Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.8% → 96.7%

Time: 9.0s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

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(Float64(x * 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[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

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(Float64(x * 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[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - 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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

5. Taylor expanded in x around 0 85.9%

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

   1. *-rgt-identity 85.9%

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

   2. times-frac 79.0%

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

   3. /-rgt-identity 79.0%

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

   4. associate-/r/ 97.2%

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

7. Simplified 97.2%

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

Alternative 2: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{\frac{z}{y}}\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-244}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+127)
   (* x (+ 1.0 (/ -1.0 (/ z y))))
   (if (<= z -7.8e-52)
     (* x (/ z (- z t)))
     (if (<= z -2.4e-244)
       (/ (* x y) (- t z))
       (if (<= z 5.2e+63) (* y (/ x (- t z))) (* x (- 1.0 (/ y z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+127) {
		tmp = x * (1.0 + (-1.0 / (z / y)));
	} else if (z <= -7.8e-52) {
		tmp = x * (z / (z - t));
	} else if (z <= -2.4e-244) {
		tmp = (x * y) / (t - z);
	} else if (z <= 5.2e+63) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.7d+127)) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z / y)))
    else if (z <= (-7.8d-52)) then
        tmp = x * (z / (z - t))
    else if (z <= (-2.4d-244)) then
        tmp = (x * y) / (t - z)
    else if (z <= 5.2d+63) then
        tmp = y * (x / (t - z))
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+127) {
		tmp = x * (1.0 + (-1.0 / (z / y)));
	} else if (z <= -7.8e-52) {
		tmp = x * (z / (z - t));
	} else if (z <= -2.4e-244) {
		tmp = (x * y) / (t - z);
	} else if (z <= 5.2e+63) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+127:
		tmp = x * (1.0 + (-1.0 / (z / y)))
	elif z <= -7.8e-52:
		tmp = x * (z / (z - t))
	elif z <= -2.4e-244:
		tmp = (x * y) / (t - z)
	elif z <= 5.2e+63:
		tmp = y * (x / (t - z))
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+127)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z / y))));
	elseif (z <= -7.8e-52)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= -2.4e-244)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (z <= 5.2e+63)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.7e+127)
		tmp = x * (1.0 + (-1.0 / (z / y)));
	elseif (z <= -7.8e-52)
		tmp = x * (z / (z - t));
	elseif (z <= -2.4e-244)
		tmp = (x * y) / (t - z);
	elseif (z <= 5.2e+63)
		tmp = y * (x / (t - z));
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+127], N[(x * N[(1.0 + N[(-1.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-52], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-244], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+63], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.69999999999999989e127

   1. Initial program 72.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate-/l* 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. distribute-frac-neg 86.5%

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

      5. sub-neg 86.5%

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

      6. distribute-neg-in 86.5%

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

      7. remove-double-neg 86.5%

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

      8. +-commutative 86.5%

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

      9. sub-neg 86.5%

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

      10. div-sub 86.5%

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

      11. *-inverses 86.5%

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

   7. Simplified 86.5%

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

      1. clear-num 86.5%

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

      2. inv-pow 86.5%

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

   9. Applied egg-rr 86.5%

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

       1. unpow-1 86.5%

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

   11. Simplified 86.5%

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

   if -1.69999999999999989e127 < z < -7.80000000000000036e-52

   1. Initial program 91.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-neg-frac2 73.1%

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

      3. sub-neg 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. remove-double-neg 73.1%

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

      6. +-commutative 73.1%

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

      7. sub-neg 73.1%

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

      8. associate-/l* 78.8%

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

   7. Simplified 78.8%

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

   if -7.80000000000000036e-52 < z < -2.40000000000000016e-244

   1. Initial program 98.3%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in y around inf 87.3%

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

   if -2.40000000000000016e-244 < z < 5.2000000000000002e63

   1. Initial program 92.2%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around 0 92.2%

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

      1. *-rgt-identity 92.2%

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

      2. times-frac 96.5%

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

      3. /-rgt-identity 96.5%

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

      4. associate-/r/ 93.2%

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

   7. Simplified 93.2%

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

   8. Taylor expanded in y around inf 75.1%

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

      1. associate-*l/ 80.5%

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

      2. *-commutative 80.5%

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

   10. Simplified 80.5%

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

   if 5.2000000000000002e63 < z

   1. Initial program 74.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-/l* 88.4%

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

      3. distribute-rgt-neg-in 88.4%

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

      4. distribute-frac-neg 88.4%

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

      5. sub-neg 88.4%

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

      6. distribute-neg-in 88.4%

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

      7. remove-double-neg 88.4%

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

      8. +-commutative 88.4%

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

      9. sub-neg 88.4%

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

      10. div-sub 88.4%

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

      11. *-inverses 88.4%

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

   7. Simplified 88.4%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{\frac{z}{y}}\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-244}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.75e+127)
     t_1
     (if (<= z -2.95e-50)
       (* x (/ z (- z t)))
       (if (<= z 5.4e+63) (* x (/ y (- t z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.75e+127) {
		tmp = t_1;
	} else if (z <= -2.95e-50) {
		tmp = x * (z / (z - t));
	} else if (z <= 5.4e+63) {
		tmp = x * (y / (t - z));
	} else {
		tmp = 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 = x * (1.0d0 - (y / z))
    if (z <= (-1.75d+127)) then
        tmp = t_1
    else if (z <= (-2.95d-50)) then
        tmp = x * (z / (z - t))
    else if (z <= 5.4d+63) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.75e+127) {
		tmp = t_1;
	} else if (z <= -2.95e-50) {
		tmp = x * (z / (z - t));
	} else if (z <= 5.4e+63) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.75e+127:
		tmp = t_1
	elif z <= -2.95e-50:
		tmp = x * (z / (z - t))
	elif z <= 5.4e+63:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.75e+127)
		tmp = t_1;
	elseif (z <= -2.95e-50)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 5.4e+63)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.75e+127)
		tmp = t_1;
	elseif (z <= -2.95e-50)
		tmp = x * (z / (z - t));
	elseif (z <= 5.4e+63)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+127], t$95$1, If[LessEqual[z, -2.95e-50], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+63], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999989e127 or 5.40000000000000035e63 < z

   1. Initial program 73.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. associate-/l* 87.5%

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

      3. distribute-rgt-neg-in 87.5%

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

      4. distribute-frac-neg 87.5%

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

      5. sub-neg 87.5%

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

      6. distribute-neg-in 87.5%

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

      7. remove-double-neg 87.5%

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

      8. +-commutative 87.5%

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

      9. sub-neg 87.5%

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

      10. div-sub 87.5%

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

      11. *-inverses 87.5%

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

   7. Simplified 87.5%

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

   if -1.74999999999999989e127 < z < -2.95e-50

   1. Initial program 91.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-neg-frac2 73.1%

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

      3. sub-neg 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. remove-double-neg 73.1%

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

      6. +-commutative 73.1%

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

      7. sub-neg 73.1%

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

      8. associate-/l* 78.8%

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

   7. Simplified 78.8%

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

   if -2.95e-50 < z < 5.40000000000000035e63

   1. Initial program 94.1%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around inf 78.9%

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

      1. associate-/l* 79.2%

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

   7. Simplified 79.2%

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

Alternative 4: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+34} \lor \neg \left(t \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.8e+34) (not (<= t 3.3e-18)))
   (* x (/ (- y z) t))
   (* x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.8e+34) || !(t <= 3.3e-18)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-7.8d+34)) .or. (.not. (t <= 3.3d-18))) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.8e+34) || !(t <= 3.3e-18)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.8e+34) or not (t <= 3.3e-18):
		tmp = x * ((y - z) / t)
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.8e+34) || !(t <= 3.3e-18))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7.8e+34) || ~((t <= 3.3e-18)))
		tmp = x * ((y - z) / t);
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.8e+34], N[Not[LessEqual[t, 3.3e-18]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.80000000000000038e34 or 3.3000000000000002e-18 < t

   1. Initial program 86.4%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around inf 71.4%

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

      1. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

   if -7.80000000000000038e34 < t < 3.3000000000000002e-18

   1. Initial program 85.6%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. associate-/l* 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. distribute-frac-neg 83.0%

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

      5. sub-neg 83.0%

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

      6. distribute-neg-in 83.0%

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

      7. remove-double-neg 83.0%

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

      8. +-commutative 83.0%

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

      9. sub-neg 83.0%

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

      10. div-sub 83.0%

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

      11. *-inverses 83.0%

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

   7. Simplified 83.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+34} \lor \neg \left(t \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-50} \lor \neg \left(z \leq 5.8 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.1e-50) (not (<= z 5.8e+63)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e-50) || !(z <= 5.8e+63)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.1d-50)) .or. (.not. (z <= 5.8d+63))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e-50) || !(z <= 5.8e+63)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.1e-50) or not (z <= 5.8e+63):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.1e-50) || !(z <= 5.8e+63))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.1e-50) || ~((z <= 5.8e+63)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.1e-50], N[Not[LessEqual[z, 5.8e+63]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e-50 or 5.7999999999999999e63 < z

   1. Initial program 78.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. associate-/l* 80.5%

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

      3. distribute-rgt-neg-in 80.5%

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

      4. distribute-frac-neg 80.5%

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

      5. sub-neg 80.5%

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

      6. distribute-neg-in 80.5%

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

      7. remove-double-neg 80.5%

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

      8. +-commutative 80.5%

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

      9. sub-neg 80.5%

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

      10. div-sub 80.5%

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

      11. *-inverses 80.5%

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

   7. Simplified 80.5%

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

   if -1.0999999999999999e-50 < z < 5.7999999999999999e63

   1. Initial program 94.1%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around inf 78.9%

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

      1. associate-/l* 79.2%

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

   7. Simplified 79.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-50} \lor \neg \left(z \leq 5.8 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.1e+32)
   (* x (/ y t))
   (if (<= t 3.6e-20) (* x (- 1.0 (/ y z))) (/ x (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e+32) {
		tmp = x * (y / t);
	} else if (t <= 3.6e-20) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / 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
    real(8) :: tmp
    if (t <= (-2.1d+32)) then
        tmp = x * (y / t)
    else if (t <= 3.6d-20) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e+32) {
		tmp = x * (y / t);
	} else if (t <= 3.6e-20) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e+32:
		tmp = x * (y / t)
	elif t <= 3.6e-20:
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.1e+32)
		tmp = Float64(x * Float64(y / t));
	elseif (t <= 3.6e-20)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.1e+32)
		tmp = x * (y / t);
	elseif (t <= 3.6e-20)
		tmp = x * (1.0 - (y / z));
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.1e+32], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-20], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1000000000000001e32

   1. Initial program 88.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 70.4%

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

      1. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

   if -2.1000000000000001e32 < t < 3.59999999999999974e-20

   1. Initial program 85.6%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. associate-/l* 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. distribute-frac-neg 83.0%

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

      5. sub-neg 83.0%

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

      6. distribute-neg-in 83.0%

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

      7. remove-double-neg 83.0%

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

      8. +-commutative 83.0%

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

      9. sub-neg 83.0%

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

      10. div-sub 83.0%

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

      11. *-inverses 83.0%

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

   7. Simplified 83.0%

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

   if 3.59999999999999974e-20 < t

   1. Initial program 84.9%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around 0 84.9%

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

      1. *-rgt-identity 84.9%

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

      2. times-frac 69.4%

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

      3. /-rgt-identity 69.4%

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

      4. associate-/r/ 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in z around 0 53.7%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.4e-50) x (if (<= z 5e+63) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.4e-50) {
		tmp = x;
	} else if (z <= 5e+63) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	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) :: tmp
    if (z <= (-7.4d-50)) then
        tmp = x
    else if (z <= 5d+63) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.4e-50) {
		tmp = x;
	} else if (z <= 5e+63) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.4e-50:
		tmp = x
	elif z <= 5e+63:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.4e-50)
		tmp = x;
	elseif (z <= 5e+63)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.4e-50)
		tmp = x;
	elseif (z <= 5e+63)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.4e-50], x, If[LessEqual[z, 5e+63], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4000000000000002e-50 or 5.00000000000000011e63 < z

   1. Initial program 78.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{x} \]

   if -7.4000000000000002e-50 < z < 5.00000000000000011e63

   1. Initial program 94.1%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around 0 62.0%

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

      1. associate-/l* 64.2%

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

   7. Simplified 64.2%

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

Alternative 8: 96.8% accurate, 1.0× speedup

Math

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

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]

Derivation

1. Initial program 85.9%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

Alternative 9: 34.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 85.9%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

5. Taylor expanded in z around inf 39.3%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - 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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ (- t z) (- y z))))

  (/ (* x (- y z)) (- t z)))