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

Percentage Accurate: 84.3% → 96.8%

Time: 12.5s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.0%

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

   1. associate-*r/ 96.1%

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

3. Simplified 96.1%

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

   1. div-sub 96.1%

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

5. Applied egg-rr 96.1%

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

6. Final simplification 96.1%

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

Alternative 2: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 50000000:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.3e+59)
     t_1
     (if (<= z -1.15e-23)
       (* (- y z) (/ x t))
       (if (<= z -6e-34)
         t_1
         (if (<= z 4.9e-72)
           (/ (* x y) (- t z))
           (if (<= z 50000000.0)
             (/ x (- 1.0 (/ t z)))
             (if (<= z 2.55e+38) (* x (/ y (- t z))) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.3e+59) {
		tmp = t_1;
	} else if (z <= -1.15e-23) {
		tmp = (y - z) * (x / t);
	} else if (z <= -6e-34) {
		tmp = t_1;
	} else if (z <= 4.9e-72) {
		tmp = (x * y) / (t - z);
	} else if (z <= 50000000.0) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 2.55e+38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-1.3d+59)) then
        tmp = t_1
    else if (z <= (-1.15d-23)) then
        tmp = (y - z) * (x / t)
    else if (z <= (-6d-34)) then
        tmp = t_1
    else if (z <= 4.9d-72) then
        tmp = (x * y) / (t - z)
    else if (z <= 50000000.0d0) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 2.55d+38) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.3e+59) {
		tmp = t_1;
	} else if (z <= -1.15e-23) {
		tmp = (y - z) * (x / t);
	} else if (z <= -6e-34) {
		tmp = t_1;
	} else if (z <= 4.9e-72) {
		tmp = (x * y) / (t - z);
	} else if (z <= 50000000.0) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 2.55e+38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.3e+59:
		tmp = t_1
	elif z <= -1.15e-23:
		tmp = (y - z) * (x / t)
	elif z <= -6e-34:
		tmp = t_1
	elif z <= 4.9e-72:
		tmp = (x * y) / (t - z)
	elif z <= 50000000.0:
		tmp = x / (1.0 - (t / z))
	elif z <= 2.55e+38:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.3e+59)
		tmp = t_1;
	elseif (z <= -1.15e-23)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= -6e-34)
		tmp = t_1;
	elseif (z <= 4.9e-72)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (z <= 50000000.0)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 2.55e+38)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.3e+59)
		tmp = t_1;
	elseif (z <= -1.15e-23)
		tmp = (y - z) * (x / t);
	elseif (z <= -6e-34)
		tmp = t_1;
	elseif (z <= 4.9e-72)
		tmp = (x * y) / (t - z);
	elseif (z <= 50000000.0)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 2.55e+38)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+59], t$95$1, If[LessEqual[z, -1.15e-23], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-34], t$95$1, If[LessEqual[z, 4.9e-72], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 50000000.0], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e+38], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.3e59 or -1.15000000000000005e-23 < z < -6e-34 or 2.5500000000000001e38 < z

   1. Initial program 71.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 83.4%

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

      1. associate-*r/ 83.4%

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

      2. neg-mul-1 83.4%

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

   6. Simplified 83.4%

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

   7. Taylor expanded in y around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

   9. Simplified 83.4%

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

   if -1.3e59 < z < -1.15000000000000005e-23

   1. Initial program 93.8%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around inf 76.5%

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

      1. associate-/l* 82.1%

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

      2. associate-/r/ 82.3%

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

   6. Simplified 82.3%

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

   if -6e-34 < z < 4.89999999999999991e-72

   1. Initial program 95.3%

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

      1. associate-*r/ 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. Taylor expanded in y around inf 88.1%

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

   if 4.89999999999999991e-72 < z < 5e7

   1. Initial program 99.8%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 69.0%

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

      1. associate-*r/ 69.0%

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

      2. *-commutative 69.0%

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

      3. associate-*r* 69.0%

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

      4. mul-1-neg 69.0%

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

      5. *-commutative 69.0%

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

      6. associate-/l* 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in t around 0 69.2%

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

       1. mul-1-neg 69.2%

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

       2. unsub-neg 69.2%

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

   11. Simplified 69.2%

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

   if 5e7 < z < 2.5500000000000001e38

   1. Initial program 99.5%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 99.5%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 50000000:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 3: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 46000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.45e+59)
     t_2
     (if (<= z -1.6e-70)
       t_1
       (if (<= z 1.25e-50)
         (* y (/ x (- t z)))
         (if (<= z 46000000.0)
           t_1
           (if (<= z 3.5e+37) (* x (/ y (- t z))) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.45e+59) {
		tmp = t_2;
	} else if (z <= -1.6e-70) {
		tmp = t_1;
	} else if (z <= 1.25e-50) {
		tmp = y * (x / (t - z));
	} else if (z <= 46000000.0) {
		tmp = t_1;
	} else if (z <= 3.5e+37) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - z) / t)
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-1.45d+59)) then
        tmp = t_2
    else if (z <= (-1.6d-70)) then
        tmp = t_1
    else if (z <= 1.25d-50) then
        tmp = y * (x / (t - z))
    else if (z <= 46000000.0d0) then
        tmp = t_1
    else if (z <= 3.5d+37) then
        tmp = x * (y / (t - z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.45e+59) {
		tmp = t_2;
	} else if (z <= -1.6e-70) {
		tmp = t_1;
	} else if (z <= 1.25e-50) {
		tmp = y * (x / (t - z));
	} else if (z <= 46000000.0) {
		tmp = t_1;
	} else if (z <= 3.5e+37) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.45e+59:
		tmp = t_2
	elif z <= -1.6e-70:
		tmp = t_1
	elif z <= 1.25e-50:
		tmp = y * (x / (t - z))
	elif z <= 46000000.0:
		tmp = t_1
	elif z <= 3.5e+37:
		tmp = x * (y / (t - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.45e+59)
		tmp = t_2;
	elseif (z <= -1.6e-70)
		tmp = t_1;
	elseif (z <= 1.25e-50)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	elseif (z <= 46000000.0)
		tmp = t_1;
	elseif (z <= 3.5e+37)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.45e+59)
		tmp = t_2;
	elseif (z <= -1.6e-70)
		tmp = t_1;
	elseif (z <= 1.25e-50)
		tmp = y * (x / (t - z));
	elseif (z <= 46000000.0)
		tmp = t_1;
	elseif (z <= 3.5e+37)
		tmp = x * (y / (t - z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+59], t$95$2, If[LessEqual[z, -1.6e-70], t$95$1, If[LessEqual[z, 1.25e-50], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 46000000.0], t$95$1, If[LessEqual[z, 3.5e+37], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.44999999999999995e59 or 3.5e37 < z

   1. Initial program 71.0%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. neg-mul-1 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in y around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. unsub-neg 83.0%

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

   9. Simplified 83.0%

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

   if -1.44999999999999995e59 < z < -1.5999999999999999e-70 or 1.24999999999999992e-50 < z < 4.6e7

   1. Initial program 97.2%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 76.0%

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

   if -1.5999999999999999e-70 < z < 1.24999999999999992e-50

   1. Initial program 95.1%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-/r/ 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in y around inf 86.7%

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

      1. associate-/l* 81.9%

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

      2. associate-/r/ 86.0%

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

   8. Simplified 86.0%

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

   if 4.6e7 < z < 3.5e37

   1. Initial program 99.5%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 99.5%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 46000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 4: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-34} \lor \neg \left(z \leq 3.3 \cdot 10^{-103}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.3e+59)
     t_1
     (if (<= z -1e-20)
       (* (/ x t) (- z))
       (if (or (<= z -5e-34) (not (<= z 3.3e-103))) t_1 (/ (* x y) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.3e+59) {
		tmp = t_1;
	} else if (z <= -1e-20) {
		tmp = (x / t) * -z;
	} else if ((z <= -5e-34) || !(z <= 3.3e-103)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-1.3d+59)) then
        tmp = t_1
    else if (z <= (-1d-20)) then
        tmp = (x / t) * -z
    else if ((z <= (-5d-34)) .or. (.not. (z <= 3.3d-103))) then
        tmp = t_1
    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 t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.3e+59) {
		tmp = t_1;
	} else if (z <= -1e-20) {
		tmp = (x / t) * -z;
	} else if ((z <= -5e-34) || !(z <= 3.3e-103)) {
		tmp = t_1;
	} else {
		tmp = (x * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.3e+59:
		tmp = t_1
	elif z <= -1e-20:
		tmp = (x / t) * -z
	elif (z <= -5e-34) or not (z <= 3.3e-103):
		tmp = t_1
	else:
		tmp = (x * y) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.3e+59)
		tmp = t_1;
	elseif (z <= -1e-20)
		tmp = Float64(Float64(x / t) * Float64(-z));
	elseif ((z <= -5e-34) || !(z <= 3.3e-103))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.3e+59)
		tmp = t_1;
	elseif (z <= -1e-20)
		tmp = (x / t) * -z;
	elseif ((z <= -5e-34) || ~((z <= 3.3e-103)))
		tmp = t_1;
	else
		tmp = (x * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+59], t$95$1, If[LessEqual[z, -1e-20], N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision], If[Or[LessEqual[z, -5e-34], N[Not[LessEqual[z, 3.3e-103]], $MachinePrecision]], t$95$1, N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e59 or -9.99999999999999945e-21 < z < -5.0000000000000003e-34 or 3.2999999999999999e-103 < z

   1. Initial program 76.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. neg-mul-1 77.7%

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

   6. Simplified 77.7%

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

   7. Taylor expanded in y around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   9. Simplified 77.7%

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

   if -1.3e59 < z < -9.99999999999999945e-21

   1. Initial program 93.4%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

      1. div-sub 99.4%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in y around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r* 67.9%

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

      4. mul-1-neg 67.9%

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

      5. *-commutative 67.9%

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

      6. associate-/l* 67.8%

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

   8. Simplified 67.8%

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

   9. Taylor expanded in t around inf 61.7%

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

       1. associate-/l* 61.5%

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

       2. associate-*r/ 61.5%

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

       3. neg-mul-1 61.5%

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

   11. Simplified 61.5%

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

       1. frac-2neg 61.5%

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

       2. associate-/r/ 61.7%

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

       3. frac-2neg 61.7%

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

   13. Applied egg-rr 61.7%

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

   if -5.0000000000000003e-34 < z < 3.2999999999999999e-103

   1. Initial program 95.1%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around 0 78.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-34} \lor \neg \left(z \leq 3.3 \cdot 10^{-103}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \end{array} \]

Alternative 5: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 12500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 (/ t z)))))
   (if (<= z -2.3e+32)
     t_1
     (if (<= z 4.15e-72)
       (* y (/ x (- t z)))
       (if (<= z 12500000.0)
         t_1
         (if (<= z 2e+38) (* x (/ y (- t z))) (* x (- 1.0 (/ y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -2.3e+32) {
		tmp = t_1;
	} else if (z <= 4.15e-72) {
		tmp = y * (x / (t - z));
	} else if (z <= 12500000.0) {
		tmp = t_1;
	} else if (z <= 2e+38) {
		tmp = x * (y / (t - z));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - (t / z))
    if (z <= (-2.3d+32)) then
        tmp = t_1
    else if (z <= 4.15d-72) then
        tmp = y * (x / (t - z))
    else if (z <= 12500000.0d0) then
        tmp = t_1
    else if (z <= 2d+38) then
        tmp = x * (y / (t - z))
    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 t_1 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -2.3e+32) {
		tmp = t_1;
	} else if (z <= 4.15e-72) {
		tmp = y * (x / (t - z));
	} else if (z <= 12500000.0) {
		tmp = t_1;
	} else if (z <= 2e+38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (1.0 - (t / z))
	tmp = 0
	if z <= -2.3e+32:
		tmp = t_1
	elif z <= 4.15e-72:
		tmp = y * (x / (t - z))
	elif z <= 12500000.0:
		tmp = t_1
	elif z <= 2e+38:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(1.0 - Float64(t / z)))
	tmp = 0.0
	if (z <= -2.3e+32)
		tmp = t_1;
	elseif (z <= 4.15e-72)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	elseif (z <= 12500000.0)
		tmp = t_1;
	elseif (z <= 2e+38)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (1.0 - (t / z));
	tmp = 0.0;
	if (z <= -2.3e+32)
		tmp = t_1;
	elseif (z <= 4.15e-72)
		tmp = y * (x / (t - z));
	elseif (z <= 12500000.0)
		tmp = t_1;
	elseif (z <= 2e+38)
		tmp = x * (y / (t - z));
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+32], t$95$1, If[LessEqual[z, 4.15e-72], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12500000.0], t$95$1, If[LessEqual[z, 2e+38], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3e32 or 4.1499999999999999e-72 < z < 1.25e7

   1. Initial program 77.3%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. div-sub 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. *-commutative 58.1%

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

      3. associate-*r* 58.1%

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

      4. mul-1-neg 58.1%

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

      5. *-commutative 58.1%

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

      6. associate-/l* 76.5%

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

   8. Simplified 76.5%

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

   9. Taylor expanded in t around 0 76.5%

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

       1. mul-1-neg 76.5%

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

       2. unsub-neg 76.5%

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

   11. Simplified 76.5%

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

   if -2.3e32 < z < 4.1499999999999999e-72

   1. Initial program 95.0%

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

      1. associate-*r/ 91.7%

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

   3. Simplified 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-/r/ 95.3%

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

   5. Applied egg-rr 95.3%

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

   6. Taylor expanded in y around inf 85.5%

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

      1. associate-/l* 82.2%

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

      2. associate-/r/ 85.0%

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

   8. Simplified 85.0%

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

   if 1.25e7 < z < 1.99999999999999995e38

   1. Initial program 99.5%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 99.5%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   if 1.99999999999999995e38 < z

   1. Initial program 73.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unsub-neg 84.1%

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

   9. Simplified 84.1%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 12500000:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 6: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.36 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.36e+59)
     t_1
     (if (<= z -4.1e-71)
       (* x (/ (- y z) t))
       (if (<= z 3.5e+38) (* x (/ y (- t z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.36e+59) {
		tmp = t_1;
	} else if (z <= -4.1e-71) {
		tmp = x * ((y - z) / t);
	} else if (z <= 3.5e+38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-1.36d+59)) then
        tmp = t_1
    else if (z <= (-4.1d-71)) then
        tmp = x * ((y - z) / t)
    else if (z <= 3.5d+38) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.36e+59) {
		tmp = t_1;
	} else if (z <= -4.1e-71) {
		tmp = x * ((y - z) / t);
	} else if (z <= 3.5e+38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.36e+59:
		tmp = t_1
	elif z <= -4.1e-71:
		tmp = x * ((y - z) / t)
	elif z <= 3.5e+38:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.36e+59)
		tmp = t_1;
	elseif (z <= -4.1e-71)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif (z <= 3.5e+38)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.36e+59)
		tmp = t_1;
	elseif (z <= -4.1e-71)
		tmp = x * ((y - z) / t);
	elseif (z <= 3.5e+38)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.36e+59], t$95$1, If[LessEqual[z, -4.1e-71], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+38], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.36e59 or 3.50000000000000002e38 < z

   1. Initial program 71.0%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. neg-mul-1 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in y around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. unsub-neg 83.0%

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

   9. Simplified 83.0%

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

   if -1.36e59 < z < -4.09999999999999993e-71

   1. Initial program 96.2%

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

      1. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 78.0%

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

   if -4.09999999999999993e-71 < z < 3.50000000000000002e38

   1. Initial program 95.7%

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

      1. associate-*r/ 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. Taylor expanded in y around inf 82.8%

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

      1. associate-*r/ 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 7: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-185}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.56e+59)
     t_1
     (if (<= z 1.12e-185)
       (* (- y z) (/ x t))
       (if (<= z 2.85e+38) (* x (/ y (- t z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.56e+59) {
		tmp = t_1;
	} else if (z <= 1.12e-185) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.85e+38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-1.56d+59)) then
        tmp = t_1
    else if (z <= 1.12d-185) then
        tmp = (y - z) * (x / t)
    else if (z <= 2.85d+38) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.56e+59) {
		tmp = t_1;
	} else if (z <= 1.12e-185) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.85e+38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.56e+59:
		tmp = t_1
	elif z <= 1.12e-185:
		tmp = (y - z) * (x / t)
	elif z <= 2.85e+38:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.56e+59)
		tmp = t_1;
	elseif (z <= 1.12e-185)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 2.85e+38)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.56e+59)
		tmp = t_1;
	elseif (z <= 1.12e-185)
		tmp = (y - z) * (x / t);
	elseif (z <= 2.85e+38)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.56e+59], t$95$1, If[LessEqual[z, 1.12e-185], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.85e+38], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.56000000000000004e59 or 2.8499999999999999e38 < z

   1. Initial program 71.0%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. neg-mul-1 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in y around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. unsub-neg 83.0%

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

   9. Simplified 83.0%

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

   if -1.56000000000000004e59 < z < 1.11999999999999993e-185

   1. Initial program 94.6%

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

      1. associate-*r/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in t around inf 81.8%

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

      1. associate-/l* 78.9%

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

      2. associate-/r/ 82.1%

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

   6. Simplified 82.1%

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

   if 1.11999999999999993e-185 < z < 2.8499999999999999e38

   1. Initial program 99.7%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 72.6%

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

      1. associate-*r/ 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-185}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 8: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e+74)
   x
   (if (<= z -8.8e-21) (/ (- x) (/ t z)) (if (<= z 2.2e+49) (/ (* x y) t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+74) {
		tmp = x;
	} else if (z <= -8.8e-21) {
		tmp = -x / (t / z);
	} else if (z <= 2.2e+49) {
		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 <= (-1.8d+74)) then
        tmp = x
    else if (z <= (-8.8d-21)) then
        tmp = -x / (t / z)
    else if (z <= 2.2d+49) 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 <= -1.8e+74) {
		tmp = x;
	} else if (z <= -8.8e-21) {
		tmp = -x / (t / z);
	} else if (z <= 2.2e+49) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e+74:
		tmp = x
	elif z <= -8.8e-21:
		tmp = -x / (t / z)
	elif z <= 2.2e+49:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e+74)
		tmp = x;
	elseif (z <= -8.8e-21)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= 2.2e+49)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e+74)
		tmp = x;
	elseif (z <= -8.8e-21)
		tmp = -x / (t / z);
	elseif (z <= 2.2e+49)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e+74], x, If[LessEqual[z, -8.8e-21], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+49], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999994e74 or 2.2000000000000001e49 < z

   1. Initial program 68.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 66.5%

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

   if -1.79999999999999994e74 < z < -8.8000000000000002e-21

   1. Initial program 95.3%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around inf 68.0%

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

   5. Taylor expanded in y around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   if -8.8000000000000002e-21 < z < 2.2000000000000001e49

   1. Initial program 96.1%

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

      1. associate-*r/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in z around 0 67.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+74)
   x
   (if (<= z -2.5e-26) (* (/ x t) (- z)) (if (<= z 2.1e+49) (/ (* x y) t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+74) {
		tmp = x;
	} else if (z <= -2.5e-26) {
		tmp = (x / t) * -z;
	} else if (z <= 2.1e+49) {
		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 <= (-1.5d+74)) then
        tmp = x
    else if (z <= (-2.5d-26)) then
        tmp = (x / t) * -z
    else if (z <= 2.1d+49) 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 <= -1.5e+74) {
		tmp = x;
	} else if (z <= -2.5e-26) {
		tmp = (x / t) * -z;
	} else if (z <= 2.1e+49) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+74:
		tmp = x
	elif z <= -2.5e-26:
		tmp = (x / t) * -z
	elif z <= 2.1e+49:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+74)
		tmp = x;
	elseif (z <= -2.5e-26)
		tmp = Float64(Float64(x / t) * Float64(-z));
	elseif (z <= 2.1e+49)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e+74)
		tmp = x;
	elseif (z <= -2.5e-26)
		tmp = (x / t) * -z;
	elseif (z <= 2.1e+49)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+74], x, If[LessEqual[z, -2.5e-26], N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, 2.1e+49], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e74 or 2.10000000000000011e49 < z

   1. Initial program 68.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 66.5%

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

   if -1.5e74 < z < -2.5000000000000001e-26

   1. Initial program 95.7%

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

      1. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

      1. div-sub 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in y around 0 61.9%

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

      1. associate-*r/ 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 61.9%

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

      4. mul-1-neg 61.9%

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

      5. *-commutative 61.9%

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

      6. associate-/l* 61.8%

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

   8. Simplified 61.8%

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

   9. Taylor expanded in t around inf 54.1%

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

       1. associate-/l* 53.9%

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

       2. associate-*r/ 53.9%

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

       3. neg-mul-1 53.9%

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

   11. Simplified 53.9%

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

       1. frac-2neg 53.9%

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

       2. associate-/r/ 58.0%

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

       3. frac-2neg 58.0%

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

   13. Applied egg-rr 58.0%

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

   if -2.5000000000000001e-26 < z < 2.10000000000000011e49

   1. Initial program 96.1%

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

      1. associate-*r/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in z around 0 67.8%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.55e+74)
   x
   (if (<= z -2.1e-18) (/ (* x (- z)) t) (if (<= z 6.6e+49) (/ (* x y) t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+74) {
		tmp = x;
	} else if (z <= -2.1e-18) {
		tmp = (x * -z) / t;
	} else if (z <= 6.6e+49) {
		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 <= (-1.55d+74)) then
        tmp = x
    else if (z <= (-2.1d-18)) then
        tmp = (x * -z) / t
    else if (z <= 6.6d+49) 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 <= -1.55e+74) {
		tmp = x;
	} else if (z <= -2.1e-18) {
		tmp = (x * -z) / t;
	} else if (z <= 6.6e+49) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e+74:
		tmp = x
	elif z <= -2.1e-18:
		tmp = (x * -z) / t
	elif z <= 6.6e+49:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.55e+74)
		tmp = x;
	elseif (z <= -2.1e-18)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (z <= 6.6e+49)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.55e+74)
		tmp = x;
	elseif (z <= -2.1e-18)
		tmp = (x * -z) / t;
	elseif (z <= 6.6e+49)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.55e+74], x, If[LessEqual[z, -2.1e-18], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 6.6e+49], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000011e74 or 6.5999999999999997e49 < z

   1. Initial program 68.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 66.5%

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

   if -1.55000000000000011e74 < z < -2.1e-18

   1. Initial program 95.3%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around inf 68.0%

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

   5. Taylor expanded in y around 0 58.8%

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

      1. associate-*r* 58.8%

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

      2. neg-mul-1 58.8%

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

   7. Simplified 58.8%

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

   if -2.1e-18 < z < 6.5999999999999997e49

   1. Initial program 96.1%

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

      1. associate-*r/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in z around 0 67.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+42} \lor \neg \left(z \leq 7 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.7e+42) (not (<= z 7e+37)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.7e+42) || !(z <= 7e+37)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.7d+42)) .or. (.not. (z <= 7d+37))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.7e+42) || !(z <= 7e+37)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.7e+42) or not (z <= 7e+37):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.7e+42) || !(z <= 7e+37))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.7e+42) || ~((z <= 7e+37)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.7e+42], N[Not[LessEqual[z, 7e+37]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.69999999999999986e42 or 7e37 < z

   1. Initial program 71.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 81.7%

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

      1. associate-*r/ 81.7%

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

      2. neg-mul-1 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in y around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

   9. Simplified 81.7%

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

   if -4.69999999999999986e42 < z < 7e37

   1. Initial program 95.7%

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

      1. associate-*r/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around inf 79.2%

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

      1. associate-*r/ 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+42} \lor \neg \left(z \leq 7 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 12: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.95e+43) x (if (<= z 2e+49) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.95e+43) {
		tmp = x;
	} else if (z <= 2e+49) {
		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 <= (-1.95d+43)) then
        tmp = x
    else if (z <= 2d+49) 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 <= -1.95e+43) {
		tmp = x;
	} else if (z <= 2e+49) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.95e+43:
		tmp = x
	elif z <= 2e+49:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.95e+43)
		tmp = x;
	elseif (z <= 2e+49)
		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 <= -1.95e+43)
		tmp = x;
	elseif (z <= 2e+49)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.95e+43], x, If[LessEqual[z, 2e+49], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e43 or 1.99999999999999989e49 < z

   1. Initial program 71.2%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 64.0%

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

   if -1.95e43 < z < 1.99999999999999989e49

   1. Initial program 95.8%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 63.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e+45) x (if (<= z 4.9e-72) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e+45) {
		tmp = x;
	} else if (z <= 4.9e-72) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.2d+45)) then
        tmp = x
    else if (z <= 4.9d-72) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e+45) {
		tmp = x;
	} else if (z <= 4.9e-72) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e+45:
		tmp = x
	elif z <= 4.9e-72:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e+45)
		tmp = x;
	elseif (z <= 4.9e-72)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.2e+45)
		tmp = x;
	elseif (z <= 4.9e-72)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e+45], x, If[LessEqual[z, 4.9e-72], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e45 or 4.89999999999999991e-72 < z

   1. Initial program 75.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.5%

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

   if -7.2e45 < z < 4.89999999999999991e-72

   1. Initial program 95.1%

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

      1. associate-*r/ 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. Taylor expanded in z around 0 72.0%

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

      1. associate-/l* 70.3%

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

      2. associate-/r/ 70.9%

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

   6. Simplified 70.9%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.35e+47) x (if (<= z 4.9e-72) (/ y (/ t x)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e+47) {
		tmp = x;
	} else if (z <= 4.9e-72) {
		tmp = y / (t / x);
	} 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 <= (-2.35d+47)) then
        tmp = x
    else if (z <= 4.9d-72) then
        tmp = y / (t / x)
    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 <= -2.35e+47) {
		tmp = x;
	} else if (z <= 4.9e-72) {
		tmp = y / (t / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.35e+47:
		tmp = x
	elif z <= 4.9e-72:
		tmp = y / (t / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.35e+47)
		tmp = x;
	elseif (z <= 4.9e-72)
		tmp = Float64(y / Float64(t / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.35e+47)
		tmp = x;
	elseif (z <= 4.9e-72)
		tmp = y / (t / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.35e+47], x, If[LessEqual[z, 4.9e-72], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.34999999999999982e47 or 4.89999999999999991e-72 < z

   1. Initial program 75.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.5%

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

   if -2.34999999999999982e47 < z < 4.89999999999999991e-72

   1. Initial program 95.1%

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

      1. associate-*r/ 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. Taylor expanded in z around 0 72.0%

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

      1. associate-/l* 70.3%

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

      2. associate-/r/ 70.9%

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

   6. Simplified 70.9%

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

      1. *-commutative 70.9%

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

      2. clear-num 70.8%

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

      3. un-div-inv 70.9%

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

   8. Applied egg-rr 70.9%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.02e+45) x (if (<= z 4.4e+49) (/ (* x y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e+45) {
		tmp = x;
	} else if (z <= 4.4e+49) {
		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 <= (-1.02d+45)) then
        tmp = x
    else if (z <= 4.4d+49) 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 <= -1.02e+45) {
		tmp = x;
	} else if (z <= 4.4e+49) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.02e+45:
		tmp = x
	elif z <= 4.4e+49:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.02e+45)
		tmp = x;
	elseif (z <= 4.4e+49)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.02e+45)
		tmp = x;
	elseif (z <= 4.4e+49)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.02e+45], x, If[LessEqual[z, 4.4e+49], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e45 or 4.4000000000000001e49 < z

   1. Initial program 71.2%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 64.0%

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

   if -1.02e45 < z < 4.4000000000000001e49

   1. Initial program 95.8%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 65.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 96.8% 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 85.0%

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

   1. associate-*r/ 96.1%

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

3. Simplified 96.1%

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

4. Final simplification 96.1%

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

Alternative 17: 35.4% 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 85.0%

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

   1. associate-*r/ 96.1%

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

3. Simplified 96.1%

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

4. Taylor expanded in z around inf 33.9%

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

5. Final simplification 33.9%

   \[\leadsto x \]

Developer target: 96.8% 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 2023301 
(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)))