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

Percentage Accurate: 84.0% → 97.0%

Time: 11.9s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% 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 83.8%

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

   1. clear-num 96.8%

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

   2. un-div-inv 97.3%

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

6. Applied egg-rr 97.3%

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

7. Final simplification 97.3%

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

Alternative 2: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+96} \lor \neg \left(z \leq -1.15 \cdot 10^{+43}\right) \land \left(z \leq -3.1 \cdot 10^{-124} \lor \neg \left(z \leq 0.75\right)\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e+96)
         (and (not (<= z -1.15e+43)) (or (<= z -3.1e-124) (not (<= z 0.75)))))
   (* x (/ z (- z t)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+96) || (!(z <= -1.15e+43) && ((z <= -3.1e-124) || !(z <= 0.75)))) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d+96)) .or. (.not. (z <= (-1.15d+43))) .and. (z <= (-3.1d-124)) .or. (.not. (z <= 0.75d0))) then
        tmp = x * (z / (z - t))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+96) || (!(z <= -1.15e+43) && ((z <= -3.1e-124) || !(z <= 0.75)))) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e+96) or (not (z <= -1.15e+43) and ((z <= -3.1e-124) or not (z <= 0.75))):
		tmp = x * (z / (z - t))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e+96) || (!(z <= -1.15e+43) && ((z <= -3.1e-124) || !(z <= 0.75))))
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e+96) || (~((z <= -1.15e+43)) && ((z <= -3.1e-124) || ~((z <= 0.75)))))
		tmp = x * (z / (z - t));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e+96], And[N[Not[LessEqual[z, -1.15e+43]], $MachinePrecision], Or[LessEqual[z, -3.1e-124], N[Not[LessEqual[z, 0.75]], $MachinePrecision]]]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000003e96 or -1.1500000000000001e43 < z < -3.0999999999999998e-124 or 0.75 < z

   1. Initial program 78.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. associate-/l* 83.4%

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

      3. distribute-rgt-neg-in 83.4%

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

      4. distribute-neg-frac2 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in x around 0 65.3%

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

      1. associate-/l* 83.4%

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

   10. Simplified 83.4%

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

   if -1.60000000000000003e96 < z < -1.1500000000000001e43 or -3.0999999999999998e-124 < z < 0.75

   1. Initial program 90.1%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf 77.2%

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

      1. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+96} \lor \neg \left(z \leq -1.15 \cdot 10^{+43}\right) \land \left(z \leq -3.1 \cdot 10^{-124} \lor \neg \left(z \leq 0.75\right)\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+42} \lor \neg \left(z \leq -4.1 \cdot 10^{-10}\right) \land z \leq 2.15 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e+96)
   x
   (if (or (<= z -4.7e+42) (and (not (<= z -4.1e-10)) (<= z 2.15e+52)))
     (* x (/ y (- t z)))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+96) {
		tmp = x;
	} else if ((z <= -4.7e+42) || (!(z <= -4.1e-10) && (z <= 2.15e+52))) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.9d+96)) then
        tmp = x
    else if ((z <= (-4.7d+42)) .or. (.not. (z <= (-4.1d-10))) .and. (z <= 2.15d+52)) then
        tmp = x * (y / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+96) {
		tmp = x;
	} else if ((z <= -4.7e+42) || (!(z <= -4.1e-10) && (z <= 2.15e+52))) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.9e+96:
		tmp = x
	elif (z <= -4.7e+42) or (not (z <= -4.1e-10) and (z <= 2.15e+52)):
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e+96)
		tmp = x;
	elseif ((z <= -4.7e+42) || (!(z <= -4.1e-10) && (z <= 2.15e+52)))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.9e+96)
		tmp = x;
	elseif ((z <= -4.7e+42) || (~((z <= -4.1e-10)) && (z <= 2.15e+52)))
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e+96], x, If[Or[LessEqual[z, -4.7e+42], And[N[Not[LessEqual[z, -4.1e-10]], $MachinePrecision], LessEqual[z, 2.15e+52]]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9000000000000001e96 or -4.69999999999999986e42 < z < -4.0999999999999998e-10 or 2.15e52 < z

   1. Initial program 76.4%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around inf 75.5%

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

   if -1.9000000000000001e96 < z < -4.69999999999999986e42 or -4.0999999999999998e-10 < z < 2.15e52

   1. Initial program 89.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+42} \lor \neg \left(z \leq -4.1 \cdot 10^{-10}\right) \land z \leq 2.15 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-11} \lor \neg \left(z \leq 3.7 \cdot 10^{+48}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -1.6e+96)
     t_1
     (if (<= z -7.8e+43)
       (* x (/ y (- t z)))
       (if (or (<= z -1.55e-11) (not (<= z 3.7e+48)))
         t_1
         (* x (/ (- y z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.6e+96) {
		tmp = t_1;
	} else if (z <= -7.8e+43) {
		tmp = x * (y / (t - z));
	} else if ((z <= -1.55e-11) || !(z <= 3.7e+48)) {
		tmp = t_1;
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-1.6d+96)) then
        tmp = t_1
    else if (z <= (-7.8d+43)) then
        tmp = x * (y / (t - z))
    else if ((z <= (-1.55d-11)) .or. (.not. (z <= 3.7d+48))) then
        tmp = t_1
    else
        tmp = x * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.6e+96) {
		tmp = t_1;
	} else if (z <= -7.8e+43) {
		tmp = x * (y / (t - z));
	} else if ((z <= -1.55e-11) || !(z <= 3.7e+48)) {
		tmp = t_1;
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -1.6e+96:
		tmp = t_1
	elif z <= -7.8e+43:
		tmp = x * (y / (t - z))
	elif (z <= -1.55e-11) or not (z <= 3.7e+48):
		tmp = t_1
	else:
		tmp = x * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.6e+96)
		tmp = t_1;
	elseif (z <= -7.8e+43)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif ((z <= -1.55e-11) || !(z <= 3.7e+48))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1.6e+96)
		tmp = t_1;
	elseif (z <= -7.8e+43)
		tmp = x * (y / (t - z));
	elseif ((z <= -1.55e-11) || ~((z <= 3.7e+48)))
		tmp = t_1;
	else
		tmp = x * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+96], t$95$1, If[LessEqual[z, -7.8e+43], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.55e-11], N[Not[LessEqual[z, 3.7e+48]], $MachinePrecision]], t$95$1, N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000003e96 or -7.8000000000000001e43 < z < -1.55000000000000014e-11 or 3.6999999999999999e48 < z

   1. Initial program 76.2%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-/l* 87.3%

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

      3. distribute-rgt-neg-in 87.3%

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

      4. distribute-neg-frac2 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 66.8%

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

      1. associate-/l* 87.3%

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

   10. Simplified 87.3%

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

   if -1.60000000000000003e96 < z < -7.8000000000000001e43

   1. Initial program 81.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around inf 61.9%

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

      1. associate-/l* 68.2%

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

   7. Simplified 68.2%

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

   if -1.55000000000000014e-11 < z < 3.6999999999999999e48

   1. Initial program 91.1%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in t around inf 80.0%

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

      1. associate-/l* 80.3%

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

   7. Simplified 80.3%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-11} \lor \neg \left(z \leq 3.7 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.75 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-14} \lor \neg \left(z \leq 3.7 \cdot 10^{+48}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -1.6e+96)
     t_1
     (if (<= z -3.75e+43)
       (* x (/ y (- t z)))
       (if (or (<= z -2.75e-14) (not (<= z 3.7e+48)))
         t_1
         (* (- y z) (/ x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.6e+96) {
		tmp = t_1;
	} else if (z <= -3.75e+43) {
		tmp = x * (y / (t - z));
	} else if ((z <= -2.75e-14) || !(z <= 3.7e+48)) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-1.6d+96)) then
        tmp = t_1
    else if (z <= (-3.75d+43)) then
        tmp = x * (y / (t - z))
    else if ((z <= (-2.75d-14)) .or. (.not. (z <= 3.7d+48))) then
        tmp = t_1
    else
        tmp = (y - z) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.6e+96) {
		tmp = t_1;
	} else if (z <= -3.75e+43) {
		tmp = x * (y / (t - z));
	} else if ((z <= -2.75e-14) || !(z <= 3.7e+48)) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -1.6e+96:
		tmp = t_1
	elif z <= -3.75e+43:
		tmp = x * (y / (t - z))
	elif (z <= -2.75e-14) or not (z <= 3.7e+48):
		tmp = t_1
	else:
		tmp = (y - z) * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.6e+96)
		tmp = t_1;
	elseif (z <= -3.75e+43)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif ((z <= -2.75e-14) || !(z <= 3.7e+48))
		tmp = t_1;
	else
		tmp = Float64(Float64(y - z) * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1.6e+96)
		tmp = t_1;
	elseif (z <= -3.75e+43)
		tmp = x * (y / (t - z));
	elseif ((z <= -2.75e-14) || ~((z <= 3.7e+48)))
		tmp = t_1;
	else
		tmp = (y - z) * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+96], t$95$1, If[LessEqual[z, -3.75e+43], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.75e-14], N[Not[LessEqual[z, 3.7e+48]], $MachinePrecision]], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000003e96 or -3.74999999999999984e43 < z < -2.74999999999999996e-14 or 3.6999999999999999e48 < z

   1. Initial program 76.2%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-/l* 87.3%

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

      3. distribute-rgt-neg-in 87.3%

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

      4. distribute-neg-frac2 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 66.8%

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

      1. associate-/l* 87.3%

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

   10. Simplified 87.3%

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

   if -1.60000000000000003e96 < z < -3.74999999999999984e43

   1. Initial program 81.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around inf 61.9%

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

      1. associate-/l* 68.2%

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

   7. Simplified 68.2%

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

   if -2.74999999999999996e-14 < z < 3.6999999999999999e48

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around inf 80.4%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -3.75 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-14} \lor \neg \left(z \leq 3.7 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+48}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -1.6e+96)
     t_1
     (if (<= z -6.3e+43)
       (* x (/ y (- t z)))
       (if (<= z -4.6e-16)
         (- x (/ (* x y) z))
         (if (<= z 3.7e+48) (* (- y z) (/ x t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.6e+96) {
		tmp = t_1;
	} else if (z <= -6.3e+43) {
		tmp = x * (y / (t - z));
	} else if (z <= -4.6e-16) {
		tmp = x - ((x * y) / z);
	} else if (z <= 3.7e+48) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-1.6d+96)) then
        tmp = t_1
    else if (z <= (-6.3d+43)) then
        tmp = x * (y / (t - z))
    else if (z <= (-4.6d-16)) then
        tmp = x - ((x * y) / z)
    else if (z <= 3.7d+48) then
        tmp = (y - z) * (x / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.6e+96) {
		tmp = t_1;
	} else if (z <= -6.3e+43) {
		tmp = x * (y / (t - z));
	} else if (z <= -4.6e-16) {
		tmp = x - ((x * y) / z);
	} else if (z <= 3.7e+48) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -1.6e+96:
		tmp = t_1
	elif z <= -6.3e+43:
		tmp = x * (y / (t - z))
	elif z <= -4.6e-16:
		tmp = x - ((x * y) / z)
	elif z <= 3.7e+48:
		tmp = (y - z) * (x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.6e+96)
		tmp = t_1;
	elseif (z <= -6.3e+43)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= -4.6e-16)
		tmp = Float64(x - Float64(Float64(x * y) / z));
	elseif (z <= 3.7e+48)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1.6e+96)
		tmp = t_1;
	elseif (z <= -6.3e+43)
		tmp = x * (y / (t - z));
	elseif (z <= -4.6e-16)
		tmp = x - ((x * y) / z);
	elseif (z <= 3.7e+48)
		tmp = (y - z) * (x / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+96], t$95$1, If[LessEqual[z, -6.3e+43], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e-16], N[(x - N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+48], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.60000000000000003e96 or 3.6999999999999999e48 < z

   1. Initial program 74.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

      4. distribute-neg-frac2 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in x around 0 65.2%

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

      1. associate-/l* 87.2%

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

   10. Simplified 87.2%

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

   if -1.60000000000000003e96 < z < -6.2999999999999998e43

   1. Initial program 81.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around inf 61.9%

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

      1. associate-/l* 68.2%

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

   7. Simplified 68.2%

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

   if -6.2999999999999998e43 < z < -4.5999999999999998e-16

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 90.6%

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

      1. associate-*r/ 90.6%

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

      2. neg-mul-1 90.6%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in y around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

   10. Simplified 99.5%

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

   if -4.5999999999999998e-16 < z < 3.6999999999999999e48

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around inf 80.4%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+48}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{-z} - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.08e-11)
   (/ x (- 1.0 (/ t z)))
   (if (<= z -3.5e-272)
     (/ (* x (- y z)) t)
     (if (<= z 5.2e+48) (* x (/ (- y z) t)) (* x (- (/ y (- z)) -1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e-11) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= -3.5e-272) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 5.2e+48) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * ((y / -z) - -1.0);
	}
	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 <= (-1.08d-11)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= (-3.5d-272)) then
        tmp = (x * (y - z)) / t
    else if (z <= 5.2d+48) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * ((y / -z) - (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e-11) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= -3.5e-272) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 5.2e+48) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * ((y / -z) - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.08e-11:
		tmp = x / (1.0 - (t / z))
	elif z <= -3.5e-272:
		tmp = (x * (y - z)) / t
	elif z <= 5.2e+48:
		tmp = x * ((y - z) / t)
	else:
		tmp = x * ((y / -z) - -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.08e-11)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= -3.5e-272)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 5.2e+48)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(-z)) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.08e-11)
		tmp = x / (1.0 - (t / z));
	elseif (z <= -3.5e-272)
		tmp = (x * (y - z)) / t;
	elseif (z <= 5.2e+48)
		tmp = x * ((y - z) / t);
	else
		tmp = x * ((y / -z) - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.08e-11], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-272], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5.2e+48], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / (-z)), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.07999999999999992e-11

   1. Initial program 84.2%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r/ 59.6%

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

      4. *-commutative 59.6%

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

      5. associate-/r/ 79.7%

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

      6. distribute-neg-frac 79.7%

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

      7. div-sub 79.8%

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

      8. sub-neg 79.8%

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

      9. *-inverses 79.8%

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

      10. metadata-eval 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in x around 0 79.8%

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

       1. mul-1-neg 79.8%

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

       2. sub-neg 79.8%

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

       3. metadata-eval 79.8%

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

       4. distribute-neg-frac2 79.8%

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

       5. +-commutative 79.8%

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

       6. distribute-neg-in 79.8%

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

       7. metadata-eval 79.8%

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

       8. unsub-neg 79.8%

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

   12. Simplified 79.8%

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

   if -1.07999999999999992e-11 < z < -3.4999999999999997e-272

   1. Initial program 97.4%

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

      1. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around inf 81.2%

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

   if -3.4999999999999997e-272 < z < 5.1999999999999999e48

   1. Initial program 88.0%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 79.7%

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

      1. associate-/l* 86.7%

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

   7. Simplified 86.7%

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

   if 5.1999999999999999e48 < z

   1. Initial program 67.4%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around 0 56.7%

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

      1. mul-1-neg 56.7%

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

      2. associate-/l* 86.5%

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

      3. distribute-lft-neg-in 86.5%

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

      4. div-sub 86.5%

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

      5. sub-neg 86.5%

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

      6. *-inverses 86.5%

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

      7. metadata-eval 86.5%

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

   7. Simplified 86.5%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{-z} - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e-126)
   (/ x (- 1.0 (/ t z)))
   (if (<= z -4.1e-280)
     (/ (* x y) (- t z))
     (if (<= z 3.8e+48) (* x (/ (- y z) t)) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e-126) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= -4.1e-280) {
		tmp = (x * y) / (t - z);
	} else if (z <= 3.8e+48) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.5d-126)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= (-4.1d-280)) then
        tmp = (x * y) / (t - z)
    else if (z <= 3.8d+48) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e-126) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= -4.1e-280) {
		tmp = (x * y) / (t - z);
	} else if (z <= 3.8e+48) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e-126:
		tmp = x / (1.0 - (t / z))
	elif z <= -4.1e-280:
		tmp = (x * y) / (t - z)
	elif z <= 3.8e+48:
		tmp = x * ((y - z) / t)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e-126)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= -4.1e-280)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (z <= 3.8e+48)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e-126)
		tmp = x / (1.0 - (t / z));
	elseif (z <= -4.1e-280)
		tmp = (x * y) / (t - z);
	elseif (z <= 3.8e+48)
		tmp = x * ((y - z) / t);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e-126], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e-280], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+48], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999987e-126

   1. Initial program 86.1%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

      1. clear-num 98.6%

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

      2. un-div-inv 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in y around 0 64.9%

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

      1. mul-1-neg 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-*r/ 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-/r/ 77.5%

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

      6. distribute-neg-frac 77.5%

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

      7. div-sub 77.5%

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

      8. sub-neg 77.5%

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

      9. *-inverses 77.5%

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

      10. metadata-eval 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in x around 0 77.5%

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

       1. mul-1-neg 77.5%

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

       2. sub-neg 77.5%

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

       3. metadata-eval 77.5%

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

       4. distribute-neg-frac2 77.5%

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

       5. +-commutative 77.5%

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

       6. distribute-neg-in 77.5%

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

       7. metadata-eval 77.5%

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

       8. unsub-neg 77.5%

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

   12. Simplified 77.5%

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

   if -5.49999999999999987e-126 < z < -4.1000000000000002e-280

   1. Initial program 96.7%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in y around inf 86.6%

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

   if -4.1000000000000002e-280 < z < 3.8e48

   1. Initial program 87.8%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 79.4%

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

      1. associate-/l* 86.5%

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

   7. Simplified 86.5%

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

   if 3.8e48 < z

   1. Initial program 68.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. associate-/l* 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

      4. distribute-neg-frac2 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in x around 0 59.1%

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

      1. associate-/l* 84.9%

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

   10. Simplified 84.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.6e-17)
   (/ x (- 1.0 (/ t z)))
   (if (<= z -5e-276)
     (/ (* x (- y z)) t)
     (if (<= z 4.5e+48) (* x (/ (- y z) t)) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.6e-17) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= -5e-276) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 4.5e+48) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.6d-17)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= (-5d-276)) then
        tmp = (x * (y - z)) / t
    else if (z <= 4.5d+48) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.6e-17) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= -5e-276) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 4.5e+48) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.6e-17:
		tmp = x / (1.0 - (t / z))
	elif z <= -5e-276:
		tmp = (x * (y - z)) / t
	elif z <= 4.5e+48:
		tmp = x * ((y - z) / t)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.6e-17)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= -5e-276)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 4.5e+48)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.6e-17)
		tmp = x / (1.0 - (t / z));
	elseif (z <= -5e-276)
		tmp = (x * (y - z)) / t;
	elseif (z <= 4.5e+48)
		tmp = x * ((y - z) / t);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.6e-17], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-276], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.5e+48], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.6000000000000002e-17

   1. Initial program 84.2%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r/ 59.6%

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

      4. *-commutative 59.6%

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

      5. associate-/r/ 79.7%

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

      6. distribute-neg-frac 79.7%

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

      7. div-sub 79.8%

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

      8. sub-neg 79.8%

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

      9. *-inverses 79.8%

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

      10. metadata-eval 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in x around 0 79.8%

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

       1. mul-1-neg 79.8%

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

       2. sub-neg 79.8%

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

       3. metadata-eval 79.8%

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

       4. distribute-neg-frac2 79.8%

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

       5. +-commutative 79.8%

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

       6. distribute-neg-in 79.8%

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

       7. metadata-eval 79.8%

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

       8. unsub-neg 79.8%

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

   12. Simplified 79.8%

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

   if -7.6000000000000002e-17 < z < -4.99999999999999967e-276

   1. Initial program 97.4%

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

      1. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around inf 81.2%

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

   if -4.99999999999999967e-276 < z < 4.49999999999999995e48

   1. Initial program 87.8%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 79.4%

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

      1. associate-/l* 86.5%

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

   7. Simplified 86.5%

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

   if 4.49999999999999995e48 < z

   1. Initial program 68.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. associate-/l* 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

      4. distribute-neg-frac2 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in x around 0 59.1%

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

      1. associate-/l* 84.9%

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

   10. Simplified 84.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-271}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.65e-14)
   x
   (if (<= z -2e-271) (/ (* x y) t) (if (<= z 4.8e+48) (* x (/ y t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.65e-14) {
		tmp = x;
	} else if (z <= -2e-271) {
		tmp = (x * y) / t;
	} else if (z <= 4.8e+48) {
		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 <= (-2.65d-14)) then
        tmp = x
    else if (z <= (-2d-271)) then
        tmp = (x * y) / t
    else if (z <= 4.8d+48) 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 <= -2.65e-14) {
		tmp = x;
	} else if (z <= -2e-271) {
		tmp = (x * y) / t;
	} else if (z <= 4.8e+48) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.65e-14:
		tmp = x
	elif z <= -2e-271:
		tmp = (x * y) / t
	elif z <= 4.8e+48:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.65e-14)
		tmp = x;
	elseif (z <= -2e-271)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 4.8e+48)
		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 <= -2.65e-14)
		tmp = x;
	elseif (z <= -2e-271)
		tmp = (x * y) / t;
	elseif (z <= 4.8e+48)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.65e-14], x, If[LessEqual[z, -2e-271], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.8e+48], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6500000000000001e-14 or 4.8000000000000002e48 < z

   1. Initial program 76.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 68.2%

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

   if -2.6500000000000001e-14 < z < -1.99999999999999993e-271

   1. Initial program 97.4%

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

      1. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in z around 0 69.2%

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

   if -1.99999999999999993e-271 < z < 4.8000000000000002e48

   1. Initial program 87.8%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 63.8%

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

      1. associate-/l* 72.0%

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

   7. Simplified 72.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-271}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+48}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e-15)
   (/ x (- 1.0 (/ t z)))
   (if (<= z 3.7e+48) (* (- y z) (/ x t)) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-15) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 3.7e+48) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.7d-15)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 3.7d+48) then
        tmp = (y - z) * (x / t)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-15) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 3.7e+48) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e-15:
		tmp = x / (1.0 - (t / z))
	elif z <= 3.7e+48:
		tmp = (y - z) * (x / t)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e-15)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 3.7e+48)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e-15)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 3.7e+48)
		tmp = (y - z) * (x / t);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e-15], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+48], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000009e-15

   1. Initial program 84.2%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r/ 59.6%

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

      4. *-commutative 59.6%

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

      5. associate-/r/ 79.7%

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

      6. distribute-neg-frac 79.7%

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

      7. div-sub 79.8%

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

      8. sub-neg 79.8%

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

      9. *-inverses 79.8%

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

      10. metadata-eval 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in x around 0 79.8%

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

       1. mul-1-neg 79.8%

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

       2. sub-neg 79.8%

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

       3. metadata-eval 79.8%

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

       4. distribute-neg-frac2 79.8%

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

       5. +-commutative 79.8%

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

       6. distribute-neg-in 79.8%

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

       7. metadata-eval 79.8%

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

       8. unsub-neg 79.8%

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

   12. Simplified 79.8%

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

   if -2.70000000000000009e-15 < z < 3.6999999999999999e48

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around inf 80.4%

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

   if 3.6999999999999999e48 < z

   1. Initial program 68.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. associate-/l* 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

      4. distribute-neg-frac2 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in x around 0 59.1%

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

      1. associate-/l* 84.9%

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

   10. Simplified 84.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+48}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e-18)
   (/ x (- 1.0 (/ t z)))
   (if (<= z 3.7e+48) (/ x (/ t (- y z))) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e-18) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 3.7e+48) {
		tmp = x / (t / (y - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9.5d-18)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 3.7d+48) then
        tmp = x / (t / (y - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e-18) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 3.7e+48) {
		tmp = x / (t / (y - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e-18:
		tmp = x / (1.0 - (t / z))
	elif z <= 3.7e+48:
		tmp = x / (t / (y - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e-18)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 3.7e+48)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e-18)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 3.7e+48)
		tmp = x / (t / (y - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e-18], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+48], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000003e-18

   1. Initial program 84.2%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r/ 59.6%

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

      4. *-commutative 59.6%

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

      5. associate-/r/ 79.7%

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

      6. distribute-neg-frac 79.7%

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

      7. div-sub 79.8%

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

      8. sub-neg 79.8%

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

      9. *-inverses 79.8%

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

      10. metadata-eval 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in x around 0 79.8%

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

       1. mul-1-neg 79.8%

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

       2. sub-neg 79.8%

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

       3. metadata-eval 79.8%

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

       4. distribute-neg-frac2 79.8%

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

       5. +-commutative 79.8%

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

       6. distribute-neg-in 79.8%

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

       7. metadata-eval 79.8%

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

       8. unsub-neg 79.8%

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

   12. Simplified 79.8%

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

   if -9.5000000000000003e-18 < z < 3.6999999999999999e48

   1. Initial program 91.1%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 93.7%

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

      2. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in t around inf 80.7%

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

   if 3.6999999999999999e48 < z

   1. Initial program 68.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. associate-/l* 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

      4. distribute-neg-frac2 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in x around 0 59.1%

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

      1. associate-/l* 84.9%

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

   10. Simplified 84.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.65e-14) x (if (<= z 4.4e+48) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.65e-14) {
		tmp = x;
	} else if (z <= 4.4e+48) {
		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 <= (-2.65d-14)) then
        tmp = x
    else if (z <= 4.4d+48) 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 <= -2.65e-14) {
		tmp = x;
	} else if (z <= 4.4e+48) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.65e-14:
		tmp = x
	elif z <= 4.4e+48:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.65e-14)
		tmp = x;
	elseif (z <= 4.4e+48)
		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 <= -2.65e-14)
		tmp = x;
	elseif (z <= 4.4e+48)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.65e-14], x, If[LessEqual[z, 4.4e+48], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6500000000000001e-14 or 4.3999999999999999e48 < z

   1. Initial program 76.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 68.2%

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

   if -2.6500000000000001e-14 < z < 4.3999999999999999e48

   1. Initial program 91.1%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around 0 65.7%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e-11) x (if (<= z 4.4e+48) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e-11) {
		tmp = x;
	} else if (z <= 4.4e+48) {
		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 <= (-4.5d-11)) then
        tmp = x
    else if (z <= 4.4d+48) 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 <= -4.5e-11) {
		tmp = x;
	} else if (z <= 4.4e+48) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e-11:
		tmp = x
	elif z <= 4.4e+48:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e-11)
		tmp = x;
	elseif (z <= 4.4e+48)
		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 <= -4.5e-11)
		tmp = x;
	elseif (z <= 4.4e+48)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e-11], x, If[LessEqual[z, 4.4e+48], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e-11 or 4.3999999999999999e48 < z

   1. Initial program 76.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 68.2%

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

   if -4.5e-11 < z < 4.3999999999999999e48

   1. Initial program 91.1%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 93.7%

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

      2. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in z around 0 67.7%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 97.0% 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 83.8%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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. Final simplification 97.2%

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

Alternative 16: 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 83.8%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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 z around inf 39.2%

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

6. Final simplification 39.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.0% 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 2024046 
(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)))