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

Percentage Accurate: 89.3% → 97.1%

Time: 11.0s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

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

Java

public static double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Python

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

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(y - z) * Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((y - z) * (t - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

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

Java

public static double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Python

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

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(y - z) * Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((y - z) * (t - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{\frac{x}{y - z}}{t - z} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- y z)) (- t z)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / (y - z)) / (t - z);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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
    code = (x / (y - z)) / (t - z)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (x / (y - z)) / (t - z);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / (y - z)) / (t - z)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(y - z)) / Float64(t - z))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (y - z)) / (t - z);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.5%

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

3. Taylor expanded in x around 0 89.5%

   \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}} \]
4. Step-by-step derivation

   1. associate-/l/ 96.5%

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

5. Simplified 96.5%

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

6. Final simplification 96.5%

   \[\leadsto \frac{\frac{x}{y - z}}{t - z} \]
7. Add Preprocessing

Alternative 2: 92.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t\_1 \leq 10^{+294}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- t z)) y)
     (if (<= t_1 1e+294) (/ x t_1) (/ (/ x z) (- z y))))))

C

assert(x < y && y < z && z < t);
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 = (x / (t - z)) / y;
	} else if (t_1 <= 1e+294) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
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 = (x / (t - z)) / y;
	} else if (t_1 <= 1e+294) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / (t - z)) / y
	elif t_1 <= 1e+294:
		tmp = x / t_1
	else:
		tmp = (x / z) / (z - y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
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(Float64(x / Float64(t - z)) / y);
	elseif (t_1 <= 1e+294)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / z) / Float64(z - y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / (t - z)) / y;
	elseif (t_1 <= 1e+294)
		tmp = x / t_1;
	else
		tmp = (x / z) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 1e+294], N[(x / t$95$1), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 66.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

      3. div-inv 99.8%

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

      4. associate-*l* 70.0%

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

   4. Applied egg-rr 70.0%

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.0%

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

      2. associate-*r* 99.8%

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

      3. div-inv 99.8%

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

      4. clear-num 99.8%

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

      5. frac-times 98.6%

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

      6. metadata-eval 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in y around inf 52.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. *-commutative 52.8%

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

      2. associate-/r* 81.9%

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

   9. Simplified 81.9%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1.00000000000000007e294

   1. Initial program 97.9%

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

   if 1.00000000000000007e294 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 82.2%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 80.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   7. Step-by-step derivation

      1. mul-1-neg 80.4%

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

      2. associate-/r* 91.7%

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

      3. distribute-neg-frac2 91.7%

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

   8. Simplified 91.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{-\left(y - z\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

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

Alternative 3: 51.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-126}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+117} \lor \neg \left(z \leq 1.2 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.02e+37)
   (/ (/ x z) (- t))
   (if (<= z 1.45e-126)
     (/ 1.0 (* t (/ y x)))
     (if (or (<= z 1.45e+117) (not (<= z 1.2e+219)))
       (/ x (* y (- z)))
       (* (/ x z) (/ -1.0 t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e+37) {
		tmp = (x / z) / -t;
	} else if (z <= 1.45e-126) {
		tmp = 1.0 / (t * (y / x));
	} else if ((z <= 1.45e+117) || !(z <= 1.2e+219)) {
		tmp = x / (y * -z);
	} else {
		tmp = (x / z) * (-1.0 / t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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) :: tmp
    if (z <= (-1.02d+37)) then
        tmp = (x / z) / -t
    else if (z <= 1.45d-126) then
        tmp = 1.0d0 / (t * (y / x))
    else if ((z <= 1.45d+117) .or. (.not. (z <= 1.2d+219))) then
        tmp = x / (y * -z)
    else
        tmp = (x / z) * ((-1.0d0) / t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e+37) {
		tmp = (x / z) / -t;
	} else if (z <= 1.45e-126) {
		tmp = 1.0 / (t * (y / x));
	} else if ((z <= 1.45e+117) || !(z <= 1.2e+219)) {
		tmp = x / (y * -z);
	} else {
		tmp = (x / z) * (-1.0 / t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.02e+37:
		tmp = (x / z) / -t
	elif z <= 1.45e-126:
		tmp = 1.0 / (t * (y / x))
	elif (z <= 1.45e+117) or not (z <= 1.2e+219):
		tmp = x / (y * -z)
	else:
		tmp = (x / z) * (-1.0 / t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.02e+37)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (z <= 1.45e-126)
		tmp = Float64(1.0 / Float64(t * Float64(y / x)));
	elseif ((z <= 1.45e+117) || !(z <= 1.2e+219))
		tmp = Float64(x / Float64(y * Float64(-z)));
	else
		tmp = Float64(Float64(x / z) * Float64(-1.0 / t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.02e+37)
		tmp = (x / z) / -t;
	elseif (z <= 1.45e-126)
		tmp = 1.0 / (t * (y / x));
	elseif ((z <= 1.45e+117) || ~((z <= 1.2e+219)))
		tmp = x / (y * -z);
	else
		tmp = (x / z) * (-1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.02e+37], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 1.45e-126], N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.45e+117], N[Not[LessEqual[z, 1.2e+219]], $MachinePrecision]], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.01999999999999995e37

   1. Initial program 89.0%

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

   3. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 78.2%

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

      2. distribute-neg-frac2 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. neg-sub0 78.2%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 78.2%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 78.2%

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

      7. mul-1-neg 78.2%

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

      8. +-commutative 78.2%

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

      9. mul-1-neg 78.2%

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

      10. unsub-neg 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in z around 0 41.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 41.5%

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

      2. mul-1-neg 41.5%

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

   8. Simplified 41.5%

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

   9. Taylor expanded in x around 0 41.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   10. Step-by-step derivation

       1. associate-*r/ 41.5%

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

       2. times-frac 49.0%

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

       3. associate-*l/ 49.0%

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

       4. associate-*r/ 49.0%

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

       5. neg-mul-1 49.0%

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

   11. Simplified 49.0%

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

   if -1.01999999999999995e37 < z < 1.44999999999999994e-126

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 61.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   4. Step-by-step derivation

      1. clear-num 60.7%

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

      2. inv-pow 60.7%

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

      3. associate-/l* 67.2%

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

   5. Applied egg-rr 67.2%

      \[\leadsto \color{blue}{{\left(t \cdot \frac{y}{x}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 67.2%

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

   7. Simplified 67.2%

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

   if 1.44999999999999994e-126 < z < 1.45000000000000014e117 or 1.2e219 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in t around 0 85.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 85.6%

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

      2. neg-mul-1 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in z around 0 43.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 43.1%

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

      2. mul-1-neg 43.1%

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

      3. *-commutative 43.1%

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

   8. Simplified 43.1%

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

   if 1.45000000000000014e117 < z < 1.2e219

   1. Initial program 72.0%

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

   3. Taylor expanded in y around 0 68.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.3%

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

      2. distribute-neg-frac2 68.3%

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

      3. distribute-rgt-neg-in 68.3%

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

      4. neg-sub0 68.3%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 68.3%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 68.3%

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

      7. mul-1-neg 68.3%

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

      8. +-commutative 68.3%

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

      9. mul-1-neg 68.3%

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

      10. unsub-neg 68.3%

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

   5. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 85.8%

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

      2. div-inv 85.7%

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

   7. Applied egg-rr 85.7%

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

   8. Taylor expanded in z around 0 32.3%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-1}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-126}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+117} \lor \neg \left(z \leq 1.2 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -37000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+27} \lor \neg \left(z \leq 3.5 \cdot 10^{+52}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z t)))))
   (if (<= z -37000000000.0)
     t_1
     (if (<= z 7.2e-127)
       (/ x (* (- y z) t))
       (if (or (<= z 1.25e+27) (not (<= z 3.5e+52))) t_1 (/ x (* y (- z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -37000000000.0) {
		tmp = t_1;
	} else if (z <= 7.2e-127) {
		tmp = x / ((y - z) * t);
	} else if ((z <= 1.25e+27) || !(z <= 3.5e+52)) {
		tmp = t_1;
	} else {
		tmp = x / (y * -z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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 / (z * (z - t))
    if (z <= (-37000000000.0d0)) then
        tmp = t_1
    else if (z <= 7.2d-127) then
        tmp = x / ((y - z) * t)
    else if ((z <= 1.25d+27) .or. (.not. (z <= 3.5d+52))) then
        tmp = t_1
    else
        tmp = x / (y * -z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -37000000000.0) {
		tmp = t_1;
	} else if (z <= 7.2e-127) {
		tmp = x / ((y - z) * t);
	} else if ((z <= 1.25e+27) || !(z <= 3.5e+52)) {
		tmp = t_1;
	} else {
		tmp = x / (y * -z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * (z - t))
	tmp = 0
	if z <= -37000000000.0:
		tmp = t_1
	elif z <= 7.2e-127:
		tmp = x / ((y - z) * t)
	elif (z <= 1.25e+27) or not (z <= 3.5e+52):
		tmp = t_1
	else:
		tmp = x / (y * -z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - t)))
	tmp = 0.0
	if (z <= -37000000000.0)
		tmp = t_1;
	elseif (z <= 7.2e-127)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif ((z <= 1.25e+27) || !(z <= 3.5e+52))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(y * Float64(-z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - t));
	tmp = 0.0;
	if (z <= -37000000000.0)
		tmp = t_1;
	elseif (z <= 7.2e-127)
		tmp = x / ((y - z) * t);
	elseif ((z <= 1.25e+27) || ~((z <= 3.5e+52)))
		tmp = t_1;
	else
		tmp = x / (y * -z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -37000000000.0], t$95$1, If[LessEqual[z, 7.2e-127], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.25e+27], N[Not[LessEqual[z, 3.5e+52]], $MachinePrecision]], t$95$1, N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7e10 or 7.1999999999999999e-127 < z < 1.24999999999999995e27 or 3.5e52 < z

   1. Initial program 88.4%

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

   3. Taylor expanded in y around 0 74.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.0%

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

      2. distribute-neg-frac2 74.0%

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

      3. distribute-rgt-neg-in 74.0%

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

      4. neg-sub0 74.0%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 74.0%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 74.0%

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

      7. mul-1-neg 74.0%

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

      8. +-commutative 74.0%

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

      9. mul-1-neg 74.0%

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

      10. unsub-neg 74.0%

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

   5. Simplified 74.0%

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

   if -3.7e10 < z < 7.1999999999999999e-127

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf 68.1%

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

   if 1.24999999999999995e27 < z < 3.5e52

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 59.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 59.8%

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

      2. neg-mul-1 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around 0 58.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 58.8%

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

      2. mul-1-neg 58.8%

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

      3. *-commutative 58.8%

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

   8. Simplified 58.8%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -37000000000:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+27} \lor \neg \left(z \leq 3.5 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y t))))
   (if (<= t -1.9e-11)
     t_1
     (if (<= t 1.15e-54)
       (/ x (* y (- z)))
       (if (<= t 2.9e+63) t_1 (/ x (* z (- t))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -1.9e-11) {
		tmp = t_1;
	} else if (t <= 1.15e-54) {
		tmp = x / (y * -z);
	} else if (t <= 2.9e+63) {
		tmp = t_1;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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 * t)
    if (t <= (-1.9d-11)) then
        tmp = t_1
    else if (t <= 1.15d-54) then
        tmp = x / (y * -z)
    else if (t <= 2.9d+63) then
        tmp = t_1
    else
        tmp = x / (z * -t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -1.9e-11) {
		tmp = t_1;
	} else if (t <= 1.15e-54) {
		tmp = x / (y * -z);
	} else if (t <= 2.9e+63) {
		tmp = t_1;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (y * t)
	tmp = 0
	if t <= -1.9e-11:
		tmp = t_1
	elif t <= 1.15e-54:
		tmp = x / (y * -z)
	elif t <= 2.9e+63:
		tmp = t_1
	else:
		tmp = x / (z * -t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * t))
	tmp = 0.0
	if (t <= -1.9e-11)
		tmp = t_1;
	elseif (t <= 1.15e-54)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (t <= 2.9e+63)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z * Float64(-t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * t);
	tmp = 0.0;
	if (t <= -1.9e-11)
		tmp = t_1;
	elseif (t <= 1.15e-54)
		tmp = x / (y * -z);
	elseif (t <= 2.9e+63)
		tmp = t_1;
	else
		tmp = x / (z * -t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e-11], t$95$1, If[LessEqual[t, 1.15e-54], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+63], t$95$1, N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8999999999999999e-11 or 1.1499999999999999e-54 < t < 2.8999999999999999e63

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 53.7%

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

   if -1.8999999999999999e-11 < t < 1.1499999999999999e-54

   1. Initial program 91.6%

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

   3. Taylor expanded in t around 0 79.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in z around 0 46.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 46.2%

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

      2. mul-1-neg 46.2%

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

      3. *-commutative 46.2%

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

   8. Simplified 46.2%

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

   if 2.8999999999999999e63 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0 61.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 61.9%

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

      2. distribute-neg-frac2 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

      4. neg-sub0 61.9%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 61.9%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 61.9%

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

      7. mul-1-neg 61.9%

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

      8. +-commutative 61.9%

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

      9. mul-1-neg 61.9%

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

      10. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in z around 0 59.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 59.4%

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

      2. mul-1-neg 59.4%

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

   8. Simplified 59.4%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y t))))
   (if (<= t -1.8e-11)
     t_1
     (if (<= t 4.4e-55)
       (/ x (* y (- z)))
       (if (<= t 6.2e+63) t_1 (/ (/ x (- t)) z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -1.8e-11) {
		tmp = t_1;
	} else if (t <= 4.4e-55) {
		tmp = x / (y * -z);
	} else if (t <= 6.2e+63) {
		tmp = t_1;
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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 * t)
    if (t <= (-1.8d-11)) then
        tmp = t_1
    else if (t <= 4.4d-55) then
        tmp = x / (y * -z)
    else if (t <= 6.2d+63) then
        tmp = t_1
    else
        tmp = (x / -t) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (t <= -1.8e-11) {
		tmp = t_1;
	} else if (t <= 4.4e-55) {
		tmp = x / (y * -z);
	} else if (t <= 6.2e+63) {
		tmp = t_1;
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (y * t)
	tmp = 0
	if t <= -1.8e-11:
		tmp = t_1
	elif t <= 4.4e-55:
		tmp = x / (y * -z)
	elif t <= 6.2e+63:
		tmp = t_1
	else:
		tmp = (x / -t) / z
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * t))
	tmp = 0.0
	if (t <= -1.8e-11)
		tmp = t_1;
	elseif (t <= 4.4e-55)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (t <= 6.2e+63)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(-t)) / z);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * t);
	tmp = 0.0;
	if (t <= -1.8e-11)
		tmp = t_1;
	elseif (t <= 4.4e-55)
		tmp = x / (y * -z);
	elseif (t <= 6.2e+63)
		tmp = t_1;
	else
		tmp = (x / -t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e-11], t$95$1, If[LessEqual[t, 4.4e-55], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+63], t$95$1, N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.79999999999999992e-11 or 4.3999999999999999e-55 < t < 6.2000000000000001e63

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 53.7%

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

   if -1.79999999999999992e-11 < t < 4.3999999999999999e-55

   1. Initial program 91.6%

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

   3. Taylor expanded in t around 0 79.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 79.8%

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

      2. neg-mul-1 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in z around 0 46.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 46.2%

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

      2. mul-1-neg 46.2%

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

      3. *-commutative 46.2%

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

   8. Simplified 46.2%

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

   if 6.2000000000000001e63 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0 61.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 61.9%

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

      2. distribute-neg-frac2 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

      4. neg-sub0 61.9%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 61.9%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 61.9%

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

      7. mul-1-neg 61.9%

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

      8. +-commutative 61.9%

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

      9. mul-1-neg 61.9%

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

      10. unsub-neg 61.9%

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

   5. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 66.9%

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

      2. div-inv 67.0%

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

   7. Applied egg-rr 67.0%

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

   8. Taylor expanded in z around 0 54.9%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-1}{t}} \]
   9. Step-by-step derivation

      1. associate-*l/ 64.3%

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

      2. frac-2neg 64.3%

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

      3. metadata-eval 64.3%

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

      4. un-div-inv 64.3%

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

   10. Applied egg-rr 64.3%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+115} \lor \neg \left(z \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e+115) (not (<= z 1.6e+63)))
   (/ x (* z (- y z)))
   (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+115) || !(z <= 1.6e+63)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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) :: tmp
    if ((z <= (-1.4d+115)) .or. (.not. (z <= 1.6d+63))) then
        tmp = x / (z * (y - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+115) || !(z <= 1.6e+63)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e+115) or not (z <= 1.6e+63):
		tmp = x / (z * (y - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e+115) || !(z <= 1.6e+63))
		tmp = Float64(x / Float64(z * Float64(y - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e+115) || ~((z <= 1.6e+63)))
		tmp = x / (z * (y - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e+115], N[Not[LessEqual[z, 1.6e+63]], $MachinePrecision]], N[(x / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e115 or 1.60000000000000006e63 < z

   1. Initial program 83.4%

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

   3. Taylor expanded in t around 0 83.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 83.2%

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

      2. neg-mul-1 83.2%

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

   5. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]
   6. Step-by-step derivation

      1. div-inv 83.1%

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

      2. add-sqr-sqrt 37.3%

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

      3. sqrt-unprod 67.2%

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

      4. sqr-neg 67.2%

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

      5. sqrt-unprod 35.0%

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

      6. add-sqr-sqrt 70.4%

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

      7. *-commutative 70.4%

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

      8. associate-/r* 70.4%

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

   7. Applied egg-rr 70.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{y - z}}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 69.3%

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

      2. associate-*l/ 69.3%

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

      3. associate-*r/ 69.3%

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

      4. associate-*l/ 69.3%

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

      5. *-rgt-identity 69.3%

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

      6. associate-/r* 70.4%

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

   9. Simplified 70.4%

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

   if -1.4e115 < z < 1.60000000000000006e63

   1. Initial program 93.6%

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

   3. Taylor expanded in t around inf 57.3%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+115} \lor \neg \left(z \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-114}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.15e-114)
   (/ 1.0 (* t (/ y x)))
   (if (<= t 7.6e-55) (/ x (* y (- z))) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e-114) {
		tmp = 1.0 / (t * (y / x));
	} else if (t <= 7.6e-55) {
		tmp = x / (y * -z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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) :: tmp
    if (t <= (-1.15d-114)) then
        tmp = 1.0d0 / (t * (y / x))
    else if (t <= 7.6d-55) then
        tmp = x / (y * -z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e-114) {
		tmp = 1.0 / (t * (y / x));
	} else if (t <= 7.6e-55) {
		tmp = x / (y * -z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.15e-114:
		tmp = 1.0 / (t * (y / x))
	elif t <= 7.6e-55:
		tmp = x / (y * -z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.15e-114)
		tmp = Float64(1.0 / Float64(t * Float64(y / x)));
	elseif (t <= 7.6e-55)
		tmp = Float64(x / Float64(y * Float64(-z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.15e-114)
		tmp = 1.0 / (t * (y / x));
	elseif (t <= 7.6e-55)
		tmp = x / (y * -z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.15e-114], N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e-55], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e-114

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0 42.7%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   4. Step-by-step derivation

      1. clear-num 42.0%

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

      2. inv-pow 42.0%

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

      3. associate-/l* 47.3%

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

   5. Applied egg-rr 47.3%

      \[\leadsto \color{blue}{{\left(t \cdot \frac{y}{x}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 47.3%

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

   7. Simplified 47.3%

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

   if -1.15e-114 < t < 7.5999999999999993e-55

   1. Initial program 94.1%

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

   3. Taylor expanded in t around 0 84.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 84.4%

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

      2. neg-mul-1 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in z around 0 48.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 48.4%

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

      2. mul-1-neg 48.4%

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

      3. *-commutative 48.4%

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

   8. Simplified 48.4%

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

   if 7.5999999999999993e-55 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in t around inf 78.9%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-114}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e+29)
   (/ x (* y (- t z)))
   (if (<= y 1.02e-157) (/ x (* z (- z t))) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+29) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.02e-157) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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) :: tmp
    if (y <= (-6.5d+29)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.02d-157) then
        tmp = x / (z * (z - t))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+29) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.02e-157) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e+29:
		tmp = x / (y * (t - z))
	elif y <= 1.02e-157:
		tmp = x / (z * (z - t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e+29)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.02e-157)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e+29)
		tmp = x / (y * (t - z));
	elseif (y <= 1.02e-157)
		tmp = x / (z * (z - t));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+29], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-157], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.49999999999999971e29

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 85.7%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   if -6.49999999999999971e29 < y < 1.0200000000000001e-157

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 78.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 78.3%

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

      2. distribute-neg-frac2 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. neg-sub0 78.3%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 78.3%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 78.3%

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

      7. mul-1-neg 78.3%

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

      8. +-commutative 78.3%

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

      9. mul-1-neg 78.3%

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

      10. unsub-neg 78.3%

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

   5. Simplified 78.3%

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

   if 1.0200000000000001e-157 < y

   1. Initial program 86.4%

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

   3. Taylor expanded in t around inf 45.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e+57)
   (/ (/ x y) (- t z))
   (if (<= y 1.9e-157) (/ x (* z (- z t))) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+57) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.9e-157) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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) :: tmp
    if (y <= (-6.5d+57)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.9d-157) then
        tmp = x / (z * (z - t))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+57) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.9e-157) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e+57:
		tmp = (x / y) / (t - z)
	elif y <= 1.9e-157:
		tmp = x / (z * (z - t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e+57)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.9e-157)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e+57)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.9e-157)
		tmp = x / (z * (z - t));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+57], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-157], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4999999999999997e57

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 87.7%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-/l/ 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in y around inf 87.8%

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

   if -6.4999999999999997e57 < y < 1.9000000000000001e-157

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 76.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 76.5%

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

      2. distribute-neg-frac2 76.5%

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

      3. distribute-rgt-neg-in 76.5%

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

      4. neg-sub0 76.5%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 76.5%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 76.5%

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

      7. mul-1-neg 76.5%

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

      8. +-commutative 76.5%

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

      9. mul-1-neg 76.5%

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

      10. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   if 1.9000000000000001e-157 < y

   1. Initial program 86.4%

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

   3. Taylor expanded in t around inf 45.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e+58)
   (/ (/ x y) (- t z))
   (if (<= y 2.35e-157) (/ (/ x (- z t)) z) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+58) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.35e-157) {
		tmp = (x / (z - t)) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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) :: tmp
    if (y <= (-1d+58)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.35d-157) then
        tmp = (x / (z - t)) / z
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+58) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.35e-157) {
		tmp = (x / (z - t)) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1e+58:
		tmp = (x / y) / (t - z)
	elif y <= 2.35e-157:
		tmp = (x / (z - t)) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e+58)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.35e-157)
		tmp = Float64(Float64(x / Float64(z - t)) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1e+58)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.35e-157)
		tmp = (x / (z - t)) / z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1e+58], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e-157], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999944e57

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 87.7%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-/l/ 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in y around inf 87.8%

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

   if -9.99999999999999944e57 < y < 2.3500000000000001e-157

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 76.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 76.5%

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

      2. distribute-neg-frac2 76.5%

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

      3. distribute-rgt-neg-in 76.5%

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

      4. neg-sub0 76.5%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 76.5%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 76.5%

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

      7. mul-1-neg 76.5%

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

      8. +-commutative 76.5%

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

      9. mul-1-neg 76.5%

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

      10. unsub-neg 76.5%

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

   5. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 80.7%

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

      2. div-inv 80.7%

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

   7. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*l/ 85.0%

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

      2. un-div-inv 85.1%

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

   9. Applied egg-rr 85.1%

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

   if 2.3500000000000001e-157 < y

   1. Initial program 86.4%

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

   3. Taylor expanded in t around inf 45.0%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-5} \lor \neg \left(y \leq 3.2 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.2e-5) (not (<= y 3.2e-150)))
   (/ x (* y t))
   (/ x (* z (- t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e-5) || !(y <= 3.2e-150)) {
		tmp = x / (y * t);
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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) :: tmp
    if ((y <= (-7.2d-5)) .or. (.not. (y <= 3.2d-150))) then
        tmp = x / (y * t)
    else
        tmp = x / (z * -t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e-5) || !(y <= 3.2e-150)) {
		tmp = x / (y * t);
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -7.2e-5) or not (y <= 3.2e-150):
		tmp = x / (y * t)
	else:
		tmp = x / (z * -t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.2e-5) || !(y <= 3.2e-150))
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(x / Float64(z * Float64(-t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.2e-5) || ~((y <= 3.2e-150)))
		tmp = x / (y * t);
	else
		tmp = x / (z * -t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.2e-5], N[Not[LessEqual[y, 3.2e-150]], $MachinePrecision]], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000018e-5 or 3.1999999999999998e-150 < y

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 42.9%

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

   if -7.20000000000000018e-5 < y < 3.1999999999999998e-150

   1. Initial program 91.8%

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

   3. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 78.2%

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

      2. distribute-neg-frac2 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. neg-sub0 78.2%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 78.2%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 78.2%

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

      7. mul-1-neg 78.2%

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

      8. +-commutative 78.2%

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

      9. mul-1-neg 78.2%

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

      10. unsub-neg 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in z around 0 37.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 37.5%

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

      2. mul-1-neg 37.5%

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

   8. Simplified 37.5%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-5} \lor \neg \left(y \leq 3.2 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-36} \lor \neg \left(z \leq 1.05 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.6e-36) (not (<= z 1.05e+102))) (/ x (* z t)) (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-36) || !(z <= 1.05e+102)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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) :: tmp
    if ((z <= (-3.6d-36)) .or. (.not. (z <= 1.05d+102))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-36) || !(z <= 1.05e+102)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.6e-36) or not (z <= 1.05e+102):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.6e-36) || !(z <= 1.05e+102))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.6e-36) || ~((z <= 1.05e+102)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.6e-36], N[Not[LessEqual[z, 1.05e+102]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.60000000000000032e-36 or 1.05000000000000001e102 < z

   1. Initial program 86.9%

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

   3. Taylor expanded in y around 0 75.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 75.2%

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

      2. distribute-neg-frac2 75.2%

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

      3. distribute-rgt-neg-in 75.2%

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

      4. neg-sub0 75.2%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]

      5. associate--r- 75.2%

         \[\leadsto \frac{x}{z \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]

      6. neg-sub0 75.2%

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

      7. mul-1-neg 75.2%

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

      8. +-commutative 75.2%

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

      9. mul-1-neg 75.2%

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

      10. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in z around 0 37.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 37.0%

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

      2. mul-1-neg 37.0%

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

   8. Simplified 37.0%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
   9. Step-by-step derivation

      1. div-inv 37.0%

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

      2. add-sqr-sqrt 20.5%

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

      3. sqrt-unprod 42.2%

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

      4. sqr-neg 42.2%

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

      5. sqrt-unprod 14.3%

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

      6. add-sqr-sqrt 34.1%

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

      7. *-commutative 34.1%

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

   10. Applied egg-rr 34.1%

       \[\leadsto \color{blue}{x \cdot \frac{1}{z \cdot t}} \]
   11. Step-by-step derivation

       1. associate-*r/ 34.1%

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

       2. *-rgt-identity 34.1%

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

   12. Simplified 34.1%

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

   if -3.60000000000000032e-36 < z < 1.05000000000000001e102

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 50.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-36} \lor \neg \left(z \leq 1.05 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- t z)) (- y z)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - z);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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
    code = (x / (t - z)) / (y - z)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - z);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / (t - z)) / (y - z)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(t - z)) / Float64(y - z))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (t - z)) / (y - z);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.5%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Step-by-step derivation

   1. associate-/l/ 97.9%

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

3. Simplified 97.9%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
4. Add Preprocessing

5. Final simplification 97.9%

   \[\leadsto \frac{\frac{x}{t - z}}{y - z} \]
6. Add Preprocessing

Alternative 15: 39.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y \cdot t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* y t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / (y * t);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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
    code = x / (y * t)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return x / (y * t);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / (y * t)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / Float64(y * t))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (y * t);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.5%

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

3. Taylor expanded in z around 0 35.0%

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

4. Final simplification 35.0%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer target: 88.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024066 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (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))))