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

Percentage Accurate: 84.2% → 97.2%

Time: 10.1s

Alternatives: 10

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: 84.2% 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: 97.2% 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 80.4%

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

   1. associate-/l* 97.9%

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

3. Simplified 97.9%

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

   1. clear-num 97.8%

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

   2. un-div-inv 98.3%

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

6. Applied egg-rr 98.3%

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

7. Final simplification 98.3%

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

Alternative 2: 70.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-73}:\\ \;\;\;\;-\frac{x \cdot z}{t}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.06e-9)
     t_1
     (if (<= z -1.95e-73)
       (- (/ (* x z) t))
       (if (<= z -3.4e-89)
         (* x (/ y t))
         (if (<= z -5.8e-136)
           (/ (* x (- y)) z)
           (if (<= z 6.9e-54) (/ x (/ t y)) 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 <= -1.06e-9) {
		tmp = t_1;
	} else if (z <= -1.95e-73) {
		tmp = -((x * z) / t);
	} else if (z <= -3.4e-89) {
		tmp = x * (y / t);
	} else if (z <= -5.8e-136) {
		tmp = (x * -y) / z;
	} else if (z <= 6.9e-54) {
		tmp = x / (t / y);
	} 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 <= (-1.06d-9)) then
        tmp = t_1
    else if (z <= (-1.95d-73)) then
        tmp = -((x * z) / t)
    else if (z <= (-3.4d-89)) then
        tmp = x * (y / t)
    else if (z <= (-5.8d-136)) then
        tmp = (x * -y) / z
    else if (z <= 6.9d-54) then
        tmp = x / (t / y)
    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 <= -1.06e-9) {
		tmp = t_1;
	} else if (z <= -1.95e-73) {
		tmp = -((x * z) / t);
	} else if (z <= -3.4e-89) {
		tmp = x * (y / t);
	} else if (z <= -5.8e-136) {
		tmp = (x * -y) / z;
	} else if (z <= 6.9e-54) {
		tmp = x / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.06e-9:
		tmp = t_1
	elif z <= -1.95e-73:
		tmp = -((x * z) / t)
	elif z <= -3.4e-89:
		tmp = x * (y / t)
	elif z <= -5.8e-136:
		tmp = (x * -y) / z
	elif z <= 6.9e-54:
		tmp = x / (t / y)
	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 <= -1.06e-9)
		tmp = t_1;
	elseif (z <= -1.95e-73)
		tmp = Float64(-Float64(Float64(x * z) / t));
	elseif (z <= -3.4e-89)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= -5.8e-136)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 6.9e-54)
		tmp = Float64(x / Float64(t / y));
	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 <= -1.06e-9)
		tmp = t_1;
	elseif (z <= -1.95e-73)
		tmp = -((x * z) / t);
	elseif (z <= -3.4e-89)
		tmp = x * (y / t);
	elseif (z <= -5.8e-136)
		tmp = (x * -y) / z;
	elseif (z <= 6.9e-54)
		tmp = x / (t / y);
	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, -1.06e-9], t$95$1, If[LessEqual[z, -1.95e-73], (-N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision]), If[LessEqual[z, -3.4e-89], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-136], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 6.9e-54], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.0600000000000001e-9 or 6.89999999999999969e-54 < z

   1. Initial program 72.3%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. associate-/l* 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. distribute-frac-neg 73.2%

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

      5. neg-sub0 73.2%

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

      6. associate--r- 73.2%

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

      7. neg-sub0 73.2%

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

      8. +-commutative 73.2%

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

      9. sub-neg 73.2%

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

      10. div-sub 73.2%

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

      11. *-inverses 73.2%

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

   7. Simplified 73.2%

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

   if -1.0600000000000001e-9 < z < -1.94999999999999991e-73

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. mul-1-neg 75.5%

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

      3. distribute-rgt-neg-out 75.5%

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

      4. associate-*l/ 75.3%

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

      5. *-commutative 75.3%

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

      6. distribute-lft-neg-out 75.3%

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

      7. distribute-rgt-neg-in 75.3%

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

   9. Simplified 75.3%

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

   10. Taylor expanded in z around 0 72.3%

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

       1. associate-*r/ 72.3%

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

       2. mul-1-neg 72.3%

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

       3. distribute-lft-neg-out 72.3%

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

       4. *-commutative 72.3%

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

   12. Simplified 72.3%

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

   if -1.94999999999999991e-73 < z < -3.4e-89

   1. Initial program 61.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 41.9%

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

      1. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   if -3.4e-89 < z < -5.79999999999999989e-136

   1. Initial program 99.7%

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

      1. associate-/l* 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in t around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. associate-/l* 5.3%

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

      3. distribute-rgt-neg-in 5.3%

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

      4. distribute-frac-neg 5.3%

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

      5. neg-sub0 5.3%

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

      6. associate--r- 5.3%

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

      7. neg-sub0 5.3%

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

      8. +-commutative 5.3%

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

      9. sub-neg 5.3%

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

      10. div-sub 5.3%

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

      11. *-inverses 5.3%

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

   7. Simplified 5.3%

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

   8. Taylor expanded in y around inf 75.7%

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

      1. associate-*r/ 75.7%

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

      2. mul-1-neg 75.7%

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

      3. distribute-rgt-neg-out 75.7%

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

   10. Simplified 75.7%

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

   if -5.79999999999999989e-136 < z < 6.89999999999999969e-54

   1. Initial program 91.1%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in z around 0 78.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-73}:\\ \;\;\;\;-\frac{x \cdot z}{t}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+39} \lor \neg \left(z \leq -1.35 \cdot 10^{+14}\right) \land \left(z \leq -2.5 \cdot 10^{-11} \lor \neg \left(z \leq 1.66 \cdot 10^{+25}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e+39)
         (and (not (<= z -1.35e+14))
              (or (<= z -2.5e-11) (not (<= z 1.66e+25)))))
   (* x (- 1.0 (/ y z)))
   (* x (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+39) || (!(z <= -1.35e+14) && ((z <= -2.5e-11) || !(z <= 1.66e+25)))) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * ((y - z) / t);
	}
	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 <= (-7.5d+39)) .or. (.not. (z <= (-1.35d+14))) .and. (z <= (-2.5d-11)) .or. (.not. (z <= 1.66d+25))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+39) || (!(z <= -1.35e+14) && ((z <= -2.5e-11) || !(z <= 1.66e+25)))) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e+39) or (not (z <= -1.35e+14) and ((z <= -2.5e-11) or not (z <= 1.66e+25))):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e+39) || (!(z <= -1.35e+14) && ((z <= -2.5e-11) || !(z <= 1.66e+25))))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e+39) || (~((z <= -1.35e+14)) && ((z <= -2.5e-11) || ~((z <= 1.66e+25)))))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e+39], And[N[Not[LessEqual[z, -1.35e+14]], $MachinePrecision], Or[LessEqual[z, -2.5e-11], N[Not[LessEqual[z, 1.66e+25]], $MachinePrecision]]]], N[(x * N[(1.0 - 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 < -7.5000000000000005e39 or -1.35e14 < z < -2.50000000000000009e-11 or 1.6600000000000001e25 < z

   1. Initial program 69.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 56.3%

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

      1. mul-1-neg 56.3%

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

      2. associate-/l* 79.8%

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

      3. distribute-rgt-neg-in 79.8%

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

      4. distribute-frac-neg 79.8%

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

      5. neg-sub0 79.8%

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

      6. associate--r- 79.8%

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

      7. neg-sub0 79.8%

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

      8. +-commutative 79.8%

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

      9. sub-neg 79.8%

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

      10. div-sub 79.8%

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

      11. *-inverses 79.8%

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

   7. Simplified 79.8%

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

   if -7.5000000000000005e39 < z < -1.35e14 or -2.50000000000000009e-11 < z < 1.6600000000000001e25

   1. Initial program 90.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf 76.4%

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

      1. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+39} \lor \neg \left(z \leq -1.35 \cdot 10^{+14}\right) \land \left(z \leq -2.5 \cdot 10^{-11} \lor \neg \left(z \leq 1.66 \cdot 10^{+25}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -5.5e+39)
     t_2
     (if (<= z -9.5e+16)
       t_1
       (if (<= z -1.6e-9) t_2 (if (<= z 2.06e+18) t_1 (- x (* x (/ y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.5e+39) {
		tmp = t_2;
	} else if (z <= -9.5e+16) {
		tmp = t_1;
	} else if (z <= -1.6e-9) {
		tmp = t_2;
	} else if (z <= 2.06e+18) {
		tmp = t_1;
	} else {
		tmp = x - (x * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - z) / t)
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-5.5d+39)) then
        tmp = t_2
    else if (z <= (-9.5d+16)) then
        tmp = t_1
    else if (z <= (-1.6d-9)) then
        tmp = t_2
    else if (z <= 2.06d+18) then
        tmp = t_1
    else
        tmp = x - (x * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.5e+39) {
		tmp = t_2;
	} else if (z <= -9.5e+16) {
		tmp = t_1;
	} else if (z <= -1.6e-9) {
		tmp = t_2;
	} else if (z <= 2.06e+18) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -5.5e+39:
		tmp = t_2
	elif z <= -9.5e+16:
		tmp = t_1
	elif z <= -1.6e-9:
		tmp = t_2
	elif z <= 2.06e+18:
		tmp = t_1
	else:
		tmp = x - (x * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -5.5e+39)
		tmp = t_2;
	elseif (z <= -9.5e+16)
		tmp = t_1;
	elseif (z <= -1.6e-9)
		tmp = t_2;
	elseif (z <= 2.06e+18)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -5.5e+39)
		tmp = t_2;
	elseif (z <= -9.5e+16)
		tmp = t_1;
	elseif (z <= -1.6e-9)
		tmp = t_2;
	elseif (z <= 2.06e+18)
		tmp = t_1;
	else
		tmp = x - (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+39], t$95$2, If[LessEqual[z, -9.5e+16], t$95$1, If[LessEqual[z, -1.6e-9], t$95$2, If[LessEqual[z, 2.06e+18], t$95$1, N[(x - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999997e39 or -9.5e16 < z < -1.60000000000000006e-9

   1. Initial program 77.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-/l* 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

      4. distribute-frac-neg 80.1%

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

      5. neg-sub0 80.1%

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

      6. associate--r- 80.1%

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

      7. neg-sub0 80.1%

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

      8. +-commutative 80.1%

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

      9. sub-neg 80.1%

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

      10. div-sub 80.1%

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

      11. *-inverses 80.1%

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

   7. Simplified 80.1%

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

   if -5.4999999999999997e39 < z < -9.5e16 or -1.60000000000000006e-9 < z < 2.06e18

   1. Initial program 90.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf 76.4%

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

      1. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

   if 2.06e18 < z

   1. Initial program 60.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 70.3%

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

      1. associate--l+ 70.3%

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

      2. distribute-lft-out-- 70.3%

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

      3. div-sub 70.3%

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

      4. mul-1-neg 70.3%

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

      5. unsub-neg 70.3%

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

      6. *-commutative 70.3%

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

      7. distribute-lft-out-- 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 79.6%

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

   10. Simplified 79.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y - z}}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -45000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t (- y z)))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -8.8e+39)
     t_2
     (if (<= z -45000000000000.0)
       t_1
       (if (<= z -5e-9) t_2 (if (<= z 2e+22) t_1 (- x (* x (/ y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / (y - z));
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -8.8e+39) {
		tmp = t_2;
	} else if (z <= -45000000000000.0) {
		tmp = t_1;
	} else if (z <= -5e-9) {
		tmp = t_2;
	} else if (z <= 2e+22) {
		tmp = t_1;
	} else {
		tmp = x - (x * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (t / (y - z))
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-8.8d+39)) then
        tmp = t_2
    else if (z <= (-45000000000000.0d0)) then
        tmp = t_1
    else if (z <= (-5d-9)) then
        tmp = t_2
    else if (z <= 2d+22) then
        tmp = t_1
    else
        tmp = x - (x * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / (y - z));
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -8.8e+39) {
		tmp = t_2;
	} else if (z <= -45000000000000.0) {
		tmp = t_1;
	} else if (z <= -5e-9) {
		tmp = t_2;
	} else if (z <= 2e+22) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / (y - z))
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -8.8e+39:
		tmp = t_2
	elif z <= -45000000000000.0:
		tmp = t_1
	elif z <= -5e-9:
		tmp = t_2
	elif z <= 2e+22:
		tmp = t_1
	else:
		tmp = x - (x * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / Float64(y - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -8.8e+39)
		tmp = t_2;
	elseif (z <= -45000000000000.0)
		tmp = t_1;
	elseif (z <= -5e-9)
		tmp = t_2;
	elseif (z <= 2e+22)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / (y - z));
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -8.8e+39)
		tmp = t_2;
	elseif (z <= -45000000000000.0)
		tmp = t_1;
	elseif (z <= -5e-9)
		tmp = t_2;
	elseif (z <= 2e+22)
		tmp = t_1;
	else
		tmp = x - (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+39], t$95$2, If[LessEqual[z, -45000000000000.0], t$95$1, If[LessEqual[z, -5e-9], t$95$2, If[LessEqual[z, 2e+22], t$95$1, N[(x - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.8000000000000006e39 or -4.5e13 < z < -5.0000000000000001e-9

   1. Initial program 77.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-/l* 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

      4. distribute-frac-neg 80.1%

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

      5. neg-sub0 80.1%

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

      6. associate--r- 80.1%

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

      7. neg-sub0 80.1%

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

      8. +-commutative 80.1%

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

      9. sub-neg 80.1%

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

      10. div-sub 80.1%

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

      11. *-inverses 80.1%

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

   7. Simplified 80.1%

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

   if -8.8000000000000006e39 < z < -4.5e13 or -5.0000000000000001e-9 < z < 2e22

   1. Initial program 90.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

      1. clear-num 96.1%

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

      2. un-div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in t around inf 84.4%

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

   if 2e22 < z

   1. Initial program 60.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 70.3%

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

      1. associate--l+ 70.3%

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

      2. distribute-lft-out-- 70.3%

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

      3. div-sub 70.3%

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

      4. mul-1-neg 70.3%

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

      5. unsub-neg 70.3%

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

      6. *-commutative 70.3%

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

      7. distribute-lft-out-- 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 79.6%

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

   10. Simplified 79.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -45000000000000:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -24000000000000 \lor \neg \left(z \leq -8.5 \cdot 10^{-10}\right) \land z \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.7e+39)
   x
   (if (or (<= z -24000000000000.0)
           (and (not (<= z -8.5e-10)) (<= z 1.95e+34)))
     (* x (/ y t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.7e+39) {
		tmp = x;
	} else if ((z <= -24000000000000.0) || (!(z <= -8.5e-10) && (z <= 1.95e+34))) {
		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 <= (-4.7d+39)) then
        tmp = x
    else if ((z <= (-24000000000000.0d0)) .or. (.not. (z <= (-8.5d-10))) .and. (z <= 1.95d+34)) 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 <= -4.7e+39) {
		tmp = x;
	} else if ((z <= -24000000000000.0) || (!(z <= -8.5e-10) && (z <= 1.95e+34))) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.7e+39:
		tmp = x
	elif (z <= -24000000000000.0) or (not (z <= -8.5e-10) and (z <= 1.95e+34)):
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.7e+39)
		tmp = x;
	elseif ((z <= -24000000000000.0) || (!(z <= -8.5e-10) && (z <= 1.95e+34)))
		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 <= -4.7e+39)
		tmp = x;
	elseif ((z <= -24000000000000.0) || (~((z <= -8.5e-10)) && (z <= 1.95e+34)))
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.7e+39], x, If[Or[LessEqual[z, -24000000000000.0], And[N[Not[LessEqual[z, -8.5e-10]], $MachinePrecision], LessEqual[z, 1.95e+34]]], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6999999999999999e39 or -2.4e13 < z < -8.4999999999999996e-10 or 1.9500000000000001e34 < z

   1. Initial program 68.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 inf 60.8%

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

   if -4.6999999999999999e39 < z < -2.4e13 or -8.4999999999999996e-10 < z < 1.9500000000000001e34

   1. Initial program 90.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 64.3%

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

      1. associate-/l* 70.2%

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

   7. Simplified 70.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -24000000000000 \lor \neg \left(z \leq -8.5 \cdot 10^{-10}\right) \land z \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -25000000000000 \lor \neg \left(z \leq -1.22 \cdot 10^{-8}\right) \land z \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.8e+39)
   x
   (if (or (<= z -25000000000000.0) (and (not (<= z -1.22e-8)) (<= z 5.5e+35)))
     (/ x (/ t y))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.8e+39) {
		tmp = x;
	} else if ((z <= -25000000000000.0) || (!(z <= -1.22e-8) && (z <= 5.5e+35))) {
		tmp = x / (t / y);
	} 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 <= (-8.8d+39)) then
        tmp = x
    else if ((z <= (-25000000000000.0d0)) .or. (.not. (z <= (-1.22d-8))) .and. (z <= 5.5d+35)) then
        tmp = x / (t / y)
    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 <= -8.8e+39) {
		tmp = x;
	} else if ((z <= -25000000000000.0) || (!(z <= -1.22e-8) && (z <= 5.5e+35))) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.8e+39:
		tmp = x
	elif (z <= -25000000000000.0) or (not (z <= -1.22e-8) and (z <= 5.5e+35)):
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.8e+39)
		tmp = x;
	elseif ((z <= -25000000000000.0) || (!(z <= -1.22e-8) && (z <= 5.5e+35)))
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.8e+39)
		tmp = x;
	elseif ((z <= -25000000000000.0) || (~((z <= -1.22e-8)) && (z <= 5.5e+35)))
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.8e+39], x, If[Or[LessEqual[z, -25000000000000.0], And[N[Not[LessEqual[z, -1.22e-8]], $MachinePrecision], LessEqual[z, 5.5e+35]]], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000006e39 or -2.5e13 < z < -1.22e-8 or 5.50000000000000001e35 < z

   1. Initial program 68.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 inf 60.8%

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

   if -8.8000000000000006e39 < z < -2.5e13 or -1.22e-8 < z < 5.50000000000000001e35

   1. Initial program 90.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

      1. clear-num 96.2%

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

      2. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around 0 70.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -25000000000000 \lor \neg \left(z \leq -1.22 \cdot 10^{-8}\right) \land z \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.6e-73)
   (* x (/ z (- z t)))
   (if (<= z 6.5e-54) (/ x (/ t y)) (* x (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e-73) {
		tmp = x * (z / (z - t));
	} else if (z <= 6.5e-54) {
		tmp = x / (t / y);
	} 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 <= (-4.6d-73)) then
        tmp = x * (z / (z - t))
    else if (z <= 6.5d-54) then
        tmp = x / (t / y)
    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 <= -4.6e-73) {
		tmp = x * (z / (z - t));
	} else if (z <= 6.5e-54) {
		tmp = x / (t / y);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.6e-73:
		tmp = x * (z / (z - t))
	elif z <= 6.5e-54:
		tmp = x / (t / y)
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.6e-73)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 6.5e-54)
		tmp = Float64(x / Float64(t / y));
	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 <= -4.6e-73)
		tmp = x * (z / (z - t));
	elseif (z <= 6.5e-54)
		tmp = x / (t / y);
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.6e-73], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-54], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.59999999999999977e-73

   1. Initial program 80.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. distribute-neg-frac2 60.8%

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

      3. neg-sub0 60.8%

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

      4. associate--r- 60.8%

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

      5. neg-sub0 60.8%

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

      6. +-commutative 60.8%

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

      7. sub-neg 60.8%

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

      8. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   if -4.59999999999999977e-73 < z < 6.49999999999999991e-54

   1. Initial program 90.1%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in z around 0 78.0%

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

   if 6.49999999999999991e-54 < z

   1. Initial program 66.6%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. associate-/l* 72.5%

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

      3. distribute-rgt-neg-in 72.5%

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

      4. distribute-frac-neg 72.5%

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

      5. neg-sub0 72.5%

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

      6. associate--r- 72.5%

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

      7. neg-sub0 72.5%

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

      8. +-commutative 72.5%

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

      9. sub-neg 72.5%

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

      10. div-sub 72.5%

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

      11. *-inverses 72.5%

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

   7. Simplified 72.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.1% 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 80.4%

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

   1. associate-/l* 97.9%

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

3. Simplified 97.9%

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

5. Final simplification 97.9%

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

Alternative 10: 35.6% 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 80.4%

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

   1. associate-/l* 97.9%

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

3. Simplified 97.9%

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

5. Taylor expanded in z around inf 33.1%

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

6. Final simplification 33.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.2% 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 2024073 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

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