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

Percentage Accurate: 84.2% → 97.2%

Time: 8.4s

Alternatives: 12

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 85.9%

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

   1. associate-*l/ 82.2%

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

3. Simplified 82.2%

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

   1. associate-/r/ 97.7%

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

5. Applied egg-rr 97.7%

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

6. Final simplification 97.7%

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

Alternative 2: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-123} \lor \neg \left(y \leq 2.3 \cdot 10^{-97}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -2.25e-41)
     t_1
     (if (<= y -4.1e-98)
       x
       (if (or (<= y -2.15e-123) (not (<= y 2.3e-97)))
         t_1
         (* z (/ x (- z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -2.25e-41) {
		tmp = t_1;
	} else if (y <= -4.1e-98) {
		tmp = x;
	} else if ((y <= -2.15e-123) || !(y <= 2.3e-97)) {
		tmp = t_1;
	} else {
		tmp = z * (x / (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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (y <= (-2.25d-41)) then
        tmp = t_1
    else if (y <= (-4.1d-98)) then
        tmp = x
    else if ((y <= (-2.15d-123)) .or. (.not. (y <= 2.3d-97))) then
        tmp = t_1
    else
        tmp = z * (x / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -2.25e-41) {
		tmp = t_1;
	} else if (y <= -4.1e-98) {
		tmp = x;
	} else if ((y <= -2.15e-123) || !(y <= 2.3e-97)) {
		tmp = t_1;
	} else {
		tmp = z * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -2.25e-41:
		tmp = t_1
	elif y <= -4.1e-98:
		tmp = x
	elif (y <= -2.15e-123) or not (y <= 2.3e-97):
		tmp = t_1
	else:
		tmp = z * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -2.25e-41)
		tmp = t_1;
	elseif (y <= -4.1e-98)
		tmp = x;
	elseif ((y <= -2.15e-123) || !(y <= 2.3e-97))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -2.25e-41)
		tmp = t_1;
	elseif (y <= -4.1e-98)
		tmp = x;
	elseif ((y <= -2.15e-123) || ~((y <= 2.3e-97)))
		tmp = t_1;
	else
		tmp = z * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e-41], t$95$1, If[LessEqual[y, -4.1e-98], x, If[Or[LessEqual[y, -2.15e-123], N[Not[LessEqual[y, 2.3e-97]], $MachinePrecision]], t$95$1, N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25e-41 or -4.0999999999999998e-98 < y < -2.15000000000000016e-123 or 2.29999999999999994e-97 < y

   1. Initial program 85.9%

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

      1. associate-*l/ 81.6%

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

   3. Simplified 81.6%

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

      1. associate-*l/ 85.9%

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

      2. clear-num 85.8%

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

   5. Applied egg-rr 85.8%

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

   6. Taylor expanded in y around inf 69.1%

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

      1. associate-/l* 70.6%

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

   8. Simplified 70.6%

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

      1. associate-/r/ 78.9%

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

   10. Applied egg-rr 78.9%

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

   if -2.25e-41 < y < -4.0999999999999998e-98

   1. Initial program 81.0%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in z around inf 87.4%

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

   if -2.15000000000000016e-123 < y < 2.29999999999999994e-97

   1. Initial program 86.9%

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

      1. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in y around 0 80.7%

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

      1. associate-*r/ 78.4%

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

      2. associate-*l* 78.4%

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

      3. neg-mul-1 78.4%

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

      4. *-commutative 78.4%

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

   6. Simplified 78.4%

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

      1. associate-*l/ 80.7%

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

      2. frac-2neg 80.7%

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

      3. add-sqr-sqrt 47.5%

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

      4. sqrt-unprod 41.6%

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

      5. sqr-neg 41.6%

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

      6. sqrt-unprod 6.0%

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

      7. add-sqr-sqrt 18.6%

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

      8. distribute-rgt-neg-out 18.6%

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

      9. add-sqr-sqrt 12.7%

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

      10. sqrt-unprod 41.7%

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

      11. sqr-neg 41.7%

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

      12. sqrt-unprod 32.8%

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

      13. add-sqr-sqrt 80.7%

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

      14. sub-neg 80.7%

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

      15. distribute-neg-in 80.7%

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

      16. add-sqr-sqrt 47.6%

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

      17. sqrt-unprod 56.0%

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

      18. sqr-neg 56.0%

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

      19. sqrt-unprod 18.0%

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

      20. add-sqr-sqrt 41.4%

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

      21. add-sqr-sqrt 23.4%

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

      22. sqrt-unprod 51.5%

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

      23. sqr-neg 51.5%

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

   8. Applied egg-rr 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*r/ 78.4%

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

      3. +-commutative 78.4%

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

      4. unsub-neg 78.4%

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

   10. Simplified 78.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-123} \lor \neg \left(y \leq 2.3 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \end{array} \]

Alternative 3: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{t - z}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-129}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x (- t z)))))
   (if (<= y -4.8e-30)
     t_1
     (if (<= y -8.2e-104)
       x
       (if (<= y -2.9e-129)
         (* (- y z) (/ x t))
         (if (<= y 1.06e-98) (* z (/ x (- z t))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double tmp;
	if (y <= -4.8e-30) {
		tmp = t_1;
	} else if (y <= -8.2e-104) {
		tmp = x;
	} else if (y <= -2.9e-129) {
		tmp = (y - z) * (x / t);
	} else if (y <= 1.06e-98) {
		tmp = z * (x / (z - t));
	} 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 = y * (x / (t - z))
    if (y <= (-4.8d-30)) then
        tmp = t_1
    else if (y <= (-8.2d-104)) then
        tmp = x
    else if (y <= (-2.9d-129)) then
        tmp = (y - z) * (x / t)
    else if (y <= 1.06d-98) then
        tmp = z * (x / (z - t))
    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 = y * (x / (t - z));
	double tmp;
	if (y <= -4.8e-30) {
		tmp = t_1;
	} else if (y <= -8.2e-104) {
		tmp = x;
	} else if (y <= -2.9e-129) {
		tmp = (y - z) * (x / t);
	} else if (y <= 1.06e-98) {
		tmp = z * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / (t - z))
	tmp = 0
	if y <= -4.8e-30:
		tmp = t_1
	elif y <= -8.2e-104:
		tmp = x
	elif y <= -2.9e-129:
		tmp = (y - z) * (x / t)
	elif y <= 1.06e-98:
		tmp = z * (x / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / Float64(t - z)))
	tmp = 0.0
	if (y <= -4.8e-30)
		tmp = t_1;
	elseif (y <= -8.2e-104)
		tmp = x;
	elseif (y <= -2.9e-129)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (y <= 1.06e-98)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / (t - z));
	tmp = 0.0;
	if (y <= -4.8e-30)
		tmp = t_1;
	elseif (y <= -8.2e-104)
		tmp = x;
	elseif (y <= -2.9e-129)
		tmp = (y - z) * (x / t);
	elseif (y <= 1.06e-98)
		tmp = z * (x / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e-30], t$95$1, If[LessEqual[y, -8.2e-104], x, If[LessEqual[y, -2.9e-129], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e-98], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7999999999999997e-30 or 1.0600000000000001e-98 < y

   1. Initial program 85.1%

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

      1. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around inf 69.3%

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

      1. associate-*r/ 72.3%

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

   6. Simplified 72.3%

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

   if -4.7999999999999997e-30 < y < -8.19999999999999968e-104

   1. Initial program 83.3%

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

      1. associate-*l/ 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in z around inf 78.0%

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

   if -8.19999999999999968e-104 < y < -2.90000000000000017e-129

   1. Initial program 99.6%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in t around inf 76.7%

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

   if -2.90000000000000017e-129 < y < 1.0600000000000001e-98

   1. Initial program 86.7%

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

      1. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in y around 0 80.4%

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

      1. associate-*r/ 78.2%

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

      2. associate-*l* 78.2%

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

      3. neg-mul-1 78.2%

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

      4. *-commutative 78.2%

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

   6. Simplified 78.2%

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

      1. associate-*l/ 80.4%

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

      2. frac-2neg 80.4%

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

      3. add-sqr-sqrt 46.9%

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

      4. sqrt-unprod 40.9%

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

      5. sqr-neg 40.9%

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

      6. sqrt-unprod 6.0%

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

      7. add-sqr-sqrt 18.8%

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

      8. distribute-rgt-neg-out 18.8%

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

      9. add-sqr-sqrt 12.8%

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

      10. sqrt-unprod 42.2%

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

      11. sqr-neg 42.2%

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

      12. sqrt-unprod 33.2%

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

      13. add-sqr-sqrt 80.4%

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

      14. sub-neg 80.4%

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

      15. distribute-neg-in 80.4%

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

      16. add-sqr-sqrt 47.0%

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

      17. sqrt-unprod 55.5%

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

      18. sqr-neg 55.5%

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

      19. sqrt-unprod 18.2%

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

      20. add-sqr-sqrt 40.7%

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

      21. add-sqr-sqrt 22.4%

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

      22. sqrt-unprod 50.9%

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

      23. sqr-neg 50.9%

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

   8. Applied egg-rr 80.4%

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

      1. *-commutative 80.4%

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

      2. associate-*r/ 78.2%

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

      3. +-commutative 78.2%

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

      4. unsub-neg 78.2%

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

   10. Simplified 78.2%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-129}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 4: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))))
   (if (<= y -7.8e-34)
     t_1
     (if (<= y -1.26e-99)
       x
       (if (<= y -2.15e-123)
         t_1
         (if (<= y 1.02e-97) (* z (/ x (- z t))) (* x (/ y (- t z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double tmp;
	if (y <= -7.8e-34) {
		tmp = t_1;
	} else if (y <= -1.26e-99) {
		tmp = x;
	} else if (y <= -2.15e-123) {
		tmp = t_1;
	} else if (y <= 1.02e-97) {
		tmp = z * (x / (z - t));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((t - z) / y)
    if (y <= (-7.8d-34)) then
        tmp = t_1
    else if (y <= (-1.26d-99)) then
        tmp = x
    else if (y <= (-2.15d-123)) then
        tmp = t_1
    else if (y <= 1.02d-97) then
        tmp = z * (x / (z - t))
    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 t_1 = x / ((t - z) / y);
	double tmp;
	if (y <= -7.8e-34) {
		tmp = t_1;
	} else if (y <= -1.26e-99) {
		tmp = x;
	} else if (y <= -2.15e-123) {
		tmp = t_1;
	} else if (y <= 1.02e-97) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	tmp = 0
	if y <= -7.8e-34:
		tmp = t_1
	elif y <= -1.26e-99:
		tmp = x
	elif y <= -2.15e-123:
		tmp = t_1
	elif y <= 1.02e-97:
		tmp = z * (x / (z - t))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) / y))
	tmp = 0.0
	if (y <= -7.8e-34)
		tmp = t_1;
	elseif (y <= -1.26e-99)
		tmp = x;
	elseif (y <= -2.15e-123)
		tmp = t_1;
	elseif (y <= 1.02e-97)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) / y);
	tmp = 0.0;
	if (y <= -7.8e-34)
		tmp = t_1;
	elseif (y <= -1.26e-99)
		tmp = x;
	elseif (y <= -2.15e-123)
		tmp = t_1;
	elseif (y <= 1.02e-97)
		tmp = z * (x / (z - t));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e-34], t$95$1, If[LessEqual[y, -1.26e-99], x, If[LessEqual[y, -2.15e-123], t$95$1, If[LessEqual[y, 1.02e-97], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.79999999999999982e-34 or -1.2599999999999999e-99 < y < -2.15000000000000016e-123

   1. Initial program 86.8%

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

      1. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

      1. associate-/r/ 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in y around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. associate-/l* 80.4%

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

   8. Simplified 80.4%

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

   if -7.79999999999999982e-34 < y < -1.2599999999999999e-99

   1. Initial program 81.0%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in z around inf 87.4%

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

   if -2.15000000000000016e-123 < y < 1.02000000000000004e-97

   1. Initial program 86.9%

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

      1. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in y around 0 80.7%

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

      1. associate-*r/ 78.4%

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

      2. associate-*l* 78.4%

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

      3. neg-mul-1 78.4%

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

      4. *-commutative 78.4%

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

   6. Simplified 78.4%

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

      1. associate-*l/ 80.7%

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

      2. frac-2neg 80.7%

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

      3. add-sqr-sqrt 47.5%

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

      4. sqrt-unprod 41.6%

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

      5. sqr-neg 41.6%

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

      6. sqrt-unprod 6.0%

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

      7. add-sqr-sqrt 18.6%

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

      8. distribute-rgt-neg-out 18.6%

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

      9. add-sqr-sqrt 12.7%

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

      10. sqrt-unprod 41.7%

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

      11. sqr-neg 41.7%

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

      12. sqrt-unprod 32.8%

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

      13. add-sqr-sqrt 80.7%

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

      14. sub-neg 80.7%

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

      15. distribute-neg-in 80.7%

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

      16. add-sqr-sqrt 47.6%

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

      17. sqrt-unprod 56.0%

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

      18. sqr-neg 56.0%

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

      19. sqrt-unprod 18.0%

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

      20. add-sqr-sqrt 41.4%

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

      21. add-sqr-sqrt 23.4%

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

      22. sqrt-unprod 51.5%

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

      23. sqr-neg 51.5%

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

   8. Applied egg-rr 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*r/ 78.4%

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

      3. +-commutative 78.4%

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

      4. unsub-neg 78.4%

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

   10. Simplified 78.4%

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

   if 1.02000000000000004e-97 < y

   1. Initial program 85.1%

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

      1. associate-*l/ 82.8%

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

   3. Simplified 82.8%

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

      1. associate-*l/ 85.1%

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

      2. clear-num 85.1%

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

   5. Applied egg-rr 85.1%

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

   6. Taylor expanded in y around inf 67.7%

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

      1. associate-/l* 70.1%

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

   8. Simplified 70.1%

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

      1. associate-/r/ 78.0%

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

   10. Applied egg-rr 78.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 5: 68.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-126}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-45)
   (/ x (/ (- t z) y))
   (if (<= y -1.35e-98)
     x
     (if (<= y -2.75e-126)
       (/ (* x y) (- t z))
       (if (<= y 5.6e-100) (* z (/ x (- z t))) (* x (/ y (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-45) {
		tmp = x / ((t - z) / y);
	} else if (y <= -1.35e-98) {
		tmp = x;
	} else if (y <= -2.75e-126) {
		tmp = (x * y) / (t - z);
	} else if (y <= 5.6e-100) {
		tmp = z * (x / (z - t));
	} 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 (y <= (-7.5d-45)) then
        tmp = x / ((t - z) / y)
    else if (y <= (-1.35d-98)) then
        tmp = x
    else if (y <= (-2.75d-126)) then
        tmp = (x * y) / (t - z)
    else if (y <= 5.6d-100) then
        tmp = z * (x / (z - t))
    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 (y <= -7.5e-45) {
		tmp = x / ((t - z) / y);
	} else if (y <= -1.35e-98) {
		tmp = x;
	} else if (y <= -2.75e-126) {
		tmp = (x * y) / (t - z);
	} else if (y <= 5.6e-100) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-45:
		tmp = x / ((t - z) / y)
	elif y <= -1.35e-98:
		tmp = x
	elif y <= -2.75e-126:
		tmp = (x * y) / (t - z)
	elif y <= 5.6e-100:
		tmp = z * (x / (z - t))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-45)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (y <= -1.35e-98)
		tmp = x;
	elseif (y <= -2.75e-126)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (y <= 5.6e-100)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	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 (y <= -7.5e-45)
		tmp = x / ((t - z) / y);
	elseif (y <= -1.35e-98)
		tmp = x;
	elseif (y <= -2.75e-126)
		tmp = (x * y) / (t - z);
	elseif (y <= 5.6e-100)
		tmp = z * (x / (z - t));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-45], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-98], x, If[LessEqual[y, -2.75e-126], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-100], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.5000000000000006e-45

   1. Initial program 84.9%

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

      1. associate-*l/ 81.7%

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

   3. Simplified 81.7%

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

      1. associate-/r/ 97.3%

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

   5. Applied egg-rr 97.3%

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

   6. Taylor expanded in y around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-/l* 82.5%

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

   8. Simplified 82.5%

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

   if -7.5000000000000006e-45 < y < -1.3499999999999999e-98

   1. Initial program 81.0%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in z around inf 87.4%

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

   if -1.3499999999999999e-98 < y < -2.74999999999999993e-126

   1. Initial program 99.7%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in y around inf 65.8%

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

   if -2.74999999999999993e-126 < y < 5.59999999999999991e-100

   1. Initial program 86.9%

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

      1. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in y around 0 80.7%

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

      1. associate-*r/ 78.4%

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

      2. associate-*l* 78.4%

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

      3. neg-mul-1 78.4%

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

      4. *-commutative 78.4%

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

   6. Simplified 78.4%

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

      1. associate-*l/ 80.7%

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

      2. frac-2neg 80.7%

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

      3. add-sqr-sqrt 47.5%

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

      4. sqrt-unprod 41.6%

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

      5. sqr-neg 41.6%

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

      6. sqrt-unprod 6.0%

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

      7. add-sqr-sqrt 18.6%

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

      8. distribute-rgt-neg-out 18.6%

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

      9. add-sqr-sqrt 12.7%

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

      10. sqrt-unprod 41.7%

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

      11. sqr-neg 41.7%

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

      12. sqrt-unprod 32.8%

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

      13. add-sqr-sqrt 80.7%

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

      14. sub-neg 80.7%

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

      15. distribute-neg-in 80.7%

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

      16. add-sqr-sqrt 47.6%

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

      17. sqrt-unprod 56.0%

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

      18. sqr-neg 56.0%

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

      19. sqrt-unprod 18.0%

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

      20. add-sqr-sqrt 41.4%

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

      21. add-sqr-sqrt 23.4%

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

      22. sqrt-unprod 51.5%

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

      23. sqr-neg 51.5%

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

   8. Applied egg-rr 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*r/ 78.4%

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

      3. +-commutative 78.4%

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

      4. unsub-neg 78.4%

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

   10. Simplified 78.4%

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

   if 5.59999999999999991e-100 < y

   1. Initial program 85.1%

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

      1. associate-*l/ 82.8%

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

   3. Simplified 82.8%

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

      1. associate-*l/ 85.1%

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

      2. clear-num 85.1%

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

   5. Applied egg-rr 85.1%

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

   6. Taylor expanded in y around inf 67.7%

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

      1. associate-/l* 70.1%

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

   8. Simplified 70.1%

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

      1. associate-/r/ 78.0%

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

   10. Applied egg-rr 78.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-126}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 6: 89.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+89} \lor \neg \left(z \leq 1.8 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{x}{\frac{-z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.7e+89) (not (<= z 1.8e+166)))
   (/ x (/ (- z) (- y z)))
   (* (- y z) (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.7e+89) || !(z <= 1.8e+166)) {
		tmp = x / (-z / (y - z));
	} else {
		tmp = (y - z) * (x / (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 <= (-3.7d+89)) .or. (.not. (z <= 1.8d+166))) then
        tmp = x / (-z / (y - z))
    else
        tmp = (y - z) * (x / (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 <= -3.7e+89) || !(z <= 1.8e+166)) {
		tmp = x / (-z / (y - z));
	} else {
		tmp = (y - z) * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.7e+89) or not (z <= 1.8e+166):
		tmp = x / (-z / (y - z))
	else:
		tmp = (y - z) * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.7e+89) || !(z <= 1.8e+166))
		tmp = Float64(x / Float64(Float64(-z) / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.7e+89) || ~((z <= 1.8e+166)))
		tmp = x / (-z / (y - z));
	else
		tmp = (y - z) * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.7e+89], N[Not[LessEqual[z, 1.8e+166]], $MachinePrecision]], N[(x / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999998e89 or 1.7999999999999999e166 < z

   1. Initial program 76.4%

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

      1. associate-*l/ 58.9%

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

   3. Simplified 58.9%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. distribute-neg-frac 89.9%

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

   8. Simplified 89.9%

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

   if -3.6999999999999998e89 < z < 1.7999999999999999e166

   1. Initial program 89.6%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+89} \lor \neg \left(z \leq 1.8 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{x}{\frac{-z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 7: 66.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7200000 \lor \neg \left(y \leq 4.6 \cdot 10^{-99}\right):\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7200000.0) (not (<= y 4.6e-99)))
   (* y (/ x (- t z)))
   (* z (/ x (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7200000.0) || !(y <= 4.6e-99)) {
		tmp = y * (x / (t - z));
	} else {
		tmp = z * (x / (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 ((y <= (-7200000.0d0)) .or. (.not. (y <= 4.6d-99))) then
        tmp = y * (x / (t - z))
    else
        tmp = z * (x / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7200000.0) || !(y <= 4.6e-99)) {
		tmp = y * (x / (t - z));
	} else {
		tmp = z * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7200000.0) or not (y <= 4.6e-99):
		tmp = y * (x / (t - z))
	else:
		tmp = z * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7200000.0) || !(y <= 4.6e-99))
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = Float64(z * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7200000.0) || ~((y <= 4.6e-99)))
		tmp = y * (x / (t - z));
	else
		tmp = z * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7200000.0], N[Not[LessEqual[y, 4.6e-99]], $MachinePrecision]], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e6 or 4.5999999999999997e-99 < y

   1. Initial program 84.5%

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

      1. associate-*l/ 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in y around inf 70.2%

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

      1. associate-*r/ 73.3%

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

   6. Simplified 73.3%

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

   if -7.2e6 < y < 4.5999999999999997e-99

   1. Initial program 87.7%

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

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in y around 0 78.0%

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

      1. associate-*r/ 72.3%

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

      2. associate-*l* 72.3%

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

      3. neg-mul-1 72.3%

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

      4. *-commutative 72.3%

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

   6. Simplified 72.3%

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

      1. associate-*l/ 78.0%

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

      2. frac-2neg 78.0%

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

      3. add-sqr-sqrt 44.1%

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

      4. sqrt-unprod 39.1%

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

      5. sqr-neg 39.1%

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

      6. sqrt-unprod 5.6%

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

      7. add-sqr-sqrt 17.1%

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

      8. distribute-rgt-neg-out 17.1%

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

      9. add-sqr-sqrt 11.5%

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

      10. sqrt-unprod 37.0%

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

      11. sqr-neg 37.0%

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

      12. sqrt-unprod 33.6%

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

      13. add-sqr-sqrt 78.0%

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

      14. sub-neg 78.0%

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

      15. distribute-neg-in 78.0%

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

      16. add-sqr-sqrt 44.2%

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

      17. sqrt-unprod 51.8%

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

      18. sqr-neg 51.8%

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

      19. sqrt-unprod 17.2%

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

      20. add-sqr-sqrt 37.5%

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

      21. add-sqr-sqrt 20.3%

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

      22. sqrt-unprod 45.1%

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

      23. sqr-neg 45.1%

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

   8. Applied egg-rr 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-*r/ 72.3%

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

      3. +-commutative 72.3%

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

      4. unsub-neg 72.3%

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

   10. Simplified 72.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7200000 \lor \neg \left(y \leq 4.6 \cdot 10^{-99}\right):\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \end{array} \]

Alternative 8: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e+64) x (if (<= z 2.2e+55) (* y (/ x (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e+64) {
		tmp = x;
	} else if (z <= 2.2e+55) {
		tmp = y * (x / (t - z));
	} 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 <= (-7.5d+64)) then
        tmp = x
    else if (z <= 2.2d+55) then
        tmp = y * (x / (t - z))
    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 <= -7.5e+64) {
		tmp = x;
	} else if (z <= 2.2e+55) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e+64:
		tmp = x
	elif z <= 2.2e+55:
		tmp = y * (x / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e+64)
		tmp = x;
	elseif (z <= 2.2e+55)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e+64)
		tmp = x;
	elseif (z <= 2.2e+55)
		tmp = y * (x / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e+64], x, If[LessEqual[z, 2.2e+55], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000005e64 or 2.2000000000000001e55 < z

   1. Initial program 76.5%

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

      1. associate-*l/ 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in z around inf 68.5%

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

   if -7.5000000000000005e64 < z < 2.2000000000000001e55

   1. Initial program 90.8%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around inf 70.3%

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

      1. associate-*r/ 72.5%

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

   6. Simplified 72.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 70.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7800000:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-51}:\\ \;\;\;\;\frac{x \cdot z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7800000.0)
   (/ x (/ (- t z) y))
   (if (<= y 6.6e-51) (/ (* x z) (- z t)) (* x (/ y (- t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7800000.0) {
		tmp = x / ((t - z) / y);
	} else if (y <= 6.6e-51) {
		tmp = (x * z) / (z - t);
	} 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 (y <= (-7800000.0d0)) then
        tmp = x / ((t - z) / y)
    else if (y <= 6.6d-51) then
        tmp = (x * z) / (z - t)
    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 (y <= -7800000.0) {
		tmp = x / ((t - z) / y);
	} else if (y <= 6.6e-51) {
		tmp = (x * z) / (z - t);
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7800000.0:
		tmp = x / ((t - z) / y)
	elif y <= 6.6e-51:
		tmp = (x * z) / (z - t)
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7800000.0)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (y <= 6.6e-51)
		tmp = Float64(Float64(x * z) / Float64(z - t));
	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 (y <= -7800000.0)
		tmp = x / ((t - z) / y);
	elseif (y <= 6.6e-51)
		tmp = (x * z) / (z - t);
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7800000.0], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-51], N[(N[(x * z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.8e6

   1. Initial program 83.6%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

      1. associate-/r/ 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-/l* 85.8%

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

   8. Simplified 85.8%

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

   if -7.8e6 < y < 6.59999999999999946e-51

   1. Initial program 88.5%

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

   2. Taylor expanded in y around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-rgt-neg-in 76.1%

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

   4. Simplified 76.1%

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

      1. frac-2neg 76.1%

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

      2. div-inv 76.0%

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

      3. distribute-rgt-neg-out 76.0%

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

      4. remove-double-neg 76.0%

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

      5. sub-neg 76.0%

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

      6. distribute-neg-in 76.0%

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

      7. add-sqr-sqrt 41.4%

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

      8. sqrt-unprod 48.5%

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

      9. sqr-neg 48.5%

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

      10. sqrt-unprod 16.2%

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

      11. add-sqr-sqrt 34.9%

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

      12. add-sqr-sqrt 18.8%

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

      13. sqrt-unprod 41.7%

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

      14. sqr-neg 41.7%

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

      15. sqrt-unprod 34.4%

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

      16. add-sqr-sqrt 76.0%

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

   6. Applied egg-rr 76.0%

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

      1. associate-*r/ 76.1%

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

      2. *-rgt-identity 76.1%

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

      3. +-commutative 76.1%

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

      4. unsub-neg 76.1%

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

   8. Simplified 76.1%

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

   if 6.59999999999999946e-51 < y

   1. Initial program 83.4%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

      1. associate-*l/ 83.4%

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

      2. clear-num 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in y around inf 72.7%

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

      1. associate-/l* 75.6%

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

   8. Simplified 75.6%

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

      1. associate-/r/ 85.1%

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

   10. Applied egg-rr 85.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7800000:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-51}:\\ \;\;\;\;\frac{x \cdot z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 10: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e+64) x (if (<= z 1.15e+45) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+64) {
		tmp = x;
	} else if (z <= 1.15e+45) {
		tmp = y * (x / 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 <= (-6.5d+64)) then
        tmp = x
    else if (z <= 1.15d+45) then
        tmp = y * (x / 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 <= -6.5e+64) {
		tmp = x;
	} else if (z <= 1.15e+45) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e+64:
		tmp = x
	elif z <= 1.15e+45:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e+64)
		tmp = x;
	elseif (z <= 1.15e+45)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.5e+64)
		tmp = x;
	elseif (z <= 1.15e+45)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.5e+64], x, If[LessEqual[z, 1.15e+45], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000007e64 or 1.15000000000000006e45 < z

   1. Initial program 76.5%

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

      1. associate-*l/ 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in z around inf 68.5%

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

   if -6.50000000000000007e64 < z < 1.15000000000000006e45

   1. Initial program 90.8%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

      1. associate-/r/ 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in z around 0 55.7%

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

      1. associate-*r/ 57.9%

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

   8. Simplified 57.9%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.6e+64) x (if (<= z 4e+53) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.6e+64) {
		tmp = x;
	} else if (z <= 4e+53) {
		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 <= (-9.6d+64)) then
        tmp = x
    else if (z <= 4d+53) 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 <= -9.6e+64) {
		tmp = x;
	} else if (z <= 4e+53) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.6e+64:
		tmp = x
	elif z <= 4e+53:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.6e+64)
		tmp = x;
	elseif (z <= 4e+53)
		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 <= -9.6e+64)
		tmp = x;
	elseif (z <= 4e+53)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.6e+64], x, If[LessEqual[z, 4e+53], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -9.59999999999999997e64 or 4e53 < z

   1. Initial program 76.5%

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

      1. associate-*l/ 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in z around inf 68.5%

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

   if -9.59999999999999997e64 < z < 4e53

   1. Initial program 90.8%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in z around 0 55.7%

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

      1. associate-/l* 57.6%

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

      2. associate-/r/ 62.2%

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

   6. Simplified 62.2%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 35.2% 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/ 82.2%

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

3. Simplified 82.2%

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

4. Taylor expanded in z around inf 31.9%

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

5. Final simplification 31.9%

   \[\leadsto x \]

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 2023268 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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