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

Percentage Accurate: 84.0% → 96.8%

Time: 8.3s

Alternatives: 7

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: 84.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y - z) / (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. associate-*r/ 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. Final simplification 96.3%

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

Alternative 2: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-29} \lor \neg \left(z \leq 6 \cdot 10^{+103}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -2.85e+85)
     t_1
     (if (<= z -5.2e+21)
       (* x (/ y (- t z)))
       (if (or (<= z -4.1e-29) (not (<= z 6e+103)))
         t_1
         (* y (/ x (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -2.85e+85) {
		tmp = t_1;
	} else if (z <= -5.2e+21) {
		tmp = x * (y / (t - z));
	} else if ((z <= -4.1e-29) || !(z <= 6e+103)) {
		tmp = t_1;
	} else {
		tmp = y * (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) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-2.85d+85)) then
        tmp = t_1
    else if (z <= (-5.2d+21)) then
        tmp = x * (y / (t - z))
    else if ((z <= (-4.1d-29)) .or. (.not. (z <= 6d+103))) then
        tmp = t_1
    else
        tmp = y * (x / (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 * (z / (z - t));
	double tmp;
	if (z <= -2.85e+85) {
		tmp = t_1;
	} else if (z <= -5.2e+21) {
		tmp = x * (y / (t - z));
	} else if ((z <= -4.1e-29) || !(z <= 6e+103)) {
		tmp = t_1;
	} else {
		tmp = y * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -2.85e+85:
		tmp = t_1
	elif z <= -5.2e+21:
		tmp = x * (y / (t - z))
	elif (z <= -4.1e-29) or not (z <= 6e+103):
		tmp = t_1
	else:
		tmp = y * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -2.85e+85)
		tmp = t_1;
	elseif (z <= -5.2e+21)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif ((z <= -4.1e-29) || !(z <= 6e+103))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -2.85e+85)
		tmp = t_1;
	elseif (z <= -5.2e+21)
		tmp = x * (y / (t - z));
	elseif ((z <= -4.1e-29) || ~((z <= 6e+103)))
		tmp = t_1;
	else
		tmp = y * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+85], t$95$1, If[LessEqual[z, -5.2e+21], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.1e-29], N[Not[LessEqual[z, 6e+103]], $MachinePrecision]], t$95$1, N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8500000000000001e85 or -5.2e21 < z < -4.0999999999999998e-29 or 6e103 < z

   1. Initial program 68.7%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. associate-/r/ 75.3%

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

      3. frac-2neg 75.3%

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

      4. neg-sub0 75.3%

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

      5. sub-neg 75.3%

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

      6. +-commutative 75.3%

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

      7. associate--r+ 75.3%

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

      8. neg-sub0 75.3%

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

      9. remove-double-neg 75.3%

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

      10. distribute-neg-frac 75.3%

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

      11. neg-sub0 75.3%

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

      12. sub-neg 75.3%

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

      13. +-commutative 75.3%

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

      14. associate--r+ 75.3%

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

      15. neg-sub0 75.3%

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

      16. remove-double-neg 75.3%

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

   5. Applied egg-rr 75.3%

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

   6. Taylor expanded in y around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-*l/ 87.9%

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

      3. *-commutative 87.9%

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

   8. Simplified 87.9%

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

   if -2.8500000000000001e85 < z < -5.2e21

   1. Initial program 93.1%

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

      1. associate-*r/ 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. Taylor expanded in y around inf 73.0%

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

   if -4.0999999999999998e-29 < z < 6e103

   1. Initial program 93.1%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around inf 77.8%

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

      1. associate-/l* 77.6%

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

      2. associate-/r/ 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-29} \lor \neg \left(z \leq 6 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 3: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+89} \lor \neg \left(z \leq 2 \cdot 10^{+106}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.3e+89) (not (<= z 2e+106)))
   (* x (/ z (- z t)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e+89) || !(z <= 2e+106)) {
		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 ((z <= (-1.3d+89)) .or. (.not. (z <= 2d+106))) 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 ((z <= -1.3e+89) || !(z <= 2e+106)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.3e+89) or not (z <= 2e+106):
		tmp = x * (z / (z - t))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.3e+89) || !(z <= 2e+106))
		tmp = Float64(x * Float64(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 ((z <= -1.3e+89) || ~((z <= 2e+106)))
		tmp = x * (z / (z - t));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.3e+89], N[Not[LessEqual[z, 2e+106]], $MachinePrecision]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e89 or 2.00000000000000018e106 < z

   1. Initial program 65.3%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/r/ 72.6%

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

      3. frac-2neg 72.6%

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

      4. neg-sub0 72.6%

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

      5. sub-neg 72.6%

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

      6. +-commutative 72.6%

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

      7. associate--r+ 72.6%

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

      8. neg-sub0 72.6%

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

      9. remove-double-neg 72.6%

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

      10. distribute-neg-frac 72.6%

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

      11. neg-sub0 72.6%

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

      12. sub-neg 72.6%

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

      13. +-commutative 72.6%

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

      14. associate--r+ 72.6%

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

      15. neg-sub0 72.6%

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

      16. remove-double-neg 72.6%

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

   5. Applied egg-rr 72.6%

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

   6. Taylor expanded in y around 0 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

   8. Simplified 90.0%

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

   if -1.3e89 < z < 2.00000000000000018e106

   1. Initial program 93.4%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around inf 75.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+89} \lor \neg \left(z \leq 2 \cdot 10^{+106}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 4: 69.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.6e+82) x (if (<= z 4.8e+120) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+82) {
		tmp = x;
	} else if (z <= 4.8e+120) {
		tmp = x * (y / (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 <= (-6.6d+82)) then
        tmp = x
    else if (z <= 4.8d+120) then
        tmp = x * (y / (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 <= -6.6e+82) {
		tmp = x;
	} else if (z <= 4.8e+120) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.6e+82:
		tmp = x
	elif z <= 4.8e+120:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.6e+82)
		tmp = x;
	elseif (z <= 4.8e+120)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.6e+82)
		tmp = x;
	elseif (z <= 4.8e+120)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.6e+82], x, If[LessEqual[z, 4.8e+120], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999997e82 or 4.80000000000000002e120 < z

   1. Initial program 63.1%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 83.8%

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

   if -6.5999999999999997e82 < z < 4.80000000000000002e120

   1. Initial program 93.6%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around inf 75.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+45}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+103}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e+45)
   (- x (* x (/ y z)))
   (if (<= z 6e+103) (* y (/ x (- t z))) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+45) {
		tmp = x - (x * (y / z));
	} else if (z <= 6e+103) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (z / (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 <= (-6.8d+45)) then
        tmp = x - (x * (y / z))
    else if (z <= 6d+103) then
        tmp = y * (x / (t - z))
    else
        tmp = x * (z / (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 <= -6.8e+45) {
		tmp = x - (x * (y / z));
	} else if (z <= 6e+103) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e+45:
		tmp = x - (x * (y / z))
	elif z <= 6e+103:
		tmp = y * (x / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e+45)
		tmp = Float64(x - Float64(x * Float64(y / z)));
	elseif (z <= 6e+103)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.8e+45)
		tmp = x - (x * (y / z));
	elseif (z <= 6e+103)
		tmp = y * (x / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+45], N[(x - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+103], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e45

   1. Initial program 69.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/r/ 71.2%

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

      3. frac-2neg 71.2%

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

      4. neg-sub0 71.2%

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

      5. sub-neg 71.2%

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

      6. +-commutative 71.2%

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

      7. associate--r+ 71.2%

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

      8. neg-sub0 71.2%

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

      9. remove-double-neg 71.2%

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

      10. distribute-neg-frac 71.2%

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

      11. neg-sub0 71.2%

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

      12. sub-neg 71.2%

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

      13. +-commutative 71.2%

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

      14. associate--r+ 71.2%

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

      15. neg-sub0 71.2%

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

      16. remove-double-neg 71.2%

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

   5. Applied egg-rr 71.2%

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

   6. Taylor expanded in t around 0 58.8%

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

   7. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. sub-neg 77.3%

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

      3. *-commutative 77.3%

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

      4. associate-*l/ 85.7%

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

      5. *-commutative 85.7%

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

   9. Simplified 85.7%

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

   if -6.8e45 < z < 6e103

   1. Initial program 93.7%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 76.1%

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

      1. associate-/l* 75.9%

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

      2. associate-/r/ 77.0%

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

   6. Simplified 77.0%

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

   if 6e103 < z

   1. Initial program 64.0%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. associate-/r/ 75.7%

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

      3. frac-2neg 75.7%

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

      4. neg-sub0 75.7%

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

      5. sub-neg 75.7%

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

      6. +-commutative 75.7%

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

      7. associate--r+ 75.7%

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

      8. neg-sub0 75.7%

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

      9. remove-double-neg 75.7%

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

      10. distribute-neg-frac 75.7%

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

      11. neg-sub0 75.7%

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

      12. sub-neg 75.7%

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

      13. +-commutative 75.7%

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

      14. associate--r+ 75.7%

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

      15. neg-sub0 75.7%

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

      16. remove-double-neg 75.7%

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

   5. Applied egg-rr 75.7%

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

   6. Taylor expanded in y around 0 57.3%

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

      1. *-commutative 57.3%

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

      2. associate-*l/ 93.3%

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

      3. *-commutative 93.3%

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

   8. Simplified 93.3%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+45}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+103}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 6: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.06e+41) x (if (<= z 4.9e+45) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.06e+41) {
		tmp = x;
	} else if (z <= 4.9e+45) {
		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 <= (-1.06d+41)) then
        tmp = x
    else if (z <= 4.9d+45) 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 <= -1.06e+41) {
		tmp = x;
	} else if (z <= 4.9e+45) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.06e+41:
		tmp = x
	elif z <= 4.9e+45:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.06e+41)
		tmp = x;
	elseif (z <= 4.9e+45)
		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 <= -1.06e+41)
		tmp = x;
	elseif (z <= 4.9e+45)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.06e+41], x, If[LessEqual[z, 4.9e+45], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.06e41 or 4.9000000000000002e45 < z

   1. Initial program 69.0%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 71.5%

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

   if -1.06e41 < z < 4.9000000000000002e45

   1. Initial program 94.4%

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

      1. associate-*r/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 66.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 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 84.4%

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

   1. associate-*r/ 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. Taylor expanded in z around inf 34.9%

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

5. Final simplification 34.9%

   \[\leadsto x \]

Developer target: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023297 
(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)))