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

Average Error: 7.2 → 1.6

Time: 14.7s

Precision: binary64

Cost: 1736

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{x}{z - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+139}:\\ \;\;\;\;t_2 \cdot \frac{1}{z - y}\\ \mathbf{elif}\;t_1 \leq 40000000000000:\\ \;\;\;\;\frac{1}{\frac{\left(z - t\right) \cdot \left(z - y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{z - y}\\ \end{array} \]

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))) (t_2 (/ x (- z t))))
   (if (<= t_1 -4e+139)
     (* t_2 (/ 1.0 (- z y)))
     (if (<= t_1 40000000000000.0)
       (/ 1.0 (/ (* (- z t) (- z y)) x))
       (/ t_2 (- z y))))))

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 t_2 = x / (z - t);
	double tmp;
	if (t_1 <= -4e+139) {
		tmp = t_2 * (1.0 / (z - y));
	} else if (t_1 <= 40000000000000.0) {
		tmp = 1.0 / (((z - t) * (z - y)) / x);
	} else {
		tmp = t_2 / (z - y);
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    t_2 = x / (z - t)
    if (t_1 <= (-4d+139)) then
        tmp = t_2 * (1.0d0 / (z - y))
    else if (t_1 <= 40000000000000.0d0) then
        tmp = 1.0d0 / (((z - t) * (z - y)) / x)
    else
        tmp = t_2 / (z - y)
    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 t_2 = x / (z - t);
	double tmp;
	if (t_1 <= -4e+139) {
		tmp = t_2 * (1.0 / (z - y));
	} else if (t_1 <= 40000000000000.0) {
		tmp = 1.0 / (((z - t) * (z - y)) / x);
	} else {
		tmp = t_2 / (z - y);
	}
	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)
	t_2 = x / (z - t)
	tmp = 0
	if t_1 <= -4e+139:
		tmp = t_2 * (1.0 / (z - y))
	elif t_1 <= 40000000000000.0:
		tmp = 1.0 / (((z - t) * (z - y)) / x)
	else:
		tmp = t_2 / (z - y)
	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))
	t_2 = Float64(x / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -4e+139)
		tmp = Float64(t_2 * Float64(1.0 / Float64(z - y)));
	elseif (t_1 <= 40000000000000.0)
		tmp = Float64(1.0 / Float64(Float64(Float64(z - t) * Float64(z - y)) / x));
	else
		tmp = Float64(t_2 / Float64(z - y));
	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);
	t_2 = x / (z - t);
	tmp = 0.0;
	if (t_1 <= -4e+139)
		tmp = t_2 * (1.0 / (z - y));
	elseif (t_1 <= 40000000000000.0)
		tmp = 1.0 / (((z - t) * (z - y)) / x);
	else
		tmp = t_2 / (z - y);
	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]}, Block[{t$95$2 = N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+139], N[(t$95$2 * N[(1.0 / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 40000000000000.0], N[(1.0 / N[(N[(N[(z - t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$2 / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	7.2
Target	7.8
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 (-.f64 y z) (-.f64 t z)) < -4.00000000000000013e139

   1. Initial program 10.7

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

   2. Simplified 0.9

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

      [Start] 10.7	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 10.7	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 10.7	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 10.7	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 10.7	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 10.7	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 10.7	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 10.7	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 10.7	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 10.7	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 10.7	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 10.7	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 10.7	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]
      associate-/l/ [<=] 0.9	\[ \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]

   3. Applied egg-rr 1.0

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

   if -4.00000000000000013e139 < (*.f64 (-.f64 y z) (-.f64 t z)) < 4e13

   1. Initial program 2.8

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

   2. Simplified 5.2

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

      [Start] 2.8	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 2.8	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 2.8	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 2.8	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 2.8	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 2.8	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 2.8	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 2.8	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 2.8	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 2.8	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 2.8	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 2.8	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 2.8	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]
      associate-/l/ [<=] 5.2	\[ \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]

   3. Applied egg-rr 5.3

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

   4. Applied egg-rr 3.1

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

   if 4e13 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 7.8

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

   2. Simplified 1.2

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

      [Start] 7.8	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 7.8	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 7.8	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 7.8	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 7.8	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 7.8	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 7.8	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 7.8	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 7.8	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 7.8	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 7.8	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 7.8	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 7.8	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]
      associate-/l/ [<=] 1.2	\[ \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -4 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{z - t} \cdot \frac{1}{z - y}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 40000000000000:\\ \;\;\;\;\frac{1}{\frac{\left(z - t\right) \cdot \left(z - y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.8
Cost	1609

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+267} \lor \neg \left(t_1 \leq 10^{+295}\right):\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1}\\ \end{array} \]

Alternative 2
Error	0.8
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{x}{z - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+267}:\\ \;\;\;\;t_2 \cdot \frac{1}{z - y}\\ \mathbf{elif}\;t_1 \leq 10^{+295}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{z - y}\\ \end{array} \]

Alternative 3
Error	28.7
Cost	1572

\[\begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ t_3 := \frac{-x}{z \cdot t}\\ t_4 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+65}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+100}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+243}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	16.2
Cost	1372

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ t_2 := \frac{\frac{x}{z}}{z}\\ t_3 := \frac{x}{\left(y - z\right) \cdot t}\\ t_4 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 31.5:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+167}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	15.3
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -20000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 28.5:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+167}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	20.8
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-254}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 0.00022:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 7
Error	15.6
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+167}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	14.1
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -2900000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 1700:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	14.1
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -16500000000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-76}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 120:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \]

Alternative 10
Error	14.1
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1650000000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \mathbf{elif}\;z \leq 53000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \]

Alternative 11
Error	10.7
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+232}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z - t}\\ \mathbf{elif}\;y \leq -0.022:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 12
Error	4.5
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+149}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 13
Error	35.2
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+44} \lor \neg \left(z \leq 3.2 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14
Error	24.6
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -6800000000000 \lor \neg \left(z \leq 44000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15
Error	23.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -19000000000000 \lor \neg \left(z \leq 30000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 16
Error	23.4
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -5800000000000 \lor \neg \left(z \leq 85000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 17
Error	21.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -28500000000000 \lor \neg \left(z \leq 122\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 18
Error	40.1
Cost	320

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

Reproduce

herbie shell --seed 2023016 
(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))))