leq 4.4 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 19
Error	24.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+32} \lor \neg \left(z \leq 5.5 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 20
Error	25.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+32} \lor \neg \left(z \leq 5.5 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 21
Error	22.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+32} \lor \neg \left(z \leq 4.4 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 22
Error	50.4
Cost	320

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

Reproduce

herbie shell --seed 2023018 
(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))))