Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 84.2% → 98.2%

Time: 8.3s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z - a}{z - t}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-/l* 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-73}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 21000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -6.8e+80)
     t_1
     (if (<= z -2.25e-73)
       (+ x (* z (/ y (- z a))))
       (if (<= z 21000.0) (+ x (/ y (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -6.8e+80) {
		tmp = t_1;
	} else if (z <= -2.25e-73) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 21000.0) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-6.8d+80)) then
        tmp = t_1
    else if (z <= (-2.25d-73)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 21000.0d0) then
        tmp = x + (y / (a / 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 a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -6.8e+80) {
		tmp = t_1;
	} else if (z <= -2.25e-73) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 21000.0) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -6.8e+80:
		tmp = t_1
	elif z <= -2.25e-73:
		tmp = x + (z * (y / (z - a)))
	elif z <= 21000.0:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -6.8e+80)
		tmp = t_1;
	elseif (z <= -2.25e-73)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 21000.0)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -6.8e+80)
		tmp = t_1;
	elseif (z <= -2.25e-73)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 21000.0)
		tmp = x + (y / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+80], t$95$1, If[LessEqual[z, -2.25e-73], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 21000.0], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999984e80 or 21000 < z

   1. Initial program 71.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around 0 91.8%

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

      1. div-sub 91.8%

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

      2. *-inverses 91.8%

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

   8. Simplified 91.8%

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

   if -6.79999999999999984e80 < z < -2.25e-73

   1. Initial program 91.2%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 78.0%

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

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

   6. Simplified 86.3%

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

   if -2.25e-73 < z < 21000

   1. Initial program 99.9%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 83.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-73}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 21000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 3: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-73}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+80)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z -5.3e-73)
     (+ x (* z (/ y (- z a))))
     (if (<= z 2.15e-107) (+ x (/ y (/ a t))) (+ x (/ y (/ (- z a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+80) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= -5.3e-73) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 2.15e-107) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+80)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= (-5.3d-73)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 2.15d-107) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+80) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= -5.3e-73) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 2.15e-107) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+80:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= -5.3e-73:
		tmp = x + (z * (y / (z - a)))
	elif z <= 2.15e-107:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+80)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= -5.3e-73)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 2.15e-107)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+80)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= -5.3e-73)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 2.15e-107)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+80], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-73], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-107], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999984e80

   1. Initial program 64.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around 0 91.4%

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

      1. div-sub 91.4%

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

      2. *-inverses 91.4%

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

   8. Simplified 91.4%

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

   if -6.79999999999999984e80 < z < -5.29999999999999972e-73

   1. Initial program 91.2%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 78.0%

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

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

   6. Simplified 86.3%

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

   if -5.29999999999999972e-73 < z < 2.1499999999999999e-107

   1. Initial program 99.9%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 84.4%

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

   if 2.1499999999999999e-107 < z

   1. Initial program 82.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 89.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-73}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 4: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+83)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z -2.6e-71)
     (+ x (/ z (/ (- z a) y)))
     (if (<= z 3.3e-106) (+ x (/ y (/ a t))) (+ x (/ y (/ (- z a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+83) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= -2.6e-71) {
		tmp = x + (z / ((z - a) / y));
	} else if (z <= 3.3e-106) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d+83)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= (-2.6d-71)) then
        tmp = x + (z / ((z - a) / y))
    else if (z <= 3.3d-106) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+83) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= -2.6e-71) {
		tmp = x + (z / ((z - a) / y));
	} else if (z <= 3.3e-106) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+83:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= -2.6e-71:
		tmp = x + (z / ((z - a) / y))
	elif z <= 3.3e-106:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+83)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= -2.6e-71)
		tmp = Float64(x + Float64(z / Float64(Float64(z - a) / y)));
	elseif (z <= 3.3e-106)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+83)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= -2.6e-71)
		tmp = x + (z / ((z - a) / y));
	elseif (z <= 3.3e-106)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+83], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-71], N[(x + N[(z / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-106], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.29999999999999985e83

   1. Initial program 64.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around 0 91.4%

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

      1. div-sub 91.4%

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

      2. *-inverses 91.4%

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

   8. Simplified 91.4%

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

   if -3.29999999999999985e83 < z < -2.5999999999999999e-71

   1. Initial program 91.2%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 78.0%

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

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

   6. Simplified 86.3%

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

      1. clear-num 86.3%

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

      2. un-div-inv 86.4%

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

   8. Applied egg-rr 86.4%

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

   if -2.5999999999999999e-71 < z < 3.30000000000000016e-106

   1. Initial program 99.9%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 84.4%

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

   if 3.30000000000000016e-106 < z

   1. Initial program 82.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 89.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 5: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-71} \lor \neg \left(z \leq 4.3 \cdot 10^{-106}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.62e-71) (not (<= z 4.3e-106)))
   (+ x (* z (/ y (- z a))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.62e-71) || !(z <= 4.3e-106)) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.62d-71)) .or. (.not. (z <= 4.3d-106))) then
        tmp = x + (z * (y / (z - a)))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.62e-71) || !(z <= 4.3e-106)) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.62e-71) or not (z <= 4.3e-106):
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.62e-71) || !(z <= 4.3e-106))
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.62e-71) || ~((z <= 4.3e-106)))
		tmp = x + (z * (y / (z - a)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.62e-71], N[Not[LessEqual[z, 4.3e-106]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6200000000000001e-71 or 4.3000000000000002e-106 < z

   1. Initial program 78.7%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in t around 0 69.5%

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

      1. associate-*l/ 84.5%

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

      2. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   if -1.6200000000000001e-71 < z < 4.3000000000000002e-106

   1. Initial program 99.9%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 84.4%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-71} \lor \neg \left(z \leq 4.3 \cdot 10^{-106}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+51} \lor \neg \left(t \leq 3.3 \cdot 10^{+37}\right):\\ \;\;\;\;x - t \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- z a))))
   (if (or (<= t -6.8e+51) (not (<= t 3.3e+37)))
     (- x (* t t_1))
     (+ x (* z t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - a);
	double tmp;
	if ((t <= -6.8e+51) || !(t <= 3.3e+37)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z - a)
    if ((t <= (-6.8d+51)) .or. (.not. (t <= 3.3d+37))) then
        tmp = x - (t * t_1)
    else
        tmp = x + (z * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - a);
	double tmp;
	if ((t <= -6.8e+51) || !(t <= 3.3e+37)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z - a)
	tmp = 0
	if (t <= -6.8e+51) or not (t <= 3.3e+37):
		tmp = x - (t * t_1)
	else:
		tmp = x + (z * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z - a))
	tmp = 0.0
	if ((t <= -6.8e+51) || !(t <= 3.3e+37))
		tmp = Float64(x - Float64(t * t_1));
	else
		tmp = Float64(x + Float64(z * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z - a);
	tmp = 0.0;
	if ((t <= -6.8e+51) || ~((t <= 3.3e+37)))
		tmp = x - (t * t_1);
	else
		tmp = x + (z * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -6.8e+51], N[Not[LessEqual[t, 3.3e+37]], $MachinePrecision]], N[(x - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.79999999999999969e51 or 3.3000000000000001e37 < t

   1. Initial program 87.5%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   6. Simplified 87.0%

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

      1. frac-2neg 87.0%

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

      2. div-inv 86.9%

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

      3. distribute-neg-frac 86.9%

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

      4. remove-double-neg 86.9%

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

      5. add-sqr-sqrt 40.4%

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

      6. sqrt-unprod 53.4%

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

      7. sqr-neg 53.4%

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

      8. sqrt-unprod 15.5%

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

      9. add-sqr-sqrt 37.2%

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

      10. clear-num 37.2%

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

      11. cancel-sign-sub-inv 37.2%

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

      12. add-sqr-sqrt 15.5%

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

      13. sqrt-unprod 53.4%

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

      14. sqr-neg 53.4%

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

      15. sqrt-unprod 40.4%

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

      16. add-sqr-sqrt 86.9%

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

   8. Applied egg-rr 86.9%

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

      1. associate-*r/ 83.0%

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

      2. associate-*l/ 85.7%

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

      3. *-commutative 85.7%

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

   10. Simplified 85.7%

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

   if -6.79999999999999969e51 < t < 3.3000000000000001e37

   1. Initial program 84.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 77.3%

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

      1. associate-*l/ 94.3%

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

      2. *-commutative 94.3%

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

   6. Simplified 94.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+51} \lor \neg \left(t \leq 3.3 \cdot 10^{+37}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 7: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+52} \lor \neg \left(t \leq 6 \cdot 10^{+37}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.1e+52) (not (<= t 6e+37)))
   (- x (* y (/ t (- z a))))
   (+ x (* z (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.1e+52) || !(t <= 6e+37)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.1d+52)) .or. (.not. (t <= 6d+37))) then
        tmp = x - (y * (t / (z - a)))
    else
        tmp = x + (z * (y / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.1e+52) || !(t <= 6e+37)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.1e+52) or not (t <= 6e+37):
		tmp = x - (y * (t / (z - a)))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.1e+52) || !(t <= 6e+37))
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.1e+52) || ~((t <= 6e+37)))
		tmp = x - (y * (t / (z - a)));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.1e+52], N[Not[LessEqual[t, 6e+37]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1e52 or 6.00000000000000043e37 < t

   1. Initial program 87.5%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   6. Simplified 87.0%

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

      1. frac-2neg 87.0%

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

      2. div-inv 86.9%

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

      3. distribute-neg-frac 86.9%

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

      4. remove-double-neg 86.9%

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

      5. add-sqr-sqrt 40.4%

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

      6. sqrt-unprod 53.4%

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

      7. sqr-neg 53.4%

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

      8. sqrt-unprod 15.5%

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

      9. add-sqr-sqrt 37.2%

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

      10. clear-num 37.2%

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

      11. cancel-sign-sub-inv 37.2%

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

      12. add-sqr-sqrt 15.5%

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

      13. sqrt-unprod 53.4%

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

      14. sqr-neg 53.4%

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

      15. sqrt-unprod 40.4%

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

      16. add-sqr-sqrt 86.9%

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

   8. Applied egg-rr 86.9%

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

   if -4.1e52 < t < 6.00000000000000043e37

   1. Initial program 84.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 77.3%

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

      1. associate-*l/ 94.3%

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

      2. *-commutative 94.3%

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

   6. Simplified 94.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+52} \lor \neg \left(t \leq 6 \cdot 10^{+37}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 8: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+51}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+37}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+51)
   (- x (/ y (/ (- z a) t)))
   (if (<= t 3.1e+37) (+ x (* z (/ y (- z a)))) (- x (* y (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+51) {
		tmp = x - (y / ((z - a) / t));
	} else if (t <= 3.1e+37) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4d+51)) then
        tmp = x - (y / ((z - a) / t))
    else if (t <= 3.1d+37) then
        tmp = x + (z * (y / (z - a)))
    else
        tmp = x - (y * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+51) {
		tmp = x - (y / ((z - a) / t));
	} else if (t <= 3.1e+37) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+51:
		tmp = x - (y / ((z - a) / t))
	elif t <= 3.1e+37:
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+51)
		tmp = Float64(x - Float64(y / Float64(Float64(z - a) / t)));
	elseif (t <= 3.1e+37)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+51)
		tmp = x - (y / ((z - a) / t));
	elseif (t <= 3.1e+37)
		tmp = x + (z * (y / (z - a)));
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+51], N[(x - N[(y / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+37], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4e51

   1. Initial program 93.1%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around inf 84.5%

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

      1. associate-*r/ 84.5%

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

      2. neg-mul-1 84.5%

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

   6. Simplified 84.5%

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

      1. frac-2neg 84.5%

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

      2. div-inv 84.4%

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

      3. distribute-neg-frac 84.4%

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

      4. remove-double-neg 84.4%

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

      5. add-sqr-sqrt 37.9%

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

      6. sqrt-unprod 46.1%

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

      7. sqr-neg 46.1%

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

      8. sqrt-unprod 9.9%

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

      9. add-sqr-sqrt 33.6%

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

      10. clear-num 33.6%

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

      11. cancel-sign-sub-inv 33.6%

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

      12. add-sqr-sqrt 9.9%

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

      13. sqrt-unprod 46.1%

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

      14. sqr-neg 46.1%

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

      15. sqrt-unprod 37.9%

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

      16. add-sqr-sqrt 84.4%

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

   8. Applied egg-rr 84.4%

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

      1. clear-num 84.4%

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

      2. un-div-inv 84.5%

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

   10. Applied egg-rr 84.5%

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

   if -4e51 < t < 3.1000000000000002e37

   1. Initial program 84.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 77.3%

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

      1. associate-*l/ 94.3%

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

      2. *-commutative 94.3%

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

   6. Simplified 94.3%

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

   if 3.1000000000000002e37 < t

   1. Initial program 81.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 89.6%

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

      1. associate-*r/ 89.6%

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

      2. neg-mul-1 89.6%

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

   6. Simplified 89.6%

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

      1. frac-2neg 89.6%

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

      2. div-inv 89.6%

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

      3. distribute-neg-frac 89.6%

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

      4. remove-double-neg 89.6%

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

      5. add-sqr-sqrt 43.1%

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

      6. sqrt-unprod 61.2%

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

      7. sqr-neg 61.2%

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

      8. sqrt-unprod 21.5%

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

      9. add-sqr-sqrt 41.1%

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

      10. clear-num 41.1%

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

      11. cancel-sign-sub-inv 41.1%

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

      12. add-sqr-sqrt 21.5%

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

      13. sqrt-unprod 61.2%

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

      14. sqr-neg 61.2%

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

      15. sqrt-unprod 43.1%

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

      16. add-sqr-sqrt 89.7%

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

   8. Applied egg-rr 89.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+51}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+37}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]

Alternative 9: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-27} \lor \neg \left(z \leq 14200\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e-27) (not (<= z 14200.0))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e-27) || !(z <= 14200.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.2d-27)) .or. (.not. (z <= 14200.0d0))) then
        tmp = x + y
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e-27) || !(z <= 14200.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e-27) or not (z <= 14200.0):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e-27) || !(z <= 14200.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e-27) || ~((z <= 14200.0)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e-27], N[Not[LessEqual[z, 14200.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999991e-27 or 14200 < z

   1. Initial program 74.0%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around inf 80.9%

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

   if -3.19999999999999991e-27 < z < 14200

   1. Initial program 98.6%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

      1. clear-num 98.4%

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

      2. associate-/r/ 98.4%

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

      3. clear-num 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in z around 0 80.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-27} \lor \neg \left(z \leq 14200\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 10: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-26} \lor \neg \left(z \leq 2050000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e-26) (not (<= z 2050000.0))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-26) || !(z <= 2050000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.7d-26)) .or. (.not. (z <= 2050000.0d0))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-26) || !(z <= 2050000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e-26) or not (z <= 2050000.0):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e-26) || !(z <= 2050000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e-26) || ~((z <= 2050000.0)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e-26], N[Not[LessEqual[z, 2050000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000007e-26 or 2.05e6 < z

   1. Initial program 74.0%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around inf 80.9%

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

   if -1.70000000000000007e-26 < z < 2.05e6

   1. Initial program 98.6%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around 0 81.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-26} \lor \neg \left(z \leq 2050000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 11: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;x + z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+170) x (if (<= a 2.6e+58) (+ x (* z (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+170) {
		tmp = x;
	} else if (a <= 2.6e+58) {
		tmp = x + (z * (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.6d+170)) then
        tmp = x
    else if (a <= 2.6d+58) then
        tmp = x + (z * (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+170) {
		tmp = x;
	} else if (a <= 2.6e+58) {
		tmp = x + (z * (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e+170:
		tmp = x
	elif a <= 2.6e+58:
		tmp = x + (z * (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+170)
		tmp = x;
	elseif (a <= 2.6e+58)
		tmp = Float64(x + Float64(z * Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e+170)
		tmp = x;
	elseif (a <= 2.6e+58)
		tmp = x + (z * (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+170], x, If[LessEqual[a, 2.6e+58], N[(x + N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6e170 or 2.59999999999999988e58 < a

   1. Initial program 87.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 91.0%

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

      1. associate-*r/ 91.0%

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

      2. neg-mul-1 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in x around inf 75.8%

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

   if -3.6e170 < a < 2.59999999999999988e58

   1. Initial program 85.4%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around 0 55.9%

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

      1. associate-*l/ 71.7%

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

      2. *-commutative 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in z around inf 67.2%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;x + z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 13: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{z - a} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-/l* 99.2%

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

3. Simplified 99.2%

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

   1. clear-num 99.1%

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

   2. associate-/r/ 99.2%

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

   3. clear-num 99.2%

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

5. Applied egg-rr 99.2%

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

6. Final simplification 99.2%

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

Alternative 14: 62.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.6e+170) x (if (<= a 3e+58) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.6e+170) {
		tmp = x;
	} else if (a <= 3e+58) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.6d+170)) then
        tmp = x
    else if (a <= 3d+58) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.6e+170) {
		tmp = x;
	} else if (a <= 3e+58) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.6e+170:
		tmp = x
	elif a <= 3e+58:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.6e+170)
		tmp = x;
	elseif (a <= 3e+58)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.6e+170)
		tmp = x;
	elseif (a <= 3e+58)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.6e+170], x, If[LessEqual[a, 3e+58], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.60000000000000047e170 or 3.0000000000000002e58 < a

   1. Initial program 87.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 91.0%

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

      1. associate-*r/ 91.0%

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

      2. neg-mul-1 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in x around inf 75.8%

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

   if -6.60000000000000047e170 < a < 3.0000000000000002e58

   1. Initial program 85.4%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 66.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 49.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-/l* 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in t around inf 76.9%

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

   1. associate-*r/ 76.9%

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

   2. neg-mul-1 76.9%

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

6. Simplified 76.9%

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

7. Taylor expanded in x around inf 52.1%

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

8. Final simplification 52.1%

   \[\leadsto x \]

Developer target: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z - a}{z - t}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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