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

Average Error: 7.6 → 0.7

Time: 14.7s

Precision: binary64

Cost: 1736

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{1}{z - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+294}:\\ \;\;\;\;\frac{t_2}{\frac{z - y}{x}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \frac{x}{z - y}\\ \end{array} \]

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 (/ 1.0 (- z t))))
   (if (<= t_1 -2e+294)
     (/ t_2 (/ (- z y) x))
     (if (<= t_1 5e+293) (/ x t_1) (* t_2 (/ x (- 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 = 1.0 / (z - t);
	double tmp;
	if (t_1 <= -2e+294) {
		tmp = t_2 / ((z - y) / x);
	} else if (t_1 <= 5e+293) {
		tmp = x / t_1;
	} else {
		tmp = t_2 * (x / (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 = 1.0d0 / (z - t)
    if (t_1 <= (-2d+294)) then
        tmp = t_2 / ((z - y) / x)
    else if (t_1 <= 5d+293) then
        tmp = x / t_1
    else
        tmp = t_2 * (x / (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 = 1.0 / (z - t);
	double tmp;
	if (t_1 <= -2e+294) {
		tmp = t_2 / ((z - y) / x);
	} else if (t_1 <= 5e+293) {
		tmp = x / t_1;
	} else {
		tmp = t_2 * (x / (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 = 1.0 / (z - t)
	tmp = 0
	if t_1 <= -2e+294:
		tmp = t_2 / ((z - y) / x)
	elif t_1 <= 5e+293:
		tmp = x / t_1
	else:
		tmp = t_2 * (x / (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(1.0 / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+294)
		tmp = Float64(t_2 / Float64(Float64(z - y) / x));
	elseif (t_1 <= 5e+293)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(t_2 * Float64(x / 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 = 1.0 / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+294)
		tmp = t_2 / ((z - y) / x);
	elseif (t_1 <= 5e+293)
		tmp = x / t_1;
	else
		tmp = t_2 * (x / (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[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+294], N[(t$95$2 / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+293], N[(x / t$95$1), $MachinePrecision], N[(t$95$2 * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	7.6
Target	8.4
Herbie	0.7

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -2.00000000000000013e294

   1. Initial program 18.2

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

   2. Simplified 18.2

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

      [Start] 18.2	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 18.2	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 18.2	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 18.2	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 18.2	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 18.2	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 18.2	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 18.2	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 18.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 18.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 18.2	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 18.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 18.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]

   3. Applied egg-rr 0.1

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

   4. Applied egg-rr 0.1

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

   if -2.00000000000000013e294 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5.00000000000000033e293

   1. Initial program 1.1

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

   if 5.00000000000000033e293 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 15.6

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

   2. Simplified 15.6

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

      [Start] 15.6	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 15.6	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 15.6	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 15.6	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 15.6	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 15.6	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 15.6	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 15.6	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 15.6	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 15.6	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 15.6	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 15.6	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 15.6	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]

   3. Applied egg-rr 0.1

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -2 \cdot 10^{+294}:\\ \;\;\;\;\frac{\frac{1}{z - t}}{\frac{z - y}{x}}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z - t} \cdot \frac{x}{z - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.7
Cost	1736

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z - t} \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 2
Error	0.7
Cost	1609

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+293}\right):\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1}\\ \end{array} \]

Alternative 3
Error	29.3
Cost	1440

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{x}{y \cdot t}\\ t_3 := \frac{-x}{y \cdot z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+147}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	28.9
Cost	1440

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{x}{y \cdot t}\\ t_3 := \frac{-\frac{x}{y}}{z}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+244}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-53}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	11.7
Cost	1304

\[\begin{array}{l} t_1 := \frac{x}{z - y}\\ t_2 := \frac{\frac{-x}{z - y}}{t}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-120}:\\ \;\;\;\;\frac{t_1}{z}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 620000000000:\\ \;\;\;\;t_1 \cdot \frac{1}{z}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z - y}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+285}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z - y}\\ \end{array} \]

Alternative 6
Error	16.5
Cost	1241

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ t_2 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-11} \lor \neg \left(t \leq 60000000\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 7
Error	12.1
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-120}:\\ \;\;\;\;\frac{t_1}{z}\\ \mathbf{elif}\;t \leq 7.9 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{-x}{z - y}}{t}\\ \mathbf{elif}\;t \leq 41000000:\\ \;\;\;\;t_1 \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z - y}\\ \end{array} \]

Alternative 8
Error	5.5
Cost	1092

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 9
Error	12.2
Cost	1040

\[\begin{array}{l} t_1 := \frac{\frac{x}{z - y}}{z}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{-149}:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.3 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 92000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z - y}\\ \end{array} \]

Alternative 10
Error	12.1
Cost	1040

\[\begin{array}{l} t_1 := \frac{\frac{x}{z - y}}{z}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{-x}{z - y}}{t}\\ \mathbf{elif}\;t \leq 78000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z - y}\\ \end{array} \]

Alternative 11
Error	16.4
Cost	977

\[\begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-142} \lor \neg \left(t \leq 6.5 \cdot 10^{-85}\right) \land t \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 12
Error	14.1
Cost	977

\[\begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-120} \lor \neg \left(t \leq 6.5 \cdot 10^{-85}\right) \land t \leq 52000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 13
Error	14.0
Cost	977

\[\begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-120} \lor \neg \left(t \leq 6.5 \cdot 10^{-85}\right) \land t \leq 112000000:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 14
Error	13.1
Cost	977

\[\begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-120} \lor \neg \left(t \leq 6.5 \cdot 10^{-85}\right) \land t \leq 27500000000:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 15
Error	17.7
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -13200000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	17.8
Cost	780

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 0.8:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 17
Error	35.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+72} \lor \neg \left(z \leq 8.2 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 18
Error	24.7
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -63 \lor \neg \left(z \leq 3 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 19
Error	23.6
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -7500000 \lor \neg \left(z \leq 38\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 20
Error	21.1
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -3000000 \lor \neg \left(z \leq 32\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 21
Error	35.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -900000000000:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]

Alternative 22
Error	50.6
Cost	320

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

Reproduce

herbie shell --seed 2023060 
(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))))