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

Percentage Accurate: 84.3% → 96.9%

Time: 9.9s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% 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 82.9%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

   1. clear-num 96.4%

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

   2. un-div-inv 96.9%

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

6. Applied egg-rr 96.9%

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

7. Final simplification 96.9%

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

Alternative 2: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+46} \lor \neg \left(z \leq -160000000\right) \land \left(z \leq -3.5 \cdot 10^{-89} \lor \neg \left(z \leq 6.8 \cdot 10^{+16}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+46)
         (and (not (<= z -160000000.0))
              (or (<= z -3.5e-89) (not (<= z 6.8e+16)))))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+46) || (!(z <= -160000000.0) && ((z <= -3.5e-89) || !(z <= 6.8e+16)))) {
		tmp = x * (1.0 - (y / 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 <= (-3.1d+46)) .or. (.not. (z <= (-160000000.0d0))) .and. (z <= (-3.5d-89)) .or. (.not. (z <= 6.8d+16))) then
        tmp = x * (1.0d0 - (y / 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 <= -3.1e+46) || (!(z <= -160000000.0) && ((z <= -3.5e-89) || !(z <= 6.8e+16)))) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+46) or (not (z <= -160000000.0) and ((z <= -3.5e-89) or not (z <= 6.8e+16))):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+46) || (!(z <= -160000000.0) && ((z <= -3.5e-89) || !(z <= 6.8e+16))))
		tmp = Float64(x * Float64(1.0 - Float64(y / 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 <= -3.1e+46) || (~((z <= -160000000.0)) && ((z <= -3.5e-89) || ~((z <= 6.8e+16)))))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+46], And[N[Not[LessEqual[z, -160000000.0]], $MachinePrecision], Or[LessEqual[z, -3.5e-89], N[Not[LessEqual[z, 6.8e+16]], $MachinePrecision]]]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999975e46 or -1.6e8 < z < -3.4999999999999997e-89 or 6.8e16 < z

   1. Initial program 73.6%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

      4. distribute-frac-neg 71.2%

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

      5. neg-sub0 71.2%

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

      6. associate--r- 71.2%

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

      7. neg-sub0 71.2%

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

      8. +-commutative 71.2%

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

      9. sub-neg 71.2%

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

      10. div-sub 71.2%

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

      11. *-inverses 71.2%

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

   7. Simplified 71.2%

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

   if -3.09999999999999975e46 < z < -1.6e8 or -3.4999999999999997e-89 < z < 6.8e16

   1. Initial program 93.5%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in y around inf 76.0%

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

      1. associate-/l* 76.7%

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

   7. Simplified 76.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+46} \lor \neg \left(z \leq -160000000\right) \land \left(z \leq -3.5 \cdot 10^{-89} \lor \neg \left(z \leq 6.8 \cdot 10^{+16}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ t_2 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.45 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))) (t_2 (* x (/ y (- t z)))))
   (if (<= y -3.5e+84)
     t_2
     (if (<= y -1.1e-80)
       t_1
       (if (<= y -4.45e-100) (/ y (/ t x)) (if (<= y 9e+113) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double t_2 = x * (y / (t - z));
	double tmp;
	if (y <= -3.5e+84) {
		tmp = t_2;
	} else if (y <= -1.1e-80) {
		tmp = t_1;
	} else if (y <= -4.45e-100) {
		tmp = y / (t / x);
	} else if (y <= 9e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    t_2 = x * (y / (t - z))
    if (y <= (-3.5d+84)) then
        tmp = t_2
    else if (y <= (-1.1d-80)) then
        tmp = t_1
    else if (y <= (-4.45d-100)) then
        tmp = y / (t / x)
    else if (y <= 9d+113) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double t_2 = x * (y / (t - z));
	double tmp;
	if (y <= -3.5e+84) {
		tmp = t_2;
	} else if (y <= -1.1e-80) {
		tmp = t_1;
	} else if (y <= -4.45e-100) {
		tmp = y / (t / x);
	} else if (y <= 9e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	t_2 = x * (y / (t - z))
	tmp = 0
	if y <= -3.5e+84:
		tmp = t_2
	elif y <= -1.1e-80:
		tmp = t_1
	elif y <= -4.45e-100:
		tmp = y / (t / x)
	elif y <= 9e+113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	t_2 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -3.5e+84)
		tmp = t_2;
	elseif (y <= -1.1e-80)
		tmp = t_1;
	elseif (y <= -4.45e-100)
		tmp = Float64(y / Float64(t / x));
	elseif (y <= 9e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	t_2 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -3.5e+84)
		tmp = t_2;
	elseif (y <= -1.1e-80)
		tmp = t_1;
	elseif (y <= -4.45e-100)
		tmp = y / (t / x);
	elseif (y <= 9e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+84], t$95$2, If[LessEqual[y, -1.1e-80], t$95$1, If[LessEqual[y, -4.45e-100], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+113], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4999999999999999e84 or 9.0000000000000001e113 < y

   1. Initial program 80.3%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around inf 73.0%

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

      1. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

   if -3.4999999999999999e84 < y < -1.10000000000000005e-80 or -4.4500000000000002e-100 < y < 9.0000000000000001e113

   1. Initial program 83.6%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-neg-frac2 63.7%

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

      3. neg-sub0 63.7%

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

      4. associate--r- 63.7%

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

      5. neg-sub0 63.7%

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

      6. +-commutative 63.7%

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

      7. sub-neg 63.7%

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

      8. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   if -1.10000000000000005e-80 < y < -4.4500000000000002e-100

   1. Initial program 99.8%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.6%

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

   7. Applied egg-rr 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 100.0%

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

   9. Applied egg-rr 100.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;y \leq -4.45 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))))
   (if (<= t -2.1e+118)
     t_1
     (if (<= t -6e+37)
       (* x (/ z (- z t)))
       (if (<= t -1.15e-105)
         (* x (/ y (- t z)))
         (if (<= t 7.2e+75) (* x (- 1.0 (/ y z))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (t <= -2.1e+118) {
		tmp = t_1;
	} else if (t <= -6e+37) {
		tmp = x * (z / (z - t));
	} else if (t <= -1.15e-105) {
		tmp = x * (y / (t - z));
	} else if (t <= 7.2e+75) {
		tmp = x * (1.0 - (y / 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 * ((y - z) / t)
    if (t <= (-2.1d+118)) then
        tmp = t_1
    else if (t <= (-6d+37)) then
        tmp = x * (z / (z - t))
    else if (t <= (-1.15d-105)) then
        tmp = x * (y / (t - z))
    else if (t <= 7.2d+75) then
        tmp = x * (1.0d0 - (y / 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 * ((y - z) / t);
	double tmp;
	if (t <= -2.1e+118) {
		tmp = t_1;
	} else if (t <= -6e+37) {
		tmp = x * (z / (z - t));
	} else if (t <= -1.15e-105) {
		tmp = x * (y / (t - z));
	} else if (t <= 7.2e+75) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	tmp = 0
	if t <= -2.1e+118:
		tmp = t_1
	elif t <= -6e+37:
		tmp = x * (z / (z - t))
	elif t <= -1.15e-105:
		tmp = x * (y / (t - z))
	elif t <= 7.2e+75:
		tmp = x * (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -2.1e+118)
		tmp = t_1;
	elseif (t <= -6e+37)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (t <= -1.15e-105)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t <= 7.2e+75)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	tmp = 0.0;
	if (t <= -2.1e+118)
		tmp = t_1;
	elseif (t <= -6e+37)
		tmp = x * (z / (z - t));
	elseif (t <= -1.15e-105)
		tmp = x * (y / (t - z));
	elseif (t <= 7.2e+75)
		tmp = x * (1.0 - (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+118], t$95$1, If[LessEqual[t, -6e+37], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e-105], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+75], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1e118 or 7.2e75 < t

   1. Initial program 82.4%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in t around inf 75.1%

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

      1. associate-/l* 82.2%

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

   7. Simplified 82.2%

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

   if -2.1e118 < t < -6.00000000000000043e37

   1. Initial program 72.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-neg-frac2 60.4%

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

      3. neg-sub0 60.4%

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

      4. associate--r- 60.4%

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

      5. neg-sub0 60.4%

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

      6. +-commutative 60.4%

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

      7. sub-neg 60.4%

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

      8. associate-/l* 87.8%

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

   7. Simplified 87.8%

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

   if -6.00000000000000043e37 < t < -1.15e-105

   1. Initial program 83.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 63.7%

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

      1. associate-/l* 66.6%

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

   7. Simplified 66.6%

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

   if -1.15e-105 < t < 7.2e75

   1. Initial program 85.4%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. associate-/l* 79.9%

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

      3. distribute-rgt-neg-in 79.9%

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

      4. distribute-frac-neg 79.9%

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

      5. neg-sub0 79.9%

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

      6. associate--r- 79.9%

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

      7. neg-sub0 79.9%

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

      8. +-commutative 79.9%

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

      9. sub-neg 79.9%

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

      10. div-sub 79.9%

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

      11. *-inverses 79.9%

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

   7. Simplified 79.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;y \leq -4.45 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))))
   (if (<= y -1.7e+87)
     t_1
     (if (<= y -2.4e-82)
       (* x (/ z (- z t)))
       (if (<= y -4.45e-100)
         (/ y (/ t x))
         (if (<= y 5.6e+114) (/ x (- 1.0 (/ t z))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double tmp;
	if (y <= -1.7e+87) {
		tmp = t_1;
	} else if (y <= -2.4e-82) {
		tmp = x * (z / (z - t));
	} else if (y <= -4.45e-100) {
		tmp = y / (t / x);
	} else if (y <= 5.6e+114) {
		tmp = x / (1.0 - (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) / y)
    if (y <= (-1.7d+87)) then
        tmp = t_1
    else if (y <= (-2.4d-82)) then
        tmp = x * (z / (z - t))
    else if (y <= (-4.45d-100)) then
        tmp = y / (t / x)
    else if (y <= 5.6d+114) then
        tmp = x / (1.0d0 - (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) / y);
	double tmp;
	if (y <= -1.7e+87) {
		tmp = t_1;
	} else if (y <= -2.4e-82) {
		tmp = x * (z / (z - t));
	} else if (y <= -4.45e-100) {
		tmp = y / (t / x);
	} else if (y <= 5.6e+114) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	tmp = 0
	if y <= -1.7e+87:
		tmp = t_1
	elif y <= -2.4e-82:
		tmp = x * (z / (z - t))
	elif y <= -4.45e-100:
		tmp = y / (t / x)
	elif y <= 5.6e+114:
		tmp = x / (1.0 - (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) / y))
	tmp = 0.0
	if (y <= -1.7e+87)
		tmp = t_1;
	elseif (y <= -2.4e-82)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (y <= -4.45e-100)
		tmp = Float64(y / Float64(t / x));
	elseif (y <= 5.6e+114)
		tmp = Float64(x / Float64(1.0 - 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) / y);
	tmp = 0.0;
	if (y <= -1.7e+87)
		tmp = t_1;
	elseif (y <= -2.4e-82)
		tmp = x * (z / (z - t));
	elseif (y <= -4.45e-100)
		tmp = y / (t / x);
	elseif (y <= 5.6e+114)
		tmp = x / (1.0 - (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] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+87], t$95$1, If[LessEqual[y, -2.4e-82], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.45e-100], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+114], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7000000000000001e87 or 5.6000000000000001e114 < y

   1. Initial program 80.3%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.4%

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

      2. un-div-inv 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around inf 85.0%

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

   if -1.7000000000000001e87 < y < -2.40000000000000008e-82

   1. Initial program 93.9%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. distribute-neg-frac2 55.5%

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

      3. neg-sub0 55.5%

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

      4. associate--r- 55.5%

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

      5. neg-sub0 55.5%

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

      6. +-commutative 55.5%

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

      7. sub-neg 55.5%

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

      8. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

   if -2.40000000000000008e-82 < y < -4.4500000000000002e-100

   1. Initial program 99.8%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.6%

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

   7. Applied egg-rr 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -4.4500000000000002e-100 < y < 5.6000000000000001e114

   1. Initial program 81.1%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

      1. clear-num 96.2%

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

      2. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in y around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. div-sub 80.3%

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

      3. sub-neg 80.3%

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

      4. *-inverses 80.3%

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

      5. metadata-eval 80.3%

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

   9. Simplified 80.3%

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

   10. Taylor expanded in x around 0 80.3%

       \[\leadsto \color{blue}{\frac{x}{1 - \frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;y \leq -4.45 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -250000000 \lor \neg \left(z \leq -7.8 \cdot 10^{-91}\right) \land z \leq 52000000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e+43)
   x
   (if (or (<= z -250000000.0)
           (and (not (<= z -7.8e-91)) (<= z 52000000000.0)))
     (* x (/ y t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e+43) {
		tmp = x;
	} else if ((z <= -250000000.0) || (!(z <= -7.8e-91) && (z <= 52000000000.0))) {
		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 <= (-7.2d+43)) then
        tmp = x
    else if ((z <= (-250000000.0d0)) .or. (.not. (z <= (-7.8d-91))) .and. (z <= 52000000000.0d0)) 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 <= -7.2e+43) {
		tmp = x;
	} else if ((z <= -250000000.0) || (!(z <= -7.8e-91) && (z <= 52000000000.0))) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e+43:
		tmp = x
	elif (z <= -250000000.0) or (not (z <= -7.8e-91) and (z <= 52000000000.0)):
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e+43)
		tmp = x;
	elseif ((z <= -250000000.0) || (!(z <= -7.8e-91) && (z <= 52000000000.0)))
		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 <= -7.2e+43)
		tmp = x;
	elseif ((z <= -250000000.0) || (~((z <= -7.8e-91)) && (z <= 52000000000.0)))
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e+43], x, If[Or[LessEqual[z, -250000000.0], And[N[Not[LessEqual[z, -7.8e-91]], $MachinePrecision], LessEqual[z, 52000000000.0]]], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000002e43 or -2.5e8 < z < -7.79999999999999987e-91 or 5.2e10 < z

   1. Initial program 74.3%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 55.2%

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

   if -7.2000000000000002e43 < z < -2.5e8 or -7.79999999999999987e-91 < z < 5.2e10

   1. Initial program 93.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 63.6%

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

      1. associate-/l* 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -250000000 \lor \neg \left(z \leq -7.8 \cdot 10^{-91}\right) \land z \leq 52000000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -200000000 \lor \neg \left(z \leq -8.8 \cdot 10^{-91}\right) \land z \leq 45000000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+49)
   x
   (if (or (<= z -200000000.0)
           (and (not (<= z -8.8e-91)) (<= z 45000000000.0)))
     (/ x (/ t y))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+49) {
		tmp = x;
	} else if ((z <= -200000000.0) || (!(z <= -8.8e-91) && (z <= 45000000000.0))) {
		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 <= (-5.5d+49)) then
        tmp = x
    else if ((z <= (-200000000.0d0)) .or. (.not. (z <= (-8.8d-91))) .and. (z <= 45000000000.0d0)) 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 <= -5.5e+49) {
		tmp = x;
	} else if ((z <= -200000000.0) || (!(z <= -8.8e-91) && (z <= 45000000000.0))) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e+49:
		tmp = x
	elif (z <= -200000000.0) or (not (z <= -8.8e-91) and (z <= 45000000000.0)):
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+49)
		tmp = x;
	elseif ((z <= -200000000.0) || (!(z <= -8.8e-91) && (z <= 45000000000.0)))
		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 <= -5.5e+49)
		tmp = x;
	elseif ((z <= -200000000.0) || (~((z <= -8.8e-91)) && (z <= 45000000000.0)))
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+49], x, If[Or[LessEqual[z, -200000000.0], And[N[Not[LessEqual[z, -8.8e-91]], $MachinePrecision], LessEqual[z, 45000000000.0]]], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000042e49 or -2e8 < z < -8.8000000000000003e-91 or 4.5e10 < z

   1. Initial program 74.3%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 55.2%

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

   if -5.50000000000000042e49 < z < -2e8 or -8.8000000000000003e-91 < z < 4.5e10

   1. Initial program 93.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. clear-num 93.3%

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

      2. un-div-inv 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in z around 0 66.9%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -200000000 \lor \neg \left(z \leq -8.8 \cdot 10^{-91}\right) \land z \leq 45000000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -55:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 2050000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+78)
   x
   (if (<= z -55.0)
     (* x (/ (- z) t))
     (if (<= z -8.8e-91)
       (* x (/ y (- z)))
       (if (<= z 2050000000.0) (/ x (/ t y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+78) {
		tmp = x;
	} else if (z <= -55.0) {
		tmp = x * (-z / t);
	} else if (z <= -8.8e-91) {
		tmp = x * (y / -z);
	} else if (z <= 2050000000.0) {
		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 <= (-4d+78)) then
        tmp = x
    else if (z <= (-55.0d0)) then
        tmp = x * (-z / t)
    else if (z <= (-8.8d-91)) then
        tmp = x * (y / -z)
    else if (z <= 2050000000.0d0) 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 <= -4e+78) {
		tmp = x;
	} else if (z <= -55.0) {
		tmp = x * (-z / t);
	} else if (z <= -8.8e-91) {
		tmp = x * (y / -z);
	} else if (z <= 2050000000.0) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e+78:
		tmp = x
	elif z <= -55.0:
		tmp = x * (-z / t)
	elif z <= -8.8e-91:
		tmp = x * (y / -z)
	elif z <= 2050000000.0:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e+78)
		tmp = x;
	elseif (z <= -55.0)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= -8.8e-91)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (z <= 2050000000.0)
		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 <= -4e+78)
		tmp = x;
	elseif (z <= -55.0)
		tmp = x * (-z / t);
	elseif (z <= -8.8e-91)
		tmp = x * (y / -z);
	elseif (z <= 2050000000.0)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e+78], x, If[LessEqual[z, -55.0], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.8e-91], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2050000000.0], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.00000000000000003e78 or 2.05e9 < z

   1. Initial program 67.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 60.5%

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

   if -4.00000000000000003e78 < z < -55

   1. Initial program 95.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 58.8%

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

      1. associate-/l* 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in y around 0 40.7%

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

      1. mul-1-neg 40.7%

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

      2. associate-/l* 40.5%

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

      3. distribute-rgt-neg-in 40.5%

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

      4. distribute-neg-frac2 40.5%

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

   10. Simplified 40.5%

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

   if -55 < z < -8.8000000000000003e-91

   1. Initial program 99.8%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around inf 51.4%

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

      1. associate-/l* 51.2%

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

   7. Simplified 51.2%

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

   8. Taylor expanded in t around 0 41.3%

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

      1. associate-*r/ 41.3%

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

      2. neg-mul-1 41.3%

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

   10. Simplified 41.3%

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

   if -8.8000000000000003e-91 < z < 2.05e9

   1. Initial program 93.4%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 92.4%

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

      2. un-div-inv 93.5%

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

   6. Applied egg-rr 93.5%

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

   7. Taylor expanded in z around 0 69.6%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -55:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 2050000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 12500000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.2e+48)
   x
   (if (<= z -8.8e-91)
     (/ (* x (- y)) z)
     (if (<= z 12500000000.0) (/ x (/ t y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e+48) {
		tmp = x;
	} else if (z <= -8.8e-91) {
		tmp = (x * -y) / z;
	} else if (z <= 12500000000.0) {
		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 <= (-8.2d+48)) then
        tmp = x
    else if (z <= (-8.8d-91)) then
        tmp = (x * -y) / z
    else if (z <= 12500000000.0d0) 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 <= -8.2e+48) {
		tmp = x;
	} else if (z <= -8.8e-91) {
		tmp = (x * -y) / z;
	} else if (z <= 12500000000.0) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.2e+48:
		tmp = x
	elif z <= -8.8e-91:
		tmp = (x * -y) / z
	elif z <= 12500000000.0:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.2e+48)
		tmp = x;
	elseif (z <= -8.8e-91)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 12500000000.0)
		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 <= -8.2e+48)
		tmp = x;
	elseif (z <= -8.8e-91)
		tmp = (x * -y) / z;
	elseif (z <= 12500000000.0)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.2e+48], x, If[LessEqual[z, -8.8e-91], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 12500000000.0], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000005e48 or 1.25e10 < z

   1. Initial program 69.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.2%

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

   if -8.2000000000000005e48 < z < -8.8000000000000003e-91

   1. Initial program 97.2%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in y around inf 54.6%

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

      1. associate-/l* 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in t around 0 38.6%

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

      1. associate-*r/ 38.6%

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

      2. mul-1-neg 38.6%

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

      3. distribute-rgt-neg-out 38.6%

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

   10. Simplified 38.6%

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

   if -8.8000000000000003e-91 < z < 1.25e10

   1. Initial program 93.4%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 92.4%

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

      2. un-div-inv 93.5%

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

   6. Applied egg-rr 93.5%

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

   7. Taylor expanded in z around 0 69.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 12500000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-98} \lor \neg \left(z \leq 210000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05e-98) (not (<= z 210000000.0)))
   (* x (- 1.0 (/ y z)))
   (/ x (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-98) || !(z <= 210000000.0)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / 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 <= (-1.05d-98)) .or. (.not. (z <= 210000000.0d0))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-98) || !(z <= 210000000.0)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05e-98) or not (z <= 210000000.0):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e-98) || !(z <= 210000000.0))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e-98) || ~((z <= 210000000.0)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e-98], N[Not[LessEqual[z, 210000000.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999996e-98 or 2.1e8 < z

   1. Initial program 75.9%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. associate-/l* 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

      4. distribute-frac-neg 68.1%

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

      5. neg-sub0 68.1%

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

      6. associate--r- 68.1%

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

      7. neg-sub0 68.1%

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

      8. +-commutative 68.1%

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

      9. sub-neg 68.1%

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

      10. div-sub 68.1%

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

      11. *-inverses 68.1%

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

   7. Simplified 68.1%

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

   if -1.04999999999999996e-98 < z < 2.1e8

   1. Initial program 93.4%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 92.4%

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

      2. un-div-inv 93.5%

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

   6. Applied egg-rr 93.5%

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

   7. Taylor expanded in z around 0 69.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-98} \lor \neg \left(z \leq 210000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 96.9% 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 82.9%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 12: 34.8% 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 82.9%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in z around inf 34.3%

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

6. Final simplification 34.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.9% 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 2024082 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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