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

Percentage Accurate: 83.8% → 97.1%

Time: 9.7s

Alternatives: 11

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: 83.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% 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 84.0%

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

   1. *-commutative 84.0%

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

   2. associate-*l/ 96.8%

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

   3. *-commutative 96.8%

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

3. Simplified 96.8%

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

   1. associate-*r/ 84.0%

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

   2. associate-/l* 97.2%

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

5. Applied egg-rr 97.2%

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

6. Final simplification 97.2%

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

Alternative 2: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{\frac{t}{z} + -1}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+33} \lor \neg \left(z \leq 6.2 \cdot 10^{+113}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (+ (/ t z) -1.0))))
   (if (<= z -2e+20)
     t_1
     (if (<= z 4.4e-11)
       (* y (/ x (- t z)))
       (if (or (<= z 6.8e+33) (not (<= z 6.2e+113)))
         t_1
         (/ (* x y) (- t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / ((t / z) + -1.0);
	double tmp;
	if (z <= -2e+20) {
		tmp = t_1;
	} else if (z <= 4.4e-11) {
		tmp = y * (x / (t - z));
	} else if ((z <= 6.8e+33) || !(z <= 6.2e+113)) {
		tmp = t_1;
	} 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) + (-1.0d0))
    if (z <= (-2d+20)) then
        tmp = t_1
    else if (z <= 4.4d-11) then
        tmp = y * (x / (t - z))
    else if ((z <= 6.8d+33) .or. (.not. (z <= 6.2d+113))) then
        tmp = t_1
    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) + -1.0);
	double tmp;
	if (z <= -2e+20) {
		tmp = t_1;
	} else if (z <= 4.4e-11) {
		tmp = y * (x / (t - z));
	} else if ((z <= 6.8e+33) || !(z <= 6.2e+113)) {
		tmp = t_1;
	} else {
		tmp = (x * y) / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / ((t / z) + -1.0)
	tmp = 0
	if z <= -2e+20:
		tmp = t_1
	elif z <= 4.4e-11:
		tmp = y * (x / (t - z))
	elif (z <= 6.8e+33) or not (z <= 6.2e+113):
		tmp = t_1
	else:
		tmp = (x * y) / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(Float64(t / z) + -1.0))
	tmp = 0.0
	if (z <= -2e+20)
		tmp = t_1;
	elseif (z <= 4.4e-11)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	elseif ((z <= 6.8e+33) || !(z <= 6.2e+113))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / ((t / z) + -1.0);
	tmp = 0.0;
	if (z <= -2e+20)
		tmp = t_1;
	elseif (z <= 4.4e-11)
		tmp = y * (x / (t - z));
	elseif ((z <= 6.8e+33) || ~((z <= 6.2e+113)))
		tmp = t_1;
	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] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+20], t$95$1, If[LessEqual[z, 4.4e-11], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6.8e+33], N[Not[LessEqual[z, 6.2e+113]], $MachinePrecision]], t$95$1, N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e20 or 4.4000000000000003e-11 < z < 6.7999999999999999e33 or 6.19999999999999982e113 < z

   1. Initial program 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. associate-/l* 83.8%

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

      3. distribute-neg-frac 83.8%

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

      4. div-sub 83.8%

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

      5. *-inverses 83.8%

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

   6. Simplified 83.8%

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

   if -2e20 < z < 4.4000000000000003e-11

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 79.5%

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

      2. *-commutative 79.5%

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

   6. Simplified 79.5%

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

   if 6.7999999999999999e33 < z < 6.19999999999999982e113

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 72.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+33} \lor \neg \left(z \leq 6.2 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \end{array} \]

Alternative 3: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{\frac{t}{z} + -1}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t - z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (+ (/ t z) -1.0))))
   (if (<= z -9.8e+27)
     t_1
     (if (<= z 1.06e-11)
       (* y (/ x (- t z)))
       (if (<= z 5.4e+36)
         (/ (* x (- z)) (- t z))
         (if (<= z 6.2e+113) (/ (* x y) (- t z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / ((t / z) + -1.0);
	double tmp;
	if (z <= -9.8e+27) {
		tmp = t_1;
	} else if (z <= 1.06e-11) {
		tmp = y * (x / (t - z));
	} else if (z <= 5.4e+36) {
		tmp = (x * -z) / (t - z);
	} else if (z <= 6.2e+113) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / ((t / z) + (-1.0d0))
    if (z <= (-9.8d+27)) then
        tmp = t_1
    else if (z <= 1.06d-11) then
        tmp = y * (x / (t - z))
    else if (z <= 5.4d+36) then
        tmp = (x * -z) / (t - z)
    else if (z <= 6.2d+113) then
        tmp = (x * y) / (t - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / ((t / z) + -1.0);
	double tmp;
	if (z <= -9.8e+27) {
		tmp = t_1;
	} else if (z <= 1.06e-11) {
		tmp = y * (x / (t - z));
	} else if (z <= 5.4e+36) {
		tmp = (x * -z) / (t - z);
	} else if (z <= 6.2e+113) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / ((t / z) + -1.0)
	tmp = 0
	if z <= -9.8e+27:
		tmp = t_1
	elif z <= 1.06e-11:
		tmp = y * (x / (t - z))
	elif z <= 5.4e+36:
		tmp = (x * -z) / (t - z)
	elif z <= 6.2e+113:
		tmp = (x * y) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(Float64(t / z) + -1.0))
	tmp = 0.0
	if (z <= -9.8e+27)
		tmp = t_1;
	elseif (z <= 1.06e-11)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	elseif (z <= 5.4e+36)
		tmp = Float64(Float64(x * Float64(-z)) / Float64(t - z));
	elseif (z <= 6.2e+113)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / ((t / z) + -1.0);
	tmp = 0.0;
	if (z <= -9.8e+27)
		tmp = t_1;
	elseif (z <= 1.06e-11)
		tmp = y * (x / (t - z));
	elseif (z <= 5.4e+36)
		tmp = (x * -z) / (t - z);
	elseif (z <= 6.2e+113)
		tmp = (x * y) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+27], t$95$1, If[LessEqual[z, 1.06e-11], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+36], N[(N[(x * (-z)), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+113], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.8000000000000003e27 or 6.19999999999999982e113 < z

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 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 0 55.9%

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

      1. mul-1-neg 55.9%

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

      2. associate-/l* 83.8%

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

      3. distribute-neg-frac 83.8%

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

      4. div-sub 83.9%

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

      5. *-inverses 83.9%

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

   6. Simplified 83.9%

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

   if -9.8000000000000003e27 < z < 1.05999999999999993e-11

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 79.5%

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

      2. *-commutative 79.5%

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

   6. Simplified 79.5%

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

   if 1.05999999999999993e-11 < z < 5.4000000000000002e36

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. distribute-rgt-neg-out 83.2%

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

   4. Simplified 83.2%

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

   if 5.4000000000000002e36 < z < 6.19999999999999982e113

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 72.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t - z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \]

Alternative 4: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.85e+29)
   x
   (if (<= z 2.85e-27)
     (/ x (/ t y))
     (if (<= z 6.2e+113) (* x (- (/ y z))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+29) {
		tmp = x;
	} else if (z <= 2.85e-27) {
		tmp = x / (t / y);
	} else if (z <= 6.2e+113) {
		tmp = x * -(y / 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 <= (-1.85d+29)) then
        tmp = x
    else if (z <= 2.85d-27) then
        tmp = x / (t / y)
    else if (z <= 6.2d+113) then
        tmp = x * -(y / 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 <= -1.85e+29) {
		tmp = x;
	} else if (z <= 2.85e-27) {
		tmp = x / (t / y);
	} else if (z <= 6.2e+113) {
		tmp = x * -(y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.85e+29:
		tmp = x
	elif z <= 2.85e-27:
		tmp = x / (t / y)
	elif z <= 6.2e+113:
		tmp = x * -(y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.85e+29)
		tmp = x;
	elseif (z <= 2.85e-27)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 6.2e+113)
		tmp = Float64(x * Float64(-Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.85e+29)
		tmp = x;
	elseif (z <= 2.85e-27)
		tmp = x / (t / y);
	elseif (z <= 6.2e+113)
		tmp = x * -(y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.85e+29], x, If[LessEqual[z, 2.85e-27], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+113], N[(x * (-N[(y / z), $MachinePrecision])), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.84999999999999987e29 or 6.19999999999999982e113 < z

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 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 z around inf 63.3%

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

   if -1.84999999999999987e29 < z < 2.8499999999999998e-27

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 59.3%

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

      1. associate-/l* 62.6%

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

   6. Simplified 62.6%

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

   if 2.8499999999999998e-27 < z < 6.19999999999999982e113

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 64.1%

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

   5. Taylor expanded in t around 0 49.2%

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

      1. associate-*r/ 49.2%

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

      2. neg-mul-1 49.2%

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

   7. Simplified 49.2%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+19} \lor \neg \left(z \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e+19) (not (<= z 2e-10)))
   (* x (- 1.0 (/ y z)))
   (* y (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+19) || !(z <= 2e-10)) {
		tmp = x * (1.0 - (y / z));
	} 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) :: tmp
    if ((z <= (-9.5d+19)) .or. (.not. (z <= 2d-10))) then
        tmp = x * (1.0d0 - (y / z))
    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 tmp;
	if ((z <= -9.5e+19) || !(z <= 2e-10)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = y * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.5e+19) or not (z <= 2e-10):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = y * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.5e+19) || !(z <= 2e-10))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(y * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.5e+19) || ~((z <= 2e-10)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = y * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.5e+19], N[Not[LessEqual[z, 2e-10]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e19 or 2.00000000000000007e-10 < z

   1. Initial program 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 74.5%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 53.9%

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

      1. associate-*r/ 53.9%

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

      2. neg-mul-1 53.9%

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

      3. neg-sub0 53.9%

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

      4. distribute-lft-out-- 53.0%

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

      5. associate--r- 53.0%

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

      6. neg-sub0 53.0%

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

      7. mul-1-neg 53.0%

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

      8. +-commutative 53.0%

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

      9. mul-1-neg 53.0%

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

      10. sub-neg 53.0%

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

      11. distribute-lft-out-- 53.9%

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

      12. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

      1. clear-num 74.4%

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

      2. associate-/r/ 74.6%

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

      3. clear-num 74.7%

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

      4. div-sub 74.7%

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

      5. *-inverses 74.7%

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

   10. Applied egg-rr 74.7%

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

   if -9.5e19 < z < 2.00000000000000007e-10

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 79.5%

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

      2. *-commutative 79.5%

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

   6. Simplified 79.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+19} \lor \neg \left(z \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 6: 69.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e+30) x (if (<= z 2e+114) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+30) {
		tmp = x;
	} else if (z <= 2e+114) {
		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 <= (-3.7d+30)) then
        tmp = x
    else if (z <= 2d+114) 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 <= -3.7e+30) {
		tmp = x;
	} else if (z <= 2e+114) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e+30:
		tmp = x
	elif z <= 2e+114:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e+30)
		tmp = x;
	elseif (z <= 2e+114)
		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 <= -3.7e+30)
		tmp = x;
	elseif (z <= 2e+114)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e+30], x, If[LessEqual[z, 2e+114], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000016e30 or 2e114 < z

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 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 z around inf 63.3%

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

   if -3.70000000000000016e30 < z < 2e114

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. associate-*l/ 95.0%

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

      3. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 75.3%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e+22)
   (* x (- 1.0 (/ y z)))
   (if (<= z 3.2e-12) (* y (/ x (- t z))) (/ x (/ z (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+22) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 3.2e-12) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x / (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.5d+22)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 3.2d-12) then
        tmp = y * (x / (t - z))
    else
        tmp = x / (z / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+22) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 3.2e-12) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x / (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e+22:
		tmp = x * (1.0 - (y / z))
	elif z <= 3.2e-12:
		tmp = y * (x / (t - z))
	else:
		tmp = x / (z / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e+22)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 3.2e-12)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x / Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.5e+22)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 3.2e-12)
		tmp = y * (x / (t - z));
	else
		tmp = x / (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e+22], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-12], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4999999999999998e22

   1. Initial program 69.3%

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

      1. *-commutative 69.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 69.3%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 50.9%

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

      1. associate-*r/ 50.9%

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

      2. neg-mul-1 50.9%

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

      3. neg-sub0 50.9%

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

      4. distribute-lft-out-- 49.3%

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

      5. associate--r- 49.3%

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

      6. neg-sub0 49.3%

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

      7. mul-1-neg 49.3%

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

      8. +-commutative 49.3%

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

      9. mul-1-neg 49.3%

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

      10. sub-neg 49.3%

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

      11. distribute-lft-out-- 50.9%

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

      12. associate-/l* 75.5%

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

   8. Simplified 75.5%

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

      1. clear-num 75.3%

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

      2. associate-/r/ 75.5%

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

      3. clear-num 75.5%

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

      4. div-sub 75.5%

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

      5. *-inverses 75.5%

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

   10. Applied egg-rr 75.5%

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

   if -4.4999999999999998e22 < z < 3.2000000000000001e-12

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 79.5%

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

      2. *-commutative 79.5%

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

   6. Simplified 79.5%

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

   if 3.2000000000000001e-12 < z

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 79.8%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 56.9%

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

      1. associate-*r/ 56.9%

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

      2. neg-mul-1 56.9%

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

      3. neg-sub0 56.9%

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

      4. distribute-lft-out-- 56.8%

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

      5. associate--r- 56.8%

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

      6. neg-sub0 56.8%

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

      7. mul-1-neg 56.8%

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

      8. +-commutative 56.8%

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

      9. mul-1-neg 56.8%

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

      10. sub-neg 56.8%

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

      11. distribute-lft-out-- 56.9%

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

      12. associate-/l* 73.9%

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

   8. Simplified 73.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \end{array} \]

Alternative 8: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.45 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.45e+21) x (if (<= z 2.6e-11) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.45e+21) {
		tmp = x;
	} else if (z <= 2.6e-11) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.45d+21)) then
        tmp = x
    else if (z <= 2.6d-11) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.45e+21) {
		tmp = x;
	} else if (z <= 2.6e-11) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.45e+21:
		tmp = x
	elif z <= 2.6e-11:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.45e+21)
		tmp = x;
	elseif (z <= 2.6e-11)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.45e+21)
		tmp = x;
	elseif (z <= 2.6e-11)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.45e+21], x, If[LessEqual[z, 2.6e-11], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.45e21 or 2.6000000000000001e-11 < z

   1. Initial program 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 56.8%

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

   if -4.45e21 < z < 2.6000000000000001e-11

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 61.4%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.45 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.7e+27) x (if (<= z 1.8e-12) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.7e+27) {
		tmp = x;
	} else if (z <= 1.8e-12) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8.7d+27)) then
        tmp = x
    else if (z <= 1.8d-12) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.7e+27) {
		tmp = x;
	} else if (z <= 1.8e-12) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.7e+27:
		tmp = x
	elif z <= 1.8e-12:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.7e+27)
		tmp = x;
	elseif (z <= 1.8e-12)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.7e+27)
		tmp = x;
	elseif (z <= 1.8e-12)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.7e+27], x, If[LessEqual[z, 1.8e-12], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.7000000000000004e27 or 1.8e-12 < z

   1. Initial program 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 56.8%

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

   if -8.7000000000000004e27 < z < 1.8e-12

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 58.6%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.0%

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

   1. *-commutative 84.0%

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

   2. associate-*l/ 96.8%

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

   3. *-commutative 96.8%

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

3. Simplified 96.8%

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

4. Final simplification 96.8%

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

Alternative 11: 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 84.0%

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

   1. *-commutative 84.0%

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

   2. associate-*l/ 96.8%

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

   3. *-commutative 96.8%

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

3. Simplified 96.8%

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

4. Taylor expanded in z around inf 32.8%

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

5. Final simplification 32.8%

   \[\leadsto x \]

Developer target: 97.1% 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 2023322 
(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)))