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

Percentage Accurate: 86.1% → 95.9%

Time: 9.5s

Alternatives: 10

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: 86.1% 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: 95.9% accurate, 1.0× speedup

Math

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

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(Float64(y / 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[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.7%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 2: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z - t}}\\ t_2 := x - y \cdot \frac{t - z}{z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -8.3 \cdot 10^{-274}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a (- z t))))) (t_2 (- x (* y (/ (- t z) z)))))
   (if (<= z -4.6e+49)
     t_2
     (if (<= z -3.3e-56)
       t_1
       (if (<= z -4.2e-74)
         (+ x (/ (- z t) (/ z y)))
         (if (<= z -8.3e-274)
           (+ x (* t (/ y a)))
           (if (<= z 9.8e-60) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / (z - t)));
	double t_2 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -4.6e+49) {
		tmp = t_2;
	} else if (z <= -3.3e-56) {
		tmp = t_1;
	} else if (z <= -4.2e-74) {
		tmp = x + ((z - t) / (z / y));
	} else if (z <= -8.3e-274) {
		tmp = x + (t * (y / a));
	} else if (z <= 9.8e-60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x - (y / (a / (z - t)))
    t_2 = x - (y * ((t - z) / z))
    if (z <= (-4.6d+49)) then
        tmp = t_2
    else if (z <= (-3.3d-56)) then
        tmp = t_1
    else if (z <= (-4.2d-74)) then
        tmp = x + ((z - t) / (z / y))
    else if (z <= (-8.3d-274)) then
        tmp = x + (t * (y / a))
    else if (z <= 9.8d-60) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / (z - t)));
	double t_2 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -4.6e+49) {
		tmp = t_2;
	} else if (z <= -3.3e-56) {
		tmp = t_1;
	} else if (z <= -4.2e-74) {
		tmp = x + ((z - t) / (z / y));
	} else if (z <= -8.3e-274) {
		tmp = x + (t * (y / a));
	} else if (z <= 9.8e-60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / (z - t)))
	t_2 = x - (y * ((t - z) / z))
	tmp = 0
	if z <= -4.6e+49:
		tmp = t_2
	elif z <= -3.3e-56:
		tmp = t_1
	elif z <= -4.2e-74:
		tmp = x + ((z - t) / (z / y))
	elif z <= -8.3e-274:
		tmp = x + (t * (y / a))
	elif z <= 9.8e-60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / Float64(z - t))))
	t_2 = Float64(x - Float64(y * Float64(Float64(t - z) / z)))
	tmp = 0.0
	if (z <= -4.6e+49)
		tmp = t_2;
	elseif (z <= -3.3e-56)
		tmp = t_1;
	elseif (z <= -4.2e-74)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	elseif (z <= -8.3e-274)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 9.8e-60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / (z - t)));
	t_2 = x - (y * ((t - z) / z));
	tmp = 0.0;
	if (z <= -4.6e+49)
		tmp = t_2;
	elseif (z <= -3.3e-56)
		tmp = t_1;
	elseif (z <= -4.2e-74)
		tmp = x + ((z - t) / (z / y));
	elseif (z <= -8.3e-274)
		tmp = x + (t * (y / a));
	elseif (z <= 9.8e-60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+49], t$95$2, If[LessEqual[z, -3.3e-56], t$95$1, If[LessEqual[z, -4.2e-74], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.3e-274], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e-60], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.60000000000000004e49 or 9.79999999999999977e-60 < z

   1. Initial program 73.8%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 84.8%

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

   6. Simplified 84.8%

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

      1. associate-/r/ 86.6%

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

   8. Applied egg-rr 86.6%

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

   if -4.60000000000000004e49 < z < -3.29999999999999984e-56 or -8.29999999999999976e-274 < z < 9.79999999999999977e-60

   1. Initial program 95.1%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

      1. clear-num 98.8%

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

      2. associate-/r/ 98.8%

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

   5. Applied egg-rr 98.8%

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

   6. Taylor expanded in a around inf 83.3%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. *-commutative 83.3%

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

      4. unsub-neg 83.3%

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

      5. associate-/l* 88.0%

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

   8. Simplified 88.0%

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

   if -3.29999999999999984e-56 < z < -4.2e-74

   1. Initial program 99.2%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 a around 0 83.3%

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

      1. +-commutative 83.3%

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

      2. associate-/l* 84.1%

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

   6. Simplified 84.1%

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

   if -4.2e-74 < z < -8.29999999999999976e-274

   1. Initial program 86.7%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 91.0%

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

      2. associate-/r/ 92.3%

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

   5. Applied egg-rr 92.3%

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

   6. Taylor expanded in z around 0 77.5%

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

      1. associate-*r/ 82.9%

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

   8. Simplified 82.9%

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

   9. Taylor expanded in y around 0 77.5%

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

       1. associate-*l/ 90.6%

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

   11. Simplified 90.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-56}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -8.3 \cdot 10^{-274}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]

Alternative 3: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t - z}{z}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- t z) z)))))
   (if (<= z -2.4e+43)
     t_1
     (if (<= z -8.8e-10)
       (- x (/ y (/ a (- z t))))
       (if (<= z -1.7e-41)
         (+ x (/ y (/ (- z a) z)))
         (if (<= z -4.5e-92)
           (/ (* y (- z t)) (- z a))
           (if (<= z 7.4e-60) (+ x (/ (- t z) (/ a y))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -2.4e+43) {
		tmp = t_1;
	} else if (z <= -8.8e-10) {
		tmp = x - (y / (a / (z - t)));
	} else if (z <= -1.7e-41) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= -4.5e-92) {
		tmp = (y * (z - t)) / (z - a);
	} else if (z <= 7.4e-60) {
		tmp = x + ((t - z) / (a / y));
	} 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 * ((t - z) / z))
    if (z <= (-2.4d+43)) then
        tmp = t_1
    else if (z <= (-8.8d-10)) then
        tmp = x - (y / (a / (z - t)))
    else if (z <= (-1.7d-41)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= (-4.5d-92)) then
        tmp = (y * (z - t)) / (z - a)
    else if (z <= 7.4d-60) then
        tmp = x + ((t - z) / (a / y))
    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 * ((t - z) / z));
	double tmp;
	if (z <= -2.4e+43) {
		tmp = t_1;
	} else if (z <= -8.8e-10) {
		tmp = x - (y / (a / (z - t)));
	} else if (z <= -1.7e-41) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= -4.5e-92) {
		tmp = (y * (z - t)) / (z - a);
	} else if (z <= 7.4e-60) {
		tmp = x + ((t - z) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((t - z) / z))
	tmp = 0
	if z <= -2.4e+43:
		tmp = t_1
	elif z <= -8.8e-10:
		tmp = x - (y / (a / (z - t)))
	elif z <= -1.7e-41:
		tmp = x + (y / ((z - a) / z))
	elif z <= -4.5e-92:
		tmp = (y * (z - t)) / (z - a)
	elif z <= 7.4e-60:
		tmp = x + ((t - z) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(t - z) / z)))
	tmp = 0.0
	if (z <= -2.4e+43)
		tmp = t_1;
	elseif (z <= -8.8e-10)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	elseif (z <= -1.7e-41)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= -4.5e-92)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(z - a));
	elseif (z <= 7.4e-60)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((t - z) / z));
	tmp = 0.0;
	if (z <= -2.4e+43)
		tmp = t_1;
	elseif (z <= -8.8e-10)
		tmp = x - (y / (a / (z - t)));
	elseif (z <= -1.7e-41)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= -4.5e-92)
		tmp = (y * (z - t)) / (z - a);
	elseif (z <= 7.4e-60)
		tmp = x + ((t - z) / (a / y));
	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[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+43], t$95$1, If[LessEqual[z, -8.8e-10], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-41], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e-92], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-60], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.40000000000000023e43 or 7.4000000000000005e-60 < z

   1. Initial program 73.8%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 84.8%

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

   6. Simplified 84.8%

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

      1. associate-/r/ 86.6%

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

   8. Applied egg-rr 86.6%

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

   if -2.40000000000000023e43 < z < -8.7999999999999996e-10

   1. Initial program 89.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around inf 78.0%

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

      1. +-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. *-commutative 78.0%

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

      4. unsub-neg 78.0%

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

      5. associate-/l* 88.4%

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

   8. Simplified 88.4%

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

   if -8.7999999999999996e-10 < z < -1.6999999999999999e-41

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   if -1.6999999999999999e-41 < z < -4.5e-92

   1. Initial program 99.6%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 76.8%

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

   if -4.5e-92 < z < 7.4000000000000005e-60

   1. Initial program 91.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 a around inf 83.7%

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

      1. +-commutative 83.7%

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

      2. *-commutative 83.7%

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

      3. mul-1-neg 83.7%

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

      4. unsub-neg 83.7%

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

      5. *-commutative 83.7%

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

      6. associate-/l* 90.0%

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

   6. Simplified 90.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]

Alternative 4: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t - z}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-9}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-60}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- t z) z)))))
   (if (<= z -2.6e+43)
     t_1
     (if (<= z -1.02e-9)
       (- x (/ y (/ a (- z t))))
       (if (<= z -2.1e-41)
         (+ x (/ y (/ (- z a) z)))
         (if (<= z -7.4e-91)
           (/ (* y (- z t)) (- z a))
           (if (<= z 9e-60) (- x (* (- z t) (/ y a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -2.6e+43) {
		tmp = t_1;
	} else if (z <= -1.02e-9) {
		tmp = x - (y / (a / (z - t)));
	} else if (z <= -2.1e-41) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= -7.4e-91) {
		tmp = (y * (z - t)) / (z - a);
	} else if (z <= 9e-60) {
		tmp = x - ((z - t) * (y / a));
	} 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 * ((t - z) / z))
    if (z <= (-2.6d+43)) then
        tmp = t_1
    else if (z <= (-1.02d-9)) then
        tmp = x - (y / (a / (z - t)))
    else if (z <= (-2.1d-41)) then
        tmp = x + (y / ((z - a) / z))
    else if (z <= (-7.4d-91)) then
        tmp = (y * (z - t)) / (z - a)
    else if (z <= 9d-60) then
        tmp = x - ((z - t) * (y / a))
    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 * ((t - z) / z));
	double tmp;
	if (z <= -2.6e+43) {
		tmp = t_1;
	} else if (z <= -1.02e-9) {
		tmp = x - (y / (a / (z - t)));
	} else if (z <= -2.1e-41) {
		tmp = x + (y / ((z - a) / z));
	} else if (z <= -7.4e-91) {
		tmp = (y * (z - t)) / (z - a);
	} else if (z <= 9e-60) {
		tmp = x - ((z - t) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((t - z) / z))
	tmp = 0
	if z <= -2.6e+43:
		tmp = t_1
	elif z <= -1.02e-9:
		tmp = x - (y / (a / (z - t)))
	elif z <= -2.1e-41:
		tmp = x + (y / ((z - a) / z))
	elif z <= -7.4e-91:
		tmp = (y * (z - t)) / (z - a)
	elif z <= 9e-60:
		tmp = x - ((z - t) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(t - z) / z)))
	tmp = 0.0
	if (z <= -2.6e+43)
		tmp = t_1;
	elseif (z <= -1.02e-9)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	elseif (z <= -2.1e-41)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	elseif (z <= -7.4e-91)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(z - a));
	elseif (z <= 9e-60)
		tmp = Float64(x - Float64(Float64(z - t) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((t - z) / z));
	tmp = 0.0;
	if (z <= -2.6e+43)
		tmp = t_1;
	elseif (z <= -1.02e-9)
		tmp = x - (y / (a / (z - t)));
	elseif (z <= -2.1e-41)
		tmp = x + (y / ((z - a) / z));
	elseif (z <= -7.4e-91)
		tmp = (y * (z - t)) / (z - a);
	elseif (z <= 9e-60)
		tmp = x - ((z - t) * (y / a));
	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[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+43], t$95$1, If[LessEqual[z, -1.02e-9], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-41], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.4e-91], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-60], N[(x - N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.60000000000000021e43 or 9.00000000000000001e-60 < z

   1. Initial program 73.8%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 84.8%

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

   6. Simplified 84.8%

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

      1. associate-/r/ 86.6%

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

   8. Applied egg-rr 86.6%

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

   if -2.60000000000000021e43 < z < -1.01999999999999999e-9

   1. Initial program 89.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around inf 78.0%

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

      1. +-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. *-commutative 78.0%

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

      4. unsub-neg 78.0%

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

      5. associate-/l* 88.4%

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

   8. Simplified 88.4%

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

   if -1.01999999999999999e-9 < z < -2.10000000000000013e-41

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   if -2.10000000000000013e-41 < z < -7.4000000000000004e-91

   1. Initial program 99.6%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 76.8%

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

   if -7.4000000000000004e-91 < z < 9.00000000000000001e-60

   1. Initial program 91.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 z around 0 90.1%

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

      1. associate-*r/ 90.1%

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

      2. neg-mul-1 90.1%

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

   6. Simplified 90.1%

      \[\leadsto x + \color{blue}{\frac{-y}{a}} \cdot \left(z - t\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-9}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-60}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]

Alternative 5: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-74} \lor \neg \left(z \leq 2.9 \cdot 10^{-91}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e-74) (not (<= z 2.9e-91)))
   (+ x (/ y (/ (- z a) z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e-74) || !(z <= 2.9e-91)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (t * (y / 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 <= (-3.6d-74)) .or. (.not. (z <= 2.9d-91))) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x + (t * (y / 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 <= -3.6e-74) || !(z <= 2.9e-91)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e-74) or not (z <= 2.9e-91):
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e-74) || !(z <= 2.9e-91))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.6e-74) || ~((z <= 2.9e-91)))
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e-74], N[Not[LessEqual[z, 2.9e-91]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6000000000000002e-74 or 2.9000000000000001e-91 < z

   1. Initial program 80.7%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in t around 0 80.2%

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

   if -3.6000000000000002e-74 < z < 2.9000000000000001e-91

   1. Initial program 91.3%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

      1. clear-num 95.0%

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

      2. associate-/r/ 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in z around 0 81.4%

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

      1. associate-*r/ 86.6%

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

   8. Simplified 86.6%

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

   9. Taylor expanded in y around 0 81.4%

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

       1. associate-*l/ 89.1%

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

   11. Simplified 89.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-74} \lor \neg \left(z \leq 2.9 \cdot 10^{-91}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+46} \lor \neg \left(z \leq 9.8 \cdot 10^{-60}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+46) (not (<= z 9.8e-60)))
   (- x (* y (/ (- t z) z)))
   (+ x (/ (- t z) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+46) || !(z <= 9.8e-60)) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	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 <= (-1.85d+46)) .or. (.not. (z <= 9.8d-60))) then
        tmp = x - (y * ((t - z) / z))
    else
        tmp = x + ((t - z) / (a / y))
    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 <= -1.85e+46) || !(z <= 9.8e-60)) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+46) or not (z <= 9.8e-60):
		tmp = x - (y * ((t - z) / z))
	else:
		tmp = x + ((t - z) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+46) || !(z <= 9.8e-60))
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.85e+46) || ~((z <= 9.8e-60)))
		tmp = x - (y * ((t - z) / z));
	else
		tmp = x + ((t - z) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+46], N[Not[LessEqual[z, 9.8e-60]], $MachinePrecision]], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999995e46 or 9.79999999999999977e-60 < z

   1. Initial program 73.8%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/l* 84.8%

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

   6. Simplified 84.8%

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

      1. associate-/r/ 86.6%

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

   8. Applied egg-rr 86.6%

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

   if -1.84999999999999995e46 < z < 9.79999999999999977e-60

   1. Initial program 92.8%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in a around inf 80.3%

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

      1. +-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. mul-1-neg 80.3%

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

      4. unsub-neg 80.3%

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

      5. *-commutative 80.3%

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

      6. associate-/l* 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+46} \lor \neg \left(z \leq 9.8 \cdot 10^{-60}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+56} \lor \neg \left(z \leq 9 \cdot 10^{-60}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+56) (not (<= z 9e-60))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+56) || !(z <= 9e-60)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / 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 <= (-1.5d+56)) .or. (.not. (z <= 9d-60))) then
        tmp = x + y
    else
        tmp = x + (t * (y / 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 <= -1.5e+56) || !(z <= 9e-60)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+56) or not (z <= 9e-60):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+56) || !(z <= 9e-60))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+56) || ~((z <= 9e-60)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+56], N[Not[LessEqual[z, 9e-60]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000003e56 or 9.00000000000000001e-60 < z

   1. Initial program 73.6%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 76.7%

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

   if -1.50000000000000003e56 < z < 9.00000000000000001e-60

   1. Initial program 92.9%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

      1. clear-num 95.9%

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

      2. associate-/r/ 96.3%

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

   5. Applied egg-rr 96.3%

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

   6. Taylor expanded in z around 0 74.7%

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

      1. associate-*r/ 79.4%

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

   8. Simplified 79.4%

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

   9. Taylor expanded in y around 0 74.7%

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

       1. associate-*l/ 80.5%

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

   11. Simplified 80.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+56} \lor \neg \left(z \leq 9 \cdot 10^{-60}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+56) (+ x y) (if (<= z 9.5e-60) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+56) {
		tmp = x + y;
	} else if (z <= 9.5e-60) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	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 <= (-1.8d+56)) then
        tmp = x + y
    else if (z <= 9.5d-60) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    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 <= -1.8e+56) {
		tmp = x + y;
	} else if (z <= 9.5e-60) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+56:
		tmp = x + y
	elif z <= 9.5e-60:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+56)
		tmp = Float64(x + y);
	elseif (z <= 9.5e-60)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+56)
		tmp = x + y;
	elseif (z <= 9.5e-60)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+56], N[(x + y), $MachinePrecision], If[LessEqual[z, 9.5e-60], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999999e56 or 9.49999999999999958e-60 < z

   1. Initial program 73.6%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 76.7%

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

   if -1.79999999999999999e56 < z < 9.49999999999999958e-60

   1. Initial program 92.9%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

      1. clear-num 95.9%

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

      2. associate-/r/ 96.3%

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

   5. Applied egg-rr 96.3%

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

   6. Taylor expanded in z around 0 74.7%

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

      1. associate-*r/ 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 62.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-182}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e-182) (+ x y) (if (<= z 3.9e-94) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e-182) {
		tmp = x + y;
	} else if (z <= 3.9e-94) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	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 <= (-5.4d-182)) then
        tmp = x + y
    else if (z <= 3.9d-94) then
        tmp = x
    else
        tmp = x + y
    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 <= -5.4e-182) {
		tmp = x + y;
	} else if (z <= 3.9e-94) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e-182:
		tmp = x + y
	elif z <= 3.9e-94:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e-182)
		tmp = Float64(x + y);
	elseif (z <= 3.9e-94)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e-182)
		tmp = x + y;
	elseif (z <= 3.9e-94)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e-182], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.9e-94], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.39999999999999999e-182 or 3.9000000000000002e-94 < z

   1. Initial program 81.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 65.5%

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

   if -5.39999999999999999e-182 < z < 3.9000000000000002e-94

   1. Initial program 93.6%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 53.0%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-182}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 51.1% 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 84.7%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in x around inf 47.7%

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

5. Final simplification 47.7%

   \[\leadsto x \]

Developer target: 98.3% 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 2023238 
(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))))