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

Percentage Accurate: 85.7% → 98.4%

Time: 8.5s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 85.2%

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

   1. associate-*l/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-37}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+48} \lor \neg \left(z \leq 3 \cdot 10^{+86}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- t (* t (/ y z))))))
   (if (<= z -7.5e+44)
     t_1
     (if (<= z 9e-37)
       (+ x (* t (/ y (- a z))))
       (if (or (<= z 1.1e+48) (not (<= z 3e+86))) t_1 (+ x (* y (/ t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - (t * (y / z)));
	double tmp;
	if (z <= -7.5e+44) {
		tmp = t_1;
	} else if (z <= 9e-37) {
		tmp = x + (t * (y / (a - z)));
	} else if ((z <= 1.1e+48) || !(z <= 3e+86)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t - (t * (y / z)))
    if (z <= (-7.5d+44)) then
        tmp = t_1
    else if (z <= 9d-37) then
        tmp = x + (t * (y / (a - z)))
    else if ((z <= 1.1d+48) .or. (.not. (z <= 3d+86))) then
        tmp = t_1
    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 t_1 = x + (t - (t * (y / z)));
	double tmp;
	if (z <= -7.5e+44) {
		tmp = t_1;
	} else if (z <= 9e-37) {
		tmp = x + (t * (y / (a - z)));
	} else if ((z <= 1.1e+48) || !(z <= 3e+86)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - (t * (y / z)))
	tmp = 0
	if z <= -7.5e+44:
		tmp = t_1
	elif z <= 9e-37:
		tmp = x + (t * (y / (a - z)))
	elif (z <= 1.1e+48) or not (z <= 3e+86):
		tmp = t_1
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - Float64(t * Float64(y / z))))
	tmp = 0.0
	if (z <= -7.5e+44)
		tmp = t_1;
	elseif (z <= 9e-37)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif ((z <= 1.1e+48) || !(z <= 3e+86))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t - (t * (y / z)));
	tmp = 0.0;
	if (z <= -7.5e+44)
		tmp = t_1;
	elseif (z <= 9e-37)
		tmp = x + (t * (y / (a - z)));
	elseif ((z <= 1.1e+48) || ~((z <= 3e+86)))
		tmp = t_1;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+44], t$95$1, If[LessEqual[z, 9e-37], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.1e+48], N[Not[LessEqual[z, 3e+86]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000027e44 or 9.00000000000000081e-37 < z < 1.1e48 or 2.99999999999999977e86 < z

   1. Initial program 75.9%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 90.8%

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

      1. mul-1-neg 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in y around 0 84.4%

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

      1. associate-+r+ 84.4%

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

      2. +-commutative 84.4%

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

      3. mul-1-neg 84.4%

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

      4. unsub-neg 84.4%

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

      5. *-commutative 84.4%

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

      6. associate-*r/ 90.8%

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

   9. Simplified 90.8%

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

   if -7.50000000000000027e44 < z < 9.00000000000000081e-37

   1. Initial program 91.8%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around inf 87.4%

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

   if 1.1e48 < z < 2.99999999999999977e86

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 76.5%

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

      1. associate-/l* 100.0%

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

      2. div-inv 100.0%

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

      3. clear-num 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-37}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+48} \lor \neg \left(z \leq 3 \cdot 10^{+86}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 3: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+46} \lor \neg \left(z \leq 4 \cdot 10^{+86}\right):\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+47)
   (+ x (- t (* t (/ y z))))
   (if (<= z 9.5e-37)
     (+ x (* t (/ y (- a z))))
     (if (or (<= z 2.6e+46) (not (<= z 4e+86)))
       (- x (/ t (/ z (- y z))))
       (+ x (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+47) {
		tmp = x + (t - (t * (y / z)));
	} else if (z <= 9.5e-37) {
		tmp = x + (t * (y / (a - z)));
	} else if ((z <= 2.6e+46) || !(z <= 4e+86)) {
		tmp = x - (t / (z / (y - z)));
	} 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 <= (-3.5d+47)) then
        tmp = x + (t - (t * (y / z)))
    else if (z <= 9.5d-37) then
        tmp = x + (t * (y / (a - z)))
    else if ((z <= 2.6d+46) .or. (.not. (z <= 4d+86))) then
        tmp = x - (t / (z / (y - z)))
    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 <= -3.5e+47) {
		tmp = x + (t - (t * (y / z)));
	} else if (z <= 9.5e-37) {
		tmp = x + (t * (y / (a - z)));
	} else if ((z <= 2.6e+46) || !(z <= 4e+86)) {
		tmp = x - (t / (z / (y - z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+47:
		tmp = x + (t - (t * (y / z)))
	elif z <= 9.5e-37:
		tmp = x + (t * (y / (a - z)))
	elif (z <= 2.6e+46) or not (z <= 4e+86):
		tmp = x - (t / (z / (y - z)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+47)
		tmp = Float64(x + Float64(t - Float64(t * Float64(y / z))));
	elseif (z <= 9.5e-37)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif ((z <= 2.6e+46) || !(z <= 4e+86))
		tmp = Float64(x - Float64(t / Float64(z / Float64(y - z))));
	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 <= -3.5e+47)
		tmp = x + (t - (t * (y / z)));
	elseif (z <= 9.5e-37)
		tmp = x + (t * (y / (a - z)));
	elseif ((z <= 2.6e+46) || ~((z <= 4e+86)))
		tmp = x - (t / (z / (y - z)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+47], N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-37], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.6e+46], N[Not[LessEqual[z, 4e+86]], $MachinePrecision]], N[(x - N[(t / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.50000000000000015e47

   1. Initial program 72.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 90.9%

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

      1. mul-1-neg 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in y around 0 80.9%

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

      1. associate-+r+ 80.9%

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

      2. +-commutative 80.9%

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

      3. mul-1-neg 80.9%

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

      4. unsub-neg 80.9%

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

      5. *-commutative 80.9%

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

      6. associate-*r/ 90.9%

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

   9. Simplified 90.9%

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

   if -3.50000000000000015e47 < z < 9.49999999999999927e-37

   1. Initial program 91.8%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around inf 87.4%

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

   if 9.49999999999999927e-37 < z < 2.60000000000000013e46 or 4.0000000000000001e86 < z

   1. Initial program 78.0%

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

      1. +-commutative 78.0%

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

      2. associate-*r/ 93.6%

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

      3. fma-def 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. associate-/l* 90.8%

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

   6. Simplified 90.8%

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

   if 2.60000000000000013e46 < z < 4.0000000000000001e86

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 76.5%

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

      1. associate-/l* 100.0%

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

      2. div-inv 100.0%

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

      3. clear-num 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+46} \lor \neg \left(z \leq 4 \cdot 10^{+86}\right):\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 4: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+55}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+90}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+55)
   (+ x t)
   (if (<= z 8.8e-37)
     (+ x (/ y (/ a t)))
     (if (<= z 1.45e+34)
       (- t (* t (/ y z)))
       (if (<= z 1.7e+90) (+ x (* y (/ t a))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+55) {
		tmp = x + t;
	} else if (z <= 8.8e-37) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.45e+34) {
		tmp = t - (t * (y / z));
	} else if (z <= 1.7e+90) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + 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+55)) then
        tmp = x + t
    else if (z <= 8.8d-37) then
        tmp = x + (y / (a / t))
    else if (z <= 1.45d+34) then
        tmp = t - (t * (y / z))
    else if (z <= 1.7d+90) then
        tmp = x + (y * (t / a))
    else
        tmp = x + 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+55) {
		tmp = x + t;
	} else if (z <= 8.8e-37) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.45e+34) {
		tmp = t - (t * (y / z));
	} else if (z <= 1.7e+90) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+55:
		tmp = x + t
	elif z <= 8.8e-37:
		tmp = x + (y / (a / t))
	elif z <= 1.45e+34:
		tmp = t - (t * (y / z))
	elif z <= 1.7e+90:
		tmp = x + (y * (t / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+55)
		tmp = Float64(x + t);
	elseif (z <= 8.8e-37)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.45e+34)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (z <= 1.7e+90)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+55)
		tmp = x + t;
	elseif (z <= 8.8e-37)
		tmp = x + (y / (a / t));
	elseif (z <= 1.45e+34)
		tmp = t - (t * (y / z));
	elseif (z <= 1.7e+90)
		tmp = x + (y * (t / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+55], N[(x + t), $MachinePrecision], If[LessEqual[z, 8.8e-37], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+34], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+90], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6999999999999999e55 or 1.70000000000000009e90 < z

   1. Initial program 70.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.9%

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

   if -1.6999999999999999e55 < z < 8.80000000000000008e-37

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-*r/ 96.0%

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

      3. fma-def 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around 0 72.1%

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

      1. associate-/l* 77.2%

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

   6. Simplified 77.2%

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

   if 8.80000000000000008e-37 < z < 1.4500000000000001e34

   1. Initial program 94.8%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 88.9%

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

      1. mul-1-neg 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in y around 0 89.0%

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

      1. associate-+r+ 89.0%

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

      2. +-commutative 89.0%

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

      3. mul-1-neg 89.0%

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

      4. unsub-neg 89.0%

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

      5. *-commutative 89.0%

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

      6. associate-*r/ 88.9%

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

   9. Simplified 88.9%

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

   10. Taylor expanded in t around inf 66.2%

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

       1. sub-neg 66.2%

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

       2. +-commutative 66.2%

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

       3. distribute-rgt1-in 66.2%

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

       4. cancel-sign-sub-inv 66.2%

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

       5. *-commutative 66.2%

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

   12. Simplified 66.2%

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

   if 1.4500000000000001e34 < z < 1.70000000000000009e90

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 72.2%

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

      1. associate-/l* 91.1%

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

      2. div-inv 91.1%

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

      3. clear-num 91.1%

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

   6. Applied egg-rr 91.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+55}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+90}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 5: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+34}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+87}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+43)
   (+ x t)
   (if (<= z 9.5e-37)
     (+ x (/ y (/ a t)))
     (if (<= z 1.15e+34)
       (- t (/ (* y t) z))
       (if (<= z 3e+87) (+ x (* y (/ t a))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+43) {
		tmp = x + t;
	} else if (z <= 9.5e-37) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.15e+34) {
		tmp = t - ((y * t) / z);
	} else if (z <= 3e+87) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + 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 <= (-5.5d+43)) then
        tmp = x + t
    else if (z <= 9.5d-37) then
        tmp = x + (y / (a / t))
    else if (z <= 1.15d+34) then
        tmp = t - ((y * t) / z)
    else if (z <= 3d+87) then
        tmp = x + (y * (t / a))
    else
        tmp = x + 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 <= -5.5e+43) {
		tmp = x + t;
	} else if (z <= 9.5e-37) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.15e+34) {
		tmp = t - ((y * t) / z);
	} else if (z <= 3e+87) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+43:
		tmp = x + t
	elif z <= 9.5e-37:
		tmp = x + (y / (a / t))
	elif z <= 1.15e+34:
		tmp = t - ((y * t) / z)
	elif z <= 3e+87:
		tmp = x + (y * (t / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+43)
		tmp = Float64(x + t);
	elseif (z <= 9.5e-37)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.15e+34)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (z <= 3e+87)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+43)
		tmp = x + t;
	elseif (z <= 9.5e-37)
		tmp = x + (y / (a / t));
	elseif (z <= 1.15e+34)
		tmp = t - ((y * t) / z);
	elseif (z <= 3e+87)
		tmp = x + (y * (t / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+43], N[(x + t), $MachinePrecision], If[LessEqual[z, 9.5e-37], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+34], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+87], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999989e43 or 2.9999999999999999e87 < z

   1. Initial program 70.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.9%

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

   if -5.49999999999999989e43 < z < 9.49999999999999927e-37

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-*r/ 96.0%

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

      3. fma-def 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around 0 72.1%

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

      1. associate-/l* 77.2%

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

   6. Simplified 77.2%

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

   if 9.49999999999999927e-37 < z < 1.1499999999999999e34

   1. Initial program 94.8%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 88.9%

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

      1. mul-1-neg 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in y around 0 89.0%

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

      1. associate-+r+ 89.0%

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

      2. +-commutative 89.0%

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

      3. mul-1-neg 89.0%

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

      4. unsub-neg 89.0%

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

      5. *-commutative 89.0%

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

      6. associate-*r/ 88.9%

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

   9. Simplified 88.9%

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

   10. Taylor expanded in x around 0 66.3%

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

   if 1.1499999999999999e34 < z < 2.9999999999999999e87

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 72.2%

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

      1. associate-/l* 91.1%

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

      2. div-inv 91.1%

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

      3. clear-num 91.1%

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

   6. Applied egg-rr 91.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+34}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+87}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 6: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+56} \lor \neg \left(z \leq 6 \cdot 10^{+169}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+56) (not (<= z 6e+169)))
   (+ x t)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+56) || !(z <= 6e+169)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / (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 <= (-1.35d+56)) .or. (.not. (z <= 6d+169))) then
        tmp = x + t
    else
        tmp = x + (y * (t / (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 <= -1.35e+56) || !(z <= 6e+169)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+56) or not (z <= 6e+169):
		tmp = x + t
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+56) || !(z <= 6e+169))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+56) || ~((z <= 6e+169)))
		tmp = x + t;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+56], N[Not[LessEqual[z, 6e+169]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000005e56 or 5.9999999999999999e169 < z

   1. Initial program 69.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 85.5%

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

   if -1.35000000000000005e56 < z < 5.9999999999999999e169

   1. Initial program 90.3%

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

      1. associate-/l* 97.3%

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

      2. *-un-lft-identity 97.3%

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

      3. div-inv 97.2%

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

      4. times-frac 90.2%

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

   3. Applied egg-rr 90.2%

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

   4. Taylor expanded in y around inf 78.1%

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

      1. associate-*r/ 84.3%

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

   6. Simplified 84.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+56} \lor \neg \left(z \leq 6 \cdot 10^{+169}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 7: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+56} \lor \neg \left(z \leq 7.6 \cdot 10^{+175}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+56) (not (<= z 7.6e+175)))
   (+ x t)
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+56) || !(z <= 7.6e+175)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (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 <= (-1.35d+56)) .or. (.not. (z <= 7.6d+175))) then
        tmp = x + t
    else
        tmp = x + (t * (y / (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 <= -1.35e+56) || !(z <= 7.6e+175)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+56) or not (z <= 7.6e+175):
		tmp = x + t
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+56) || !(z <= 7.6e+175))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+56) || ~((z <= 7.6e+175)))
		tmp = x + t;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+56], N[Not[LessEqual[z, 7.6e+175]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000005e56 or 7.5999999999999994e175 < z

   1. Initial program 68.9%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 86.8%

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

   if -1.35000000000000005e56 < z < 7.5999999999999994e175

   1. Initial program 90.3%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around inf 84.9%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+56} \lor \neg \left(z \leq 7.6 \cdot 10^{+175}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 8: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-100} \lor \neg \left(y \leq 1.56 \cdot 10^{+78}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.5e-100) (not (<= y 1.56e+78)))
   (+ x (* t (/ y (- a z))))
   (- x (/ t (/ (- a z) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.5e-100) || !(y <= 1.56e+78)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t / ((a - z) / 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 ((y <= (-4.5d-100)) .or. (.not. (y <= 1.56d+78))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x - (t / ((a - z) / 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 ((y <= -4.5e-100) || !(y <= 1.56e+78)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t / ((a - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.5e-100) or not (y <= 1.56e+78):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x - (t / ((a - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.5e-100) || !(y <= 1.56e+78))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.5e-100) || ~((y <= 1.56e+78)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x - (t / ((a - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.5e-100], N[Not[LessEqual[y, 1.56e+78]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000001e-100 or 1.5599999999999999e78 < y

   1. Initial program 81.4%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around inf 89.3%

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

   if -4.5000000000000001e-100 < y < 1.5599999999999999e78

   1. Initial program 89.0%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

      1. associate-/r/ 94.8%

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

      2. div-inv 94.7%

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

      3. associate-/r* 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in y around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. associate-/l* 93.0%

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

   8. Simplified 93.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-100} \lor \neg \left(y \leq 1.56 \cdot 10^{+78}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \end{array} \]

Alternative 9: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+46} \lor \neg \left(z \leq 2.2 \cdot 10^{+86}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e+46) (not (<= z 2.2e+86))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+46) || !(z <= 2.2e+86)) {
		tmp = x + t;
	} 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 <= (-2.3d+46)) .or. (.not. (z <= 2.2d+86))) then
        tmp = x + t
    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 <= -2.3e+46) || !(z <= 2.2e+86)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e+46) or not (z <= 2.2e+86):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e+46) || !(z <= 2.2e+86))
		tmp = Float64(x + t);
	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 <= -2.3e+46) || ~((z <= 2.2e+86)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e+46], N[Not[LessEqual[z, 2.2e+86]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e46 or 2.20000000000000003e86 < z

   1. Initial program 70.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.9%

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

   if -2.3000000000000001e46 < z < 2.20000000000000003e86

   1. Initial program 91.5%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 73.8%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+46} \lor \neg \left(z \leq 2.2 \cdot 10^{+86}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+50}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+50) (+ x t) (if (<= z 2.15e+86) (+ x (/ y (/ a t))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+50) {
		tmp = x + t;
	} else if (z <= 2.15e+86) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + 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 <= (-1.2d+50)) then
        tmp = x + t
    else if (z <= 2.15d+86) then
        tmp = x + (y / (a / t))
    else
        tmp = x + 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 <= -1.2e+50) {
		tmp = x + t;
	} else if (z <= 2.15e+86) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+50:
		tmp = x + t
	elif z <= 2.15e+86:
		tmp = x + (y / (a / t))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+50)
		tmp = Float64(x + t);
	elseif (z <= 2.15e+86)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+50)
		tmp = x + t;
	elseif (z <= 2.15e+86)
		tmp = x + (y / (a / t));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+50], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.15e+86], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2000000000000001e50 or 2.1500000000000001e86 < z

   1. Initial program 70.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.9%

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

   if -1.2000000000000001e50 < z < 2.1500000000000001e86

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-*r/ 96.6%

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

      3. fma-def 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 68.0%

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

      1. associate-/l* 73.8%

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

   6. Simplified 73.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+50}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 11: 58.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.1e+106) (* t (/ (- y) z)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.1e+106) {
		tmp = t * (-y / z);
	} else {
		tmp = x + 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 (y <= (-2.1d+106)) then
        tmp = t * (-y / z)
    else
        tmp = x + 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 (y <= -2.1e+106) {
		tmp = t * (-y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.1e+106:
		tmp = t * (-y / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.1e+106)
		tmp = Float64(t * Float64(Float64(-y) / z));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.1e+106)
		tmp = t * (-y / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.1e+106], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000005e106

   1. Initial program 81.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around 0 64.2%

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

      1. mul-1-neg 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in y around 0 63.0%

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

      1. associate-+r+ 63.0%

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

      2. +-commutative 63.0%

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

      3. mul-1-neg 63.0%

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

      4. unsub-neg 63.0%

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

      5. *-commutative 63.0%

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

      6. associate-*r/ 64.2%

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

   9. Simplified 64.2%

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

   10. Taylor expanded in y around inf 43.6%

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

       1. mul-1-neg 43.6%

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

       2. *-commutative 43.6%

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

       3. associate-*r/ 44.8%

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

       4. distribute-rgt-neg-in 44.8%

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

   12. Simplified 44.8%

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

   if -2.10000000000000005e106 < y

   1. Initial program 86.1%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 60.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 12: 62.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+19}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+19) (+ x t) (if (<= z 2.2e-235) x (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+19) {
		tmp = x + t;
	} else if (z <= 2.2e-235) {
		tmp = x;
	} else {
		tmp = x + 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+19)) then
        tmp = x + t
    else if (z <= 2.2d-235) then
        tmp = x
    else
        tmp = x + 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+19) {
		tmp = x + t;
	} else if (z <= 2.2e-235) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+19:
		tmp = x + t
	elif z <= 2.2e-235:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+19)
		tmp = Float64(x + t);
	elseif (z <= 2.2e-235)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+19)
		tmp = x + t;
	elseif (z <= 2.2e-235)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+19], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.2e-235], x, N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e19 or 2.19999999999999984e-235 < z

   1. Initial program 82.0%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around inf 65.0%

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

   if -1.7e19 < z < 2.19999999999999984e-235

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. associate-*r/ 95.0%

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

      3. fma-def 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 48.0%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+19}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 13: 50.5% 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 85.2%

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

   1. +-commutative 85.2%

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

   2. associate-*r/ 95.4%

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

   3. fma-def 95.4%

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

3. Simplified 95.4%

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

4. Taylor expanded in t around 0 46.4%

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

5. Final simplification 46.4%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} 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 - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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