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

Average Error: 7.3 → 1.0

Time: 19.4s

Precision: binary64

Cost: 1736

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{z - t}{x} \cdot \left(z - y\right)}\\ \mathbf{elif}\;t_1 \leq 10^{+302}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z - y}{\frac{x}{z - t}}}\\ \end{array} \]

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 (<= t_1 (- INFINITY))
     (/ 1.0 (* (/ (- z t) x) (- z y)))
     (if (<= t_1 1e+302) (/ x t_1) (/ 1.0 (/ (- z y) (/ x (- z t))))))))

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 <= -((double) INFINITY)) {
		tmp = 1.0 / (((z - t) / x) * (z - y));
	} else if (t_1 <= 1e+302) {
		tmp = x / t_1;
	} else {
		tmp = 1.0 / ((z - y) / (x / (z - t)));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 / (((z - t) / x) * (z - y));
	} else if (t_1 <= 1e+302) {
		tmp = x / t_1;
	} else {
		tmp = 1.0 / ((z - y) / (x / (z - t)));
	}
	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 <= -math.inf:
		tmp = 1.0 / (((z - t) / x) * (z - y))
	elif t_1 <= 1e+302:
		tmp = x / t_1
	else:
		tmp = 1.0 / ((z - y) / (x / (z - t)))
	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 <= Float64(-Inf))
		tmp = Float64(1.0 / Float64(Float64(Float64(z - t) / x) * Float64(z - y)));
	elseif (t_1 <= 1e+302)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(1.0 / Float64(Float64(z - y) / Float64(x / Float64(z - t))));
	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 <= -Inf)
		tmp = 1.0 / (((z - t) / x) * (z - y));
	elseif (t_1 <= 1e+302)
		tmp = x / t_1;
	else
		tmp = 1.0 / ((z - y) / (x / (z - t)));
	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[LessEqual[t$95$1, (-Infinity)], N[(1.0 / N[(N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+302], N[(x / t$95$1), $MachinePrecision], N[(1.0 / N[(N[(z - y), $MachinePrecision] / N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	7.3
Target	8.1
Herbie	1.0

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 20.5

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

   2. Simplified 0.1

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

      [Start] 20.5	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 20.5	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 20.5	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 20.5	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 20.5	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 20.5	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 20.5	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 20.5	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 20.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 20.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 20.5	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 20.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 20.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]
      associate-/l/ [<=] 0.1	\[ \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]

   3. Applied egg-rr 0.1

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

   4. Applied egg-rr 0.8

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1.0000000000000001e302

   1. Initial program 1.2

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

   if 1.0000000000000001e302 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 15.5

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

   2. Simplified 15.5

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

      [Start] 15.5	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 15.5	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 15.5	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 15.5	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 15.5	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 15.5	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 15.5	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 15.5	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 15.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 15.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 15.5	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 15.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 15.5	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]

   3. Applied egg-rr 15.5

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

   4. Applied egg-rr 0.7

      \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{\frac{x}{z - t}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{z - t}{x} \cdot \left(z - y\right)}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 10^{+302}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z - y}{\frac{x}{z - t}}}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.8
Cost	1609

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+302}\right):\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1}\\ \end{array} \]

Alternative 2
Error	0.8
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{z - t}{x} \cdot \left(z - y\right)}\\ \mathbf{elif}\;t_1 \leq 10^{+302}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \end{array} \]

Alternative 3
Error	27.8
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+80}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-247}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-305}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 4
Error	27.8
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -1.14 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-303}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-257}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 5
Error	27.8
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-246}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-306}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-257}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]

Alternative 6
Error	27.8
Cost	1440

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+246}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-247}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-303}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 7
Error	22.0
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.1 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]

Alternative 8
Error	21.1
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{z}}{z - y}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -6.1 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.1 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]

Alternative 9
Error	14.1
Cost	1172

\[\begin{array}{l} t_1 := \frac{\frac{-x}{t}}{z - y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \]

Alternative 10
Error	22.8
Cost	1108

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+80}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]

Alternative 11
Error	20.5
Cost	1108

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+246}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]

Alternative 12
Error	19.6
Cost	1108

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]

Alternative 13
Error	19.2
Cost	1108

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]

Alternative 14
Error	11.8
Cost	1040

\[\begin{array}{l} t_1 := \frac{\frac{-x}{y}}{z - t}\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+71}:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z - y}\\ \end{array} \]

Alternative 15
Error	23.2
Cost	980

\[\begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-58}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 16
Error	23.2
Cost	980

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 17
Error	13.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+50}:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]

Alternative 18
Error	6.2
Cost	708

\[\begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z - y}\\ \end{array} \]

Alternative 19
Error	35.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+42} \lor \neg \left(z \leq 6.2 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 20
Error	34.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+41} \lor \neg \left(z \leq 7 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 21
Error	25.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+38} \lor \neg \left(z \leq 3.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 22
Error	24.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+37} \lor \neg \left(z \leq 1.65 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 23
Error	22.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 24
Error	50.9
Cost	320

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

Reproduce

herbie shell --seed 2023055 
(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))))