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

Percentage Accurate: 84.1% → 97.4%

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: 84.1% 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: 97.4% 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 84.6%

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

   1. associate-*r/ 97.0%

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

3. Simplified 97.0%

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

4. Final simplification 97.0%

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

Alternative 2: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+33}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+91}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+126} \lor \neg \left(z \leq 2.7 \cdot 10^{+155}\right) \land z \leq 6.2 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -2.7e+119)
     x
     (if (<= z -8.2e-215)
       t_1
       (if (<= z 3.8e+33)
         (* (- y z) (/ x t))
         (if (<= z 1.45e+91)
           (/ z (/ z x))
           (if (or (<= z 6e+126) (and (not (<= z 2.7e+155)) (<= z 6.2e+188)))
             t_1
             x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -2.7e+119) {
		tmp = x;
	} else if (z <= -8.2e-215) {
		tmp = t_1;
	} else if (z <= 3.8e+33) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.45e+91) {
		tmp = z / (z / x);
	} else if ((z <= 6e+126) || (!(z <= 2.7e+155) && (z <= 6.2e+188))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-2.7d+119)) then
        tmp = x
    else if (z <= (-8.2d-215)) then
        tmp = t_1
    else if (z <= 3.8d+33) then
        tmp = (y - z) * (x / t)
    else if (z <= 1.45d+91) then
        tmp = z / (z / x)
    else if ((z <= 6d+126) .or. (.not. (z <= 2.7d+155)) .and. (z <= 6.2d+188)) then
        tmp = t_1
    else
        tmp = x
    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 (z <= -2.7e+119) {
		tmp = x;
	} else if (z <= -8.2e-215) {
		tmp = t_1;
	} else if (z <= 3.8e+33) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.45e+91) {
		tmp = z / (z / x);
	} else if ((z <= 6e+126) || (!(z <= 2.7e+155) && (z <= 6.2e+188))) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -2.7e+119:
		tmp = x
	elif z <= -8.2e-215:
		tmp = t_1
	elif z <= 3.8e+33:
		tmp = (y - z) * (x / t)
	elif z <= 1.45e+91:
		tmp = z / (z / x)
	elif (z <= 6e+126) or (not (z <= 2.7e+155) and (z <= 6.2e+188)):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -2.7e+119)
		tmp = x;
	elseif (z <= -8.2e-215)
		tmp = t_1;
	elseif (z <= 3.8e+33)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 1.45e+91)
		tmp = Float64(z / Float64(z / x));
	elseif ((z <= 6e+126) || (!(z <= 2.7e+155) && (z <= 6.2e+188)))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -2.7e+119)
		tmp = x;
	elseif (z <= -8.2e-215)
		tmp = t_1;
	elseif (z <= 3.8e+33)
		tmp = (y - z) * (x / t);
	elseif (z <= 1.45e+91)
		tmp = z / (z / x);
	elseif ((z <= 6e+126) || (~((z <= 2.7e+155)) && (z <= 6.2e+188)))
		tmp = t_1;
	else
		tmp = x;
	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[z, -2.7e+119], x, If[LessEqual[z, -8.2e-215], t$95$1, If[LessEqual[z, 3.8e+33], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+91], N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6e+126], And[N[Not[LessEqual[z, 2.7e+155]], $MachinePrecision], LessEqual[z, 6.2e+188]]], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6999999999999998e119 or 6.0000000000000005e126 < z < 2.69999999999999994e155 or 6.2000000000000004e188 < z

   1. Initial program 72.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. Taylor expanded in z around inf 76.2%

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

   if -2.6999999999999998e119 < z < -8.1999999999999997e-215 or 1.45000000000000007e91 < z < 6.0000000000000005e126 or 2.69999999999999994e155 < z < 6.2000000000000004e188

   1. Initial program 86.8%

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

      1. associate-*r/ 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 72.1%

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

   if -8.1999999999999997e-215 < z < 3.80000000000000002e33

   1. Initial program 94.3%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 78.1%

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

   if 3.80000000000000002e33 < z < 1.45000000000000007e91

   1. Initial program 88.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

      3. neg-sub0 87.3%

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

      4. associate--r- 87.3%

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

      5. neg-sub0 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around 0 75.7%

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

      1. associate-/l* 87.3%

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

   9. Simplified 87.3%

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

   10. Taylor expanded in z around inf 71.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+33}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+91}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+126} \lor \neg \left(z \leq 2.7 \cdot 10^{+155}\right) \land z \leq 6.2 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+36}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{1 + \frac{y}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -1.28e+123)
     x
     (if (<= z -2.7e-213)
       t_1
       (if (<= z 8.5e+36)
         (* (- y z) (/ x t))
         (if (<= z 7.2e+89)
           (/ z (/ z x))
           (if (<= z 6e+126)
             t_1
             (if (<= z 2.1e+155)
               (/ x (+ 1.0 (/ y z)))
               (if (<= z 6.2e+188) t_1 x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -1.28e+123) {
		tmp = x;
	} else if (z <= -2.7e-213) {
		tmp = t_1;
	} else if (z <= 8.5e+36) {
		tmp = (y - z) * (x / t);
	} else if (z <= 7.2e+89) {
		tmp = z / (z / x);
	} else if (z <= 6e+126) {
		tmp = t_1;
	} else if (z <= 2.1e+155) {
		tmp = x / (1.0 + (y / z));
	} else if (z <= 6.2e+188) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-1.28d+123)) then
        tmp = x
    else if (z <= (-2.7d-213)) then
        tmp = t_1
    else if (z <= 8.5d+36) then
        tmp = (y - z) * (x / t)
    else if (z <= 7.2d+89) then
        tmp = z / (z / x)
    else if (z <= 6d+126) then
        tmp = t_1
    else if (z <= 2.1d+155) then
        tmp = x / (1.0d0 + (y / z))
    else if (z <= 6.2d+188) then
        tmp = t_1
    else
        tmp = x
    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 (z <= -1.28e+123) {
		tmp = x;
	} else if (z <= -2.7e-213) {
		tmp = t_1;
	} else if (z <= 8.5e+36) {
		tmp = (y - z) * (x / t);
	} else if (z <= 7.2e+89) {
		tmp = z / (z / x);
	} else if (z <= 6e+126) {
		tmp = t_1;
	} else if (z <= 2.1e+155) {
		tmp = x / (1.0 + (y / z));
	} else if (z <= 6.2e+188) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -1.28e+123:
		tmp = x
	elif z <= -2.7e-213:
		tmp = t_1
	elif z <= 8.5e+36:
		tmp = (y - z) * (x / t)
	elif z <= 7.2e+89:
		tmp = z / (z / x)
	elif z <= 6e+126:
		tmp = t_1
	elif z <= 2.1e+155:
		tmp = x / (1.0 + (y / z))
	elif z <= 6.2e+188:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -1.28e+123)
		tmp = x;
	elseif (z <= -2.7e-213)
		tmp = t_1;
	elseif (z <= 8.5e+36)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 7.2e+89)
		tmp = Float64(z / Float64(z / x));
	elseif (z <= 6e+126)
		tmp = t_1;
	elseif (z <= 2.1e+155)
		tmp = Float64(x / Float64(1.0 + Float64(y / z)));
	elseif (z <= 6.2e+188)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -1.28e+123)
		tmp = x;
	elseif (z <= -2.7e-213)
		tmp = t_1;
	elseif (z <= 8.5e+36)
		tmp = (y - z) * (x / t);
	elseif (z <= 7.2e+89)
		tmp = z / (z / x);
	elseif (z <= 6e+126)
		tmp = t_1;
	elseif (z <= 2.1e+155)
		tmp = x / (1.0 + (y / z));
	elseif (z <= 6.2e+188)
		tmp = t_1;
	else
		tmp = x;
	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[z, -1.28e+123], x, If[LessEqual[z, -2.7e-213], t$95$1, If[LessEqual[z, 8.5e+36], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+89], N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+126], t$95$1, If[LessEqual[z, 2.1e+155], N[(x / N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+188], t$95$1, x]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.28000000000000005e123 or 6.2000000000000004e188 < z

   1. Initial program 71.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 76.7%

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

   if -1.28000000000000005e123 < z < -2.7000000000000001e-213 or 7.2e89 < z < 6.0000000000000005e126 or 2.1e155 < z < 6.2000000000000004e188

   1. Initial program 86.8%

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

      1. associate-*r/ 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 72.1%

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

   if -2.7000000000000001e-213 < z < 8.50000000000000014e36

   1. Initial program 94.3%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 78.1%

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

   if 8.50000000000000014e36 < z < 7.2e89

   1. Initial program 88.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

      3. neg-sub0 87.3%

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

      4. associate--r- 87.3%

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

      5. neg-sub0 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around 0 75.7%

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

      1. associate-/l* 87.3%

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

   9. Simplified 87.3%

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

   10. Taylor expanded in z around inf 71.6%

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

   if 6.0000000000000005e126 < z < 2.1e155

   1. Initial program 78.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 78.8%

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

      1. neg-mul-1 78.8%

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

      2. distribute-neg-frac 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in z around inf 75.0%

      \[\leadsto \frac{x}{\color{blue}{1 + \frac{y}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+36}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{1 + \frac{y}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+89}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+126} \lor \neg \left(z \leq 9.5 \cdot 10^{+154}\right) \land z \leq 6.2 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -5.5e+118)
     x
     (if (<= z 7.9e+34)
       t_1
       (if (<= z 3.9e+89)
         (/ z (/ z x))
         (if (or (<= z 6.2e+126) (and (not (<= z 9.5e+154)) (<= z 6.2e+188)))
           t_1
           x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -5.5e+118) {
		tmp = x;
	} else if (z <= 7.9e+34) {
		tmp = t_1;
	} else if (z <= 3.9e+89) {
		tmp = z / (z / x);
	} else if ((z <= 6.2e+126) || (!(z <= 9.5e+154) && (z <= 6.2e+188))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-5.5d+118)) then
        tmp = x
    else if (z <= 7.9d+34) then
        tmp = t_1
    else if (z <= 3.9d+89) then
        tmp = z / (z / x)
    else if ((z <= 6.2d+126) .or. (.not. (z <= 9.5d+154)) .and. (z <= 6.2d+188)) then
        tmp = t_1
    else
        tmp = x
    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 (z <= -5.5e+118) {
		tmp = x;
	} else if (z <= 7.9e+34) {
		tmp = t_1;
	} else if (z <= 3.9e+89) {
		tmp = z / (z / x);
	} else if ((z <= 6.2e+126) || (!(z <= 9.5e+154) && (z <= 6.2e+188))) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -5.5e+118:
		tmp = x
	elif z <= 7.9e+34:
		tmp = t_1
	elif z <= 3.9e+89:
		tmp = z / (z / x)
	elif (z <= 6.2e+126) or (not (z <= 9.5e+154) and (z <= 6.2e+188)):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -5.5e+118)
		tmp = x;
	elseif (z <= 7.9e+34)
		tmp = t_1;
	elseif (z <= 3.9e+89)
		tmp = Float64(z / Float64(z / x));
	elseif ((z <= 6.2e+126) || (!(z <= 9.5e+154) && (z <= 6.2e+188)))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -5.5e+118)
		tmp = x;
	elseif (z <= 7.9e+34)
		tmp = t_1;
	elseif (z <= 3.9e+89)
		tmp = z / (z / x);
	elseif ((z <= 6.2e+126) || (~((z <= 9.5e+154)) && (z <= 6.2e+188)))
		tmp = t_1;
	else
		tmp = x;
	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[z, -5.5e+118], x, If[LessEqual[z, 7.9e+34], t$95$1, If[LessEqual[z, 3.9e+89], N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6.2e+126], And[N[Not[LessEqual[z, 9.5e+154]], $MachinePrecision], LessEqual[z, 6.2e+188]]], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000003e118 or 6.2e126 < z < 9.5000000000000001e154 or 6.2000000000000004e188 < z

   1. Initial program 72.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. Taylor expanded in z around inf 76.2%

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

   if -5.5000000000000003e118 < z < 7.89999999999999997e34 or 3.90000000000000011e89 < z < 6.2e126 or 9.5000000000000001e154 < z < 6.2000000000000004e188

   1. Initial program 90.8%

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

      1. associate-*r/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in y around inf 71.6%

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

   if 7.89999999999999997e34 < z < 3.90000000000000011e89

   1. Initial program 88.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

      3. neg-sub0 87.3%

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

      4. associate--r- 87.3%

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

      5. neg-sub0 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around 0 75.7%

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

      1. associate-/l* 87.3%

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

   9. Simplified 87.3%

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

   10. Taylor expanded in z around inf 71.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+89}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+126} \lor \neg \left(z \leq 9.5 \cdot 10^{+154}\right) \land z \leq 6.2 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.14 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \frac{z}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.3e+14)
   (/ x (- 1.0 (/ t z)))
   (if (<= z -1.14e-275)
     (/ x (/ (- t z) y))
     (if (<= z 8e-83) (/ y (/ (- t z) x)) (- (* x (/ z (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.3e+14) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= -1.14e-275) {
		tmp = x / ((t - z) / y);
	} else if (z <= 8e-83) {
		tmp = y / ((t - z) / x);
	} else {
		tmp = -(x * (z / (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 <= (-4.3d+14)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= (-1.14d-275)) then
        tmp = x / ((t - z) / y)
    else if (z <= 8d-83) then
        tmp = y / ((t - z) / x)
    else
        tmp = -(x * (z / (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 <= -4.3e+14) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= -1.14e-275) {
		tmp = x / ((t - z) / y);
	} else if (z <= 8e-83) {
		tmp = y / ((t - z) / x);
	} else {
		tmp = -(x * (z / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.3e+14:
		tmp = x / (1.0 - (t / z))
	elif z <= -1.14e-275:
		tmp = x / ((t - z) / y)
	elif z <= 8e-83:
		tmp = y / ((t - z) / x)
	else:
		tmp = -(x * (z / (t - z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.3e+14)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= -1.14e-275)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (z <= 8e-83)
		tmp = Float64(y / Float64(Float64(t - z) / x));
	else
		tmp = Float64(-Float64(x * Float64(z / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.3e+14)
		tmp = x / (1.0 - (t / z));
	elseif (z <= -1.14e-275)
		tmp = x / ((t - z) / y);
	elseif (z <= 8e-83)
		tmp = y / ((t - z) / x);
	else
		tmp = -(x * (z / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.3e+14], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.14e-275], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-83], N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], (-N[(x * N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.3e14

   1. Initial program 76.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 79.0%

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

      1. associate-*r/ 79.0%

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

      2. neg-mul-1 79.0%

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

      3. neg-sub0 79.0%

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

      4. associate--r- 79.0%

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

      5. neg-sub0 79.0%

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

   6. Simplified 79.0%

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

   7. Taylor expanded in t around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

   9. Simplified 79.1%

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

   if -4.3e14 < z < -1.13999999999999995e-275

   1. Initial program 91.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 89.0%

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

   if -1.13999999999999995e-275 < z < 8.0000000000000003e-83

   1. Initial program 92.4%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

      1. associate-/l* 92.4%

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

      2. clear-num 92.2%

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

      3. associate-/r/ 92.2%

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

   5. Applied egg-rr 92.2%

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

   6. Taylor expanded in y around inf 86.5%

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

      1. associate-/l* 93.9%

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

   8. Simplified 93.9%

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

   if 8.0000000000000003e-83 < z

   1. Initial program 82.8%

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

      1. associate-*r/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. neg-mul-1 74.8%

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

      2. distribute-neg-frac 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.14 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \frac{z}{t - z}\\ \end{array} \]

Alternative 6: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-276}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 (/ t z)))))
   (if (<= z -4.5e+15)
     t_1
     (if (<= z -1.45e-276)
       (/ x (/ (- t z) y))
       (if (<= z 4.5e-82) (/ y (/ (- t z) x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -4.5e+15) {
		tmp = t_1;
	} else if (z <= -1.45e-276) {
		tmp = x / ((t - z) / y);
	} else if (z <= 4.5e-82) {
		tmp = y / ((t - z) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - (t / z))
    if (z <= (-4.5d+15)) then
        tmp = t_1
    else if (z <= (-1.45d-276)) then
        tmp = x / ((t - z) / y)
    else if (z <= 4.5d-82) then
        tmp = y / ((t - z) / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -4.5e+15) {
		tmp = t_1;
	} else if (z <= -1.45e-276) {
		tmp = x / ((t - z) / y);
	} else if (z <= 4.5e-82) {
		tmp = y / ((t - z) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (1.0 - (t / z))
	tmp = 0
	if z <= -4.5e+15:
		tmp = t_1
	elif z <= -1.45e-276:
		tmp = x / ((t - z) / y)
	elif z <= 4.5e-82:
		tmp = y / ((t - z) / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(1.0 - Float64(t / z)))
	tmp = 0.0
	if (z <= -4.5e+15)
		tmp = t_1;
	elseif (z <= -1.45e-276)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (z <= 4.5e-82)
		tmp = Float64(y / Float64(Float64(t - z) / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (1.0 - (t / z));
	tmp = 0.0;
	if (z <= -4.5e+15)
		tmp = t_1;
	elseif (z <= -1.45e-276)
		tmp = x / ((t - z) / y);
	elseif (z <= 4.5e-82)
		tmp = y / ((t - z) / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+15], t$95$1, If[LessEqual[z, -1.45e-276], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-82], N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5e15 or 4.4999999999999998e-82 < z

   1. Initial program 80.3%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

      3. neg-sub0 76.3%

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

      4. associate--r- 76.3%

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

      5. neg-sub0 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in t around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

   9. Simplified 76.3%

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

   if -4.5e15 < z < -1.44999999999999994e-276

   1. Initial program 91.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 89.0%

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

   if -1.44999999999999994e-276 < z < 4.4999999999999998e-82

   1. Initial program 92.4%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

      1. associate-/l* 92.4%

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

      2. clear-num 92.2%

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

      3. associate-/r/ 92.2%

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

   5. Applied egg-rr 92.2%

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

   6. Taylor expanded in y around inf 86.5%

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

      1. associate-/l* 93.9%

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

   8. Simplified 93.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-276}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 7: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+14} \lor \neg \left(z \leq 2.6 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e+14) (not (<= z 2.6e-81)))
   (/ x (- 1.0 (/ t z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e+14) || !(z <= 2.6e-81)) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5d+14)) .or. (.not. (z <= 2.6d-81))) then
        tmp = x / (1.0d0 - (t / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e+14) || !(z <= 2.6e-81)) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e+14) or not (z <= 2.6e-81):
		tmp = x / (1.0 - (t / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5e+14) || !(z <= 2.6e-81))
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5e+14) || ~((z <= 2.6e-81)))
		tmp = x / (1.0 - (t / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5e+14], N[Not[LessEqual[z, 2.6e-81]], $MachinePrecision]], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e14 or 2.5999999999999999e-81 < z

   1. Initial program 80.2%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. neg-mul-1 76.7%

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

      3. neg-sub0 76.7%

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

      4. associate--r- 76.7%

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

      5. neg-sub0 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in t around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

   9. Simplified 76.8%

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

   if -5e14 < z < 2.5999999999999999e-81

   1. Initial program 92.0%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 86.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+14} \lor \neg \left(z \leq 2.6 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 8: 40.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e-94) x (if (<= z 1.85e-127) (* z (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e-94) {
		tmp = x;
	} else if (z <= 1.85e-127) {
		tmp = z * (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 <= (-1.2d-94)) then
        tmp = x
    else if (z <= 1.85d-127) then
        tmp = z * (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 <= -1.2e-94) {
		tmp = x;
	} else if (z <= 1.85e-127) {
		tmp = z * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e-94:
		tmp = x
	elif z <= 1.85e-127:
		tmp = z * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e-94)
		tmp = x;
	elseif (z <= 1.85e-127)
		tmp = Float64(z * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e-94)
		tmp = x;
	elseif (z <= 1.85e-127)
		tmp = z * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e-94], x, If[LessEqual[z, 1.85e-127], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e-94 or 1.8500000000000002e-127 < z

   1. Initial program 80.6%

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

      1. associate-*r/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around inf 50.1%

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

   if -1.2e-94 < z < 1.8500000000000002e-127

   1. Initial program 94.8%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around inf 79.6%

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

   5. Taylor expanded in y around 0 27.6%

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

      1. associate-*r/ 29.1%

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

      2. associate-*l* 29.1%

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

      3. neg-mul-1 29.1%

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

      4. *-commutative 29.1%

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

   7. Simplified 29.1%

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

      1. expm1-log1p-u 28.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t} \cdot \left(-z\right)\right)\right)} \]

      2. expm1-udef 24.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \left(-z\right)\right)} - 1} \]

      3. add-sqr-sqrt 15.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}\right)} - 1 \]

      4. sqrt-unprod 22.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right)} - 1 \]

      5. sqr-neg 22.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \sqrt{\color{blue}{z \cdot z}}\right)} - 1 \]

      6. sqrt-unprod 12.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right)} - 1 \]

      7. add-sqr-sqrt 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \color{blue}{z}\right)} - 1 \]

      8. *-commutative 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{z \cdot \frac{x}{t}}\right)} - 1 \]

   9. Applied egg-rr 23.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(z \cdot \frac{x}{t}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 23.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z \cdot \frac{x}{t}\right)\right)} \]

       2. expm1-log1p 30.7%

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

   11. Simplified 30.7%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.2e+14) x (if (<= z 9.5e-81) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.2e+14) {
		tmp = x;
	} else if (z <= 9.5e-81) {
		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 <= (-3.2d+14)) then
        tmp = x
    else if (z <= 9.5d-81) 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 <= -3.2e+14) {
		tmp = x;
	} else if (z <= 9.5e-81) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.2e+14:
		tmp = x
	elif z <= 9.5e-81:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.2e+14)
		tmp = x;
	elseif (z <= 9.5e-81)
		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 <= -3.2e+14)
		tmp = x;
	elseif (z <= 9.5e-81)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.2e+14], x, If[LessEqual[z, 9.5e-81], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e14 or 9.49999999999999917e-81 < z

   1. Initial program 79.8%

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

      1. associate-*r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around inf 55.5%

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

   if -3.2e14 < z < 9.49999999999999917e-81

   1. Initial program 92.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 72.7%

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

      1. associate-/r/ 71.6%

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

   6. Applied egg-rr 71.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e+112) x (if (<= z 2.1e+30) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e+112) {
		tmp = x;
	} else if (z <= 2.1e+30) {
		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 <= (-1.75d+112)) then
        tmp = x
    else if (z <= 2.1d+30) 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 <= -1.75e+112) {
		tmp = x;
	} else if (z <= 2.1e+30) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e+112:
		tmp = x
	elif z <= 2.1e+30:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e+112)
		tmp = x;
	elseif (z <= 2.1e+30)
		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 <= -1.75e+112)
		tmp = x;
	elseif (z <= 2.1e+30)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e+112], x, If[LessEqual[z, 2.1e+30], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.74999999999999998e112 or 2.1e30 < z

   1. Initial program 76.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 63.3%

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

   if -1.74999999999999998e112 < z < 2.1e30

   1. Initial program 92.1%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in z around 0 61.2%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 35.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.6%

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

   1. associate-*r/ 97.0%

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

3. Simplified 97.0%

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

4. Taylor expanded in z around inf 37.1%

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

5. Final simplification 37.1%

   \[\leadsto x \]

Developer target: 97.3% 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 2023196 
(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)))