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

Percentage Accurate: 85.1% → 97.0%

Time: 11.4s

Alternatives: 10

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: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% 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 82.8%

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

   1. associate-/l* 95.6%

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

3. Simplified 95.6%

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

5. Final simplification 95.6%

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

Alternative 2: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 1500000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.4e+128)
   x
   (if (<= z -7.5e-17)
     (* x (/ y (- z)))
     (if (<= z 6.3e-242)
       (/ (* x y) t)
       (if (<= z 1500000000.0) (/ x (/ t y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e+128) {
		tmp = x;
	} else if (z <= -7.5e-17) {
		tmp = x * (y / -z);
	} else if (z <= 6.3e-242) {
		tmp = (x * y) / t;
	} else if (z <= 1500000000.0) {
		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 <= (-1.4d+128)) then
        tmp = x
    else if (z <= (-7.5d-17)) then
        tmp = x * (y / -z)
    else if (z <= 6.3d-242) then
        tmp = (x * y) / t
    else if (z <= 1500000000.0d0) 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 <= -1.4e+128) {
		tmp = x;
	} else if (z <= -7.5e-17) {
		tmp = x * (y / -z);
	} else if (z <= 6.3e-242) {
		tmp = (x * y) / t;
	} else if (z <= 1500000000.0) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.4e+128:
		tmp = x
	elif z <= -7.5e-17:
		tmp = x * (y / -z)
	elif z <= 6.3e-242:
		tmp = (x * y) / t
	elif z <= 1500000000.0:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.4e+128)
		tmp = x;
	elseif (z <= -7.5e-17)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (z <= 6.3e-242)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 1500000000.0)
		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 <= -1.4e+128)
		tmp = x;
	elseif (z <= -7.5e-17)
		tmp = x * (y / -z);
	elseif (z <= 6.3e-242)
		tmp = (x * y) / t;
	elseif (z <= 1500000000.0)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.4e+128], x, If[LessEqual[z, -7.5e-17], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.3e-242], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1500000000.0], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.39999999999999991e128 or 1.5e9 < z

   1. Initial program 66.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 70.5%

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

   if -1.39999999999999991e128 < z < -7.49999999999999984e-17

   1. Initial program 85.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 t around 0 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-/l* 50.3%

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

      3. associate-*l* 50.3%

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

      4. associate-*l/ 50.3%

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

      5. *-commutative 50.3%

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

      6. neg-mul-1 50.3%

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

      7. neg-sub0 50.3%

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

      8. associate--r- 50.3%

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

      9. neg-sub0 50.3%

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

      10. +-commutative 50.3%

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

      11. sub-neg 50.3%

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

      12. div-sub 50.3%

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

      13. *-inverses 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in y around inf 43.4%

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

      1. associate-*r/ 43.4%

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

      2. mul-1-neg 43.4%

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

      3. distribute-rgt-neg-out 43.4%

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

      4. associate-*r/ 43.4%

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

   10. Simplified 43.4%

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

   if -7.49999999999999984e-17 < z < 6.3000000000000001e-242

   1. Initial program 96.2%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in z around 0 72.7%

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

   if 6.3000000000000001e-242 < z < 1.5e9

   1. Initial program 89.8%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.4%

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

   6. Applied egg-rr 93.4%

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

   7. Taylor expanded in z around 0 58.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 1500000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 920000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.9e+114)
   x
   (if (<= z -6.4e-18)
     (* x (/ (- z) t))
     (if (<= z 6.6e-242)
       (/ (* x y) t)
       (if (<= z 920000000.0) (/ x (/ t y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.9e+114) {
		tmp = x;
	} else if (z <= -6.4e-18) {
		tmp = x * (-z / t);
	} else if (z <= 6.6e-242) {
		tmp = (x * y) / t;
	} else if (z <= 920000000.0) {
		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 <= (-7.9d+114)) then
        tmp = x
    else if (z <= (-6.4d-18)) then
        tmp = x * (-z / t)
    else if (z <= 6.6d-242) then
        tmp = (x * y) / t
    else if (z <= 920000000.0d0) 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 <= -7.9e+114) {
		tmp = x;
	} else if (z <= -6.4e-18) {
		tmp = x * (-z / t);
	} else if (z <= 6.6e-242) {
		tmp = (x * y) / t;
	} else if (z <= 920000000.0) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.9e+114:
		tmp = x
	elif z <= -6.4e-18:
		tmp = x * (-z / t)
	elif z <= 6.6e-242:
		tmp = (x * y) / t
	elif z <= 920000000.0:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.9e+114)
		tmp = x;
	elseif (z <= -6.4e-18)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= 6.6e-242)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 920000000.0)
		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 <= -7.9e+114)
		tmp = x;
	elseif (z <= -6.4e-18)
		tmp = x * (-z / t);
	elseif (z <= 6.6e-242)
		tmp = (x * y) / t;
	elseif (z <= 920000000.0)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.9e+114], x, If[LessEqual[z, -6.4e-18], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-242], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 920000000.0], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.9000000000000001e114 or 9.2e8 < z

   1. Initial program 66.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 69.8%

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

   if -7.9000000000000001e114 < z < -6.3999999999999998e-18

   1. Initial program 85.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 t around inf 44.2%

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

      1. associate-/l* 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in y around 0 44.2%

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

      1. neg-mul-1 44.2%

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

      2. distribute-neg-frac 44.2%

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

   10. Simplified 44.2%

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

   if -6.3999999999999998e-18 < z < 6.59999999999999963e-242

   1. Initial program 96.1%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in z around 0 73.6%

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

   if 6.59999999999999963e-242 < z < 9.2e8

   1. Initial program 89.8%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.4%

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

   6. Applied egg-rr 93.4%

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

   7. Taylor expanded in z around 0 58.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 920000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 25500000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.5e+124)
   x
   (if (<= z -7.8e-17)
     (* y (/ x (- z)))
     (if (<= z 7.3e-242)
       (/ (* x y) t)
       (if (<= z 25500000.0) (/ x (/ t y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+124) {
		tmp = x;
	} else if (z <= -7.8e-17) {
		tmp = y * (x / -z);
	} else if (z <= 7.3e-242) {
		tmp = (x * y) / t;
	} else if (z <= 25500000.0) {
		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 <= (-8.5d+124)) then
        tmp = x
    else if (z <= (-7.8d-17)) then
        tmp = y * (x / -z)
    else if (z <= 7.3d-242) then
        tmp = (x * y) / t
    else if (z <= 25500000.0d0) 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 <= -8.5e+124) {
		tmp = x;
	} else if (z <= -7.8e-17) {
		tmp = y * (x / -z);
	} else if (z <= 7.3e-242) {
		tmp = (x * y) / t;
	} else if (z <= 25500000.0) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.5e+124:
		tmp = x
	elif z <= -7.8e-17:
		tmp = y * (x / -z)
	elif z <= 7.3e-242:
		tmp = (x * y) / t
	elif z <= 25500000.0:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.5e+124)
		tmp = x;
	elseif (z <= -7.8e-17)
		tmp = Float64(y * Float64(x / Float64(-z)));
	elseif (z <= 7.3e-242)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 25500000.0)
		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 <= -8.5e+124)
		tmp = x;
	elseif (z <= -7.8e-17)
		tmp = y * (x / -z);
	elseif (z <= 7.3e-242)
		tmp = (x * y) / t;
	elseif (z <= 25500000.0)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.5e+124], x, If[LessEqual[z, -7.8e-17], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.3e-242], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 25500000.0], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.4999999999999997e124 or 2.55e7 < z

   1. Initial program 66.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 70.5%

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

   if -8.4999999999999997e124 < z < -7.79999999999999979e-17

   1. Initial program 85.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 t around 0 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-/l* 50.3%

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

      3. associate-*l* 50.3%

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

      4. associate-*l/ 50.3%

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

      5. *-commutative 50.3%

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

      6. neg-mul-1 50.3%

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

      7. neg-sub0 50.3%

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

      8. associate--r- 50.3%

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

      9. neg-sub0 50.3%

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

      10. +-commutative 50.3%

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

      11. sub-neg 50.3%

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

      12. div-sub 50.3%

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

      13. *-inverses 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in y around inf 43.4%

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

      1. associate-*r/ 43.4%

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

      2. mul-1-neg 43.4%

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

      3. distribute-rgt-neg-out 43.4%

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

      4. associate-*r/ 43.4%

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

   10. Simplified 43.4%

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

       1. clear-num 43.3%

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

       2. un-div-inv 43.4%

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

       3. add-sqr-sqrt 23.1%

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

       4. sqrt-unprod 17.6%

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

       5. sqr-neg 17.6%

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

       6. sqrt-unprod 1.7%

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

       7. add-sqr-sqrt 3.1%

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

   12. Applied egg-rr 3.1%

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

       1. associate-/r/ 6.7%

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

       2. associate-*l/ 3.1%

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

       3. associate-*r/ 3.1%

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

   14. Simplified 3.1%

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

       1. associate-*r/ 3.1%

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

       2. frac-2neg 3.1%

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

       3. *-commutative 3.1%

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

       4. distribute-rgt-neg-in 3.1%

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

       5. add-sqr-sqrt 1.4%

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

       6. sqrt-unprod 20.5%

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

       7. sqr-neg 20.5%

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

       8. sqrt-unprod 15.6%

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

       9. add-sqr-sqrt 43.4%

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

   16. Applied egg-rr 43.4%

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

       1. associate-/l* 46.9%

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

   18. Simplified 46.9%

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

   if -7.79999999999999979e-17 < z < 7.3000000000000001e-242

   1. Initial program 96.2%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in z around 0 72.7%

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

   if 7.3000000000000001e-242 < z < 2.55e7

   1. Initial program 89.8%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.4%

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

   6. Applied egg-rr 93.4%

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

   7. Taylor expanded in z around 0 58.5%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 25500000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -0.00014:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.05 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))))
   (if (<= t -0.00014)
     t_1
     (if (<= t 4.05e-22)
       (* x (- 1.0 (/ y z)))
       (if (<= t 2e+183) (* x (/ z (- z t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (t <= -0.00014) {
		tmp = t_1;
	} else if (t <= 4.05e-22) {
		tmp = x * (1.0 - (y / z));
	} else if (t <= 2e+183) {
		tmp = x * (z / (z - 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 / (t / y)
    if (t <= (-0.00014d0)) then
        tmp = t_1
    else if (t <= 4.05d-22) then
        tmp = x * (1.0d0 - (y / z))
    else if (t <= 2d+183) then
        tmp = x * (z / (z - 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 / (t / y);
	double tmp;
	if (t <= -0.00014) {
		tmp = t_1;
	} else if (t <= 4.05e-22) {
		tmp = x * (1.0 - (y / z));
	} else if (t <= 2e+183) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	tmp = 0
	if t <= -0.00014:
		tmp = t_1
	elif t <= 4.05e-22:
		tmp = x * (1.0 - (y / z))
	elif t <= 2e+183:
		tmp = x * (z / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	tmp = 0.0
	if (t <= -0.00014)
		tmp = t_1;
	elseif (t <= 4.05e-22)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (t <= 2e+183)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	tmp = 0.0;
	if (t <= -0.00014)
		tmp = t_1;
	elseif (t <= 4.05e-22)
		tmp = x * (1.0 - (y / z));
	elseif (t <= 2e+183)
		tmp = x * (z / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.00014], t$95$1, If[LessEqual[t, 4.05e-22], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+183], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3999999999999999e-4 or 1.99999999999999989e183 < t

   1. Initial program 80.1%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

      1. clear-num 91.4%

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

      2. un-div-inv 91.6%

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

   6. Applied egg-rr 91.6%

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

   7. Taylor expanded in z around 0 65.5%

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

   if -1.3999999999999999e-4 < t < 4.05000000000000007e-22

   1. Initial program 85.1%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in t around 0 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-/l* 80.8%

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

      3. associate-*l* 80.8%

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

      4. associate-*l/ 80.8%

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

      5. *-commutative 80.8%

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

      6. neg-mul-1 80.8%

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

      7. neg-sub0 80.8%

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

      8. associate--r- 80.8%

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

      9. neg-sub0 80.8%

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

      10. +-commutative 80.8%

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

      11. sub-neg 80.8%

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

      12. div-sub 80.8%

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

      13. *-inverses 80.8%

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

   7. Simplified 80.8%

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

   if 4.05000000000000007e-22 < t < 1.99999999999999989e183

   1. Initial program 82.1%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. distribute-neg-frac2 46.4%

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

      3. neg-sub0 46.4%

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

      4. associate--r- 46.4%

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

      5. neg-sub0 46.4%

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

      6. mul-1-neg 46.4%

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

      7. +-commutative 46.4%

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

      8. mul-1-neg 46.4%

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

      9. sub-neg 46.4%

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

      10. associate-/l* 60.7%

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

   7. Simplified 60.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00014:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 4.05 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-22} \lor \neg \left(t \leq 8.6 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.7e-22) (not (<= t 8.6e+60)))
   (* x (/ (- y z) t))
   (* x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.7e-22) || !(t <= 8.6e+60)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / 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 ((t <= (-1.7d-22)) .or. (.not. (t <= 8.6d+60))) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.7e-22) || !(t <= 8.6e+60)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.7e-22) or not (t <= 8.6e+60):
		tmp = x * ((y - z) / t)
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.7e-22) || !(t <= 8.6e+60))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.7e-22) || ~((t <= 8.6e+60)))
		tmp = x * ((y - z) / t);
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.7e-22], N[Not[LessEqual[t, 8.6e+60]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e-22 or 8.59999999999999942e60 < t

   1. Initial program 81.7%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in t around inf 69.5%

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

      1. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

   if -1.6999999999999999e-22 < t < 8.59999999999999942e60

   1. Initial program 84.0%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-/l* 79.4%

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

      3. associate-*l* 79.4%

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

      4. associate-*l/ 79.4%

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

      5. *-commutative 79.4%

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

      6. neg-mul-1 79.4%

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

      7. neg-sub0 79.4%

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

      8. associate--r- 79.4%

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

      9. neg-sub0 79.4%

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

      10. +-commutative 79.4%

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

      11. sub-neg 79.4%

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

      12. div-sub 79.4%

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

      13. *-inverses 79.4%

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

   7. Simplified 79.4%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-22} \lor \neg \left(t \leq 8.6 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.3e-5)
   (/ x (/ t y))
   (if (<= t 6e+146) (* x (- 1.0 (/ y z))) (* x (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-5) {
		tmp = x / (t / y);
	} else if (t <= 6e+146) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / 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 (t <= (-2.3d-5)) then
        tmp = x / (t / y)
    else if (t <= 6d+146) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-5) {
		tmp = x / (t / y);
	} else if (t <= 6e+146) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.3e-5:
		tmp = x / (t / y)
	elif t <= 6e+146:
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.3e-5)
		tmp = Float64(x / Float64(t / y));
	elseif (t <= 6e+146)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.3e-5)
		tmp = x / (t / y);
	elseif (t <= 6e+146)
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.3e-5], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+146], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e-5

   1. Initial program 84.7%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.2%

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

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in z around 0 66.2%

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

   if -2.3e-5 < t < 6.00000000000000005e146

   1. Initial program 84.3%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around 0 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-/l* 74.7%

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

      3. associate-*l* 74.7%

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

      4. associate-*l/ 74.7%

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

      5. *-commutative 74.7%

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

      6. neg-mul-1 74.7%

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

      7. neg-sub0 74.7%

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

      8. associate--r- 74.7%

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

      9. neg-sub0 74.7%

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

      10. +-commutative 74.7%

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

      11. sub-neg 74.7%

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

      12. div-sub 74.7%

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

      13. *-inverses 74.7%

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

   7. Simplified 74.7%

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

   if 6.00000000000000005e146 < t

   1. Initial program 75.7%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around 0 50.1%

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

      1. associate-/l* 61.3%

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

   7. Simplified 61.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+111) x (if (<= z 5.4e+14) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+111) {
		tmp = x;
	} else if (z <= 5.4e+14) {
		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 <= (-2.8d+111)) then
        tmp = x
    else if (z <= 5.4d+14) 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 <= -2.8e+111) {
		tmp = x;
	} else if (z <= 5.4e+14) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+111:
		tmp = x
	elif z <= 5.4e+14:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+111)
		tmp = x;
	elseif (z <= 5.4e+14)
		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 <= -2.8e+111)
		tmp = x;
	elseif (z <= 5.4e+14)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+111], x, If[LessEqual[z, 5.4e+14], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e111 or 5.4e14 < z

   1. Initial program 66.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 68.4%

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

   if -2.7999999999999999e111 < z < 5.4e14

   1. Initial program 92.6%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around 0 57.9%

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

      1. associate-/l* 60.8%

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

   7. Simplified 60.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+111) x (if (<= z 3.8e+14) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+111) {
		tmp = x;
	} else if (z <= 3.8e+14) {
		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 <= (-2.8d+111)) then
        tmp = x
    else if (z <= 3.8d+14) 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 <= -2.8e+111) {
		tmp = x;
	} else if (z <= 3.8e+14) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+111:
		tmp = x
	elif z <= 3.8e+14:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+111)
		tmp = x;
	elseif (z <= 3.8e+14)
		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 <= -2.8e+111)
		tmp = x;
	elseif (z <= 3.8e+14)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+111], x, If[LessEqual[z, 3.8e+14], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e111 or 3.8e14 < z

   1. Initial program 66.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 68.4%

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

   if -2.7999999999999999e111 < z < 3.8e14

   1. Initial program 92.6%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

      1. clear-num 92.7%

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

      2. un-div-inv 92.8%

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

   6. Applied egg-rr 92.8%

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

   7. Taylor expanded in z around 0 60.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.3% 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 82.8%

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

   1. associate-/l* 95.6%

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

3. Simplified 95.6%

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

5. Taylor expanded in z around inf 34.0%

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

6. Final simplification 34.0%

   \[\leadsto x \]
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 2024039 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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