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

Percentage Accurate: 84.8% → 98.2%

Time: 14.4s

Alternatives: 17

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: 84.8% 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: 98.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-176}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3e-176)
   (+ x (/ (- y z) (/ (- a z) t)))
   (fma (/ (- y z) (- a z)) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3e-176) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = fma(((y - z) / (a - z)), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3e-176)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3e-176], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e-176

   1. Initial program 79.0%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -3e-176 < x

   1. Initial program 86.3%

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

      1. +-commutative 86.3%

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

      2. associate-*l/ 99.3%

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

      3. fma-def 99.3%

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

   3. Simplified 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-176}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \end{array} \]

Alternative 2: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+122}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -39000000000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+122)
   (+ x t)
   (if (<= z -2.5e+38)
     (- x (* t (/ y z)))
     (if (<= z -39000000000000.0)
       (+ x t)
       (if (<= z 6e+54) (+ x (/ t (/ a y))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+122) {
		tmp = x + t;
	} else if (z <= -2.5e+38) {
		tmp = x - (t * (y / z));
	} else if (z <= -39000000000000.0) {
		tmp = x + t;
	} else if (z <= 6e+54) {
		tmp = x + (t / (a / y));
	} 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 <= (-1.45d+122)) then
        tmp = x + t
    else if (z <= (-2.5d+38)) then
        tmp = x - (t * (y / z))
    else if (z <= (-39000000000000.0d0)) then
        tmp = x + t
    else if (z <= 6d+54) then
        tmp = x + (t / (a / y))
    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 <= -1.45e+122) {
		tmp = x + t;
	} else if (z <= -2.5e+38) {
		tmp = x - (t * (y / z));
	} else if (z <= -39000000000000.0) {
		tmp = x + t;
	} else if (z <= 6e+54) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+122:
		tmp = x + t
	elif z <= -2.5e+38:
		tmp = x - (t * (y / z))
	elif z <= -39000000000000.0:
		tmp = x + t
	elif z <= 6e+54:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+122)
		tmp = Float64(x + t);
	elseif (z <= -2.5e+38)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -39000000000000.0)
		tmp = Float64(x + t);
	elseif (z <= 6e+54)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+122)
		tmp = x + t;
	elseif (z <= -2.5e+38)
		tmp = x - (t * (y / z));
	elseif (z <= -39000000000000.0)
		tmp = x + t;
	elseif (z <= 6e+54)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+122], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.5e+38], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -39000000000000.0], N[(x + t), $MachinePrecision], If[LessEqual[z, 6e+54], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e122 or -2.49999999999999985e38 < z < -3.9e13 or 5.9999999999999998e54 < z

   1. Initial program 69.2%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 83.9%

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

   if -1.45e122 < z < -2.49999999999999985e38

   1. Initial program 78.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 75.7%

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

   5. Taylor expanded in a around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

      3. associate-/l* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 64.4%

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

      1. associate-*r/ 64.5%

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

   10. Simplified 64.5%

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

   if -3.9e13 < z < 5.9999999999999998e54

   1. Initial program 94.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+122}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -39000000000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+126}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+38}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -39000000000000:\\ \;\;\;\;x + z \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+126)
   (+ x t)
   (if (<= z -3.6e+38)
     (- x (* t (/ y z)))
     (if (<= z -39000000000000.0)
       (+ x (* z (/ t z)))
       (if (<= z 3.7e+50) (+ x (/ t (/ a y))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+126) {
		tmp = x + t;
	} else if (z <= -3.6e+38) {
		tmp = x - (t * (y / z));
	} else if (z <= -39000000000000.0) {
		tmp = x + (z * (t / z));
	} else if (z <= 3.7e+50) {
		tmp = x + (t / (a / y));
	} 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 <= (-2.3d+126)) then
        tmp = x + t
    else if (z <= (-3.6d+38)) then
        tmp = x - (t * (y / z))
    else if (z <= (-39000000000000.0d0)) then
        tmp = x + (z * (t / z))
    else if (z <= 3.7d+50) then
        tmp = x + (t / (a / y))
    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 <= -2.3e+126) {
		tmp = x + t;
	} else if (z <= -3.6e+38) {
		tmp = x - (t * (y / z));
	} else if (z <= -39000000000000.0) {
		tmp = x + (z * (t / z));
	} else if (z <= 3.7e+50) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+126:
		tmp = x + t
	elif z <= -3.6e+38:
		tmp = x - (t * (y / z))
	elif z <= -39000000000000.0:
		tmp = x + (z * (t / z))
	elif z <= 3.7e+50:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+126)
		tmp = Float64(x + t);
	elseif (z <= -3.6e+38)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -39000000000000.0)
		tmp = Float64(x + Float64(z * Float64(t / z)));
	elseif (z <= 3.7e+50)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+126)
		tmp = x + t;
	elseif (z <= -3.6e+38)
		tmp = x - (t * (y / z));
	elseif (z <= -39000000000000.0)
		tmp = x + (z * (t / z));
	elseif (z <= 3.7e+50)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+126], N[(x + t), $MachinePrecision], If[LessEqual[z, -3.6e+38], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -39000000000000.0], N[(x + N[(z * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+50], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3000000000000001e126 or 3.7000000000000001e50 < z

   1. Initial program 66.8%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 84.8%

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

   if -2.3000000000000001e126 < z < -3.59999999999999969e38

   1. Initial program 78.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 75.7%

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

   5. Taylor expanded in a around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

      3. associate-/l* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 64.4%

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

      1. associate-*r/ 64.5%

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

   10. Simplified 64.5%

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

   if -3.59999999999999969e38 < z < -3.9e13

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. div-inv 99.8%

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

      2. clear-num 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-*r/ 72.3%

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

   10. Simplified 72.3%

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

   11. Taylor expanded in a around 0 72.3%

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

       1. associate-*r/ 72.3%

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

       2. neg-mul-1 72.3%

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

   13. Simplified 72.3%

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

   if -3.9e13 < z < 3.7000000000000001e50

   1. Initial program 94.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+126}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+38}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -39000000000000:\\ \;\;\;\;x + z \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+14} \lor \neg \left(z \leq 2.2 \cdot 10^{+50}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+14) (not (<= z 2.2e+50)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+14) || !(z <= 2.2e+50)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (t / (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 <= (-1.5d+14)) .or. (.not. (z <= 2.2d+50))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else
        tmp = x + (t / (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 <= -1.5e+14) || !(z <= 2.2e+50)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+14) or not (z <= 2.2e+50):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+14) || !(z <= 2.2e+50))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+14) || ~((z <= 2.2e+50)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+14], N[Not[LessEqual[z, 2.2e+50]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e14 or 2.20000000000000017e50 < z

   1. Initial program 70.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 88.6%

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

      1. associate-*r/ 88.6%

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

      2. neg-mul-1 88.6%

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

   6. Simplified 88.6%

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

   7. Taylor expanded in y around 0 88.6%

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

      1. mul-1-neg 88.6%

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

      2. unsub-neg 88.6%

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

   9. Simplified 88.6%

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

   if -1.5e14 < z < 2.20000000000000017e50

   1. Initial program 94.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+14} \lor \neg \left(z \leq 2.2 \cdot 10^{+50}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+14} \lor \neg \left(z \leq 0.00075\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+14) (not (<= z 0.00075)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (* (- y z) (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+14) || !(z <= 0.00075)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + ((y - z) * (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 <= (-1.5d+14)) .or. (.not. (z <= 0.00075d0))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else
        tmp = x + ((y - z) * (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 <= -1.5e+14) || !(z <= 0.00075)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + ((y - z) * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+14) or not (z <= 0.00075):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + ((y - z) * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+14) || !(z <= 0.00075))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+14) || ~((z <= 0.00075)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + ((y - z) * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+14], N[Not[LessEqual[z, 0.00075]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e14 or 7.5000000000000002e-4 < z

   1. Initial program 71.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 86.2%

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

      1. associate-*r/ 86.2%

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

      2. neg-mul-1 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in y around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   9. Simplified 86.3%

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

   if -1.5e14 < z < 7.5000000000000002e-4

   1. Initial program 94.7%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

      1. associate-/r/ 99.1%

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

   5. Applied egg-rr 99.1%

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

      1. div-inv 98.4%

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

      2. clear-num 98.4%

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

   7. Applied egg-rr 98.4%

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

   8. Taylor expanded in a around inf 83.8%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+14} \lor \neg \left(z \leq 0.00075\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]

Alternative 6: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+16} \lor \neg \left(z \leq 1.2 \cdot 10^{+54}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+16) (not (<= z 1.2e+54)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+16) || !(z <= 1.2e+54)) {
		tmp = x + (t * (1.0 - (y / z)));
	} 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 <= (-4.8d+16)) .or. (.not. (z <= 1.2d+54))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    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 <= -4.8e+16) || !(z <= 1.2e+54)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+16) or not (z <= 1.2e+54):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+16) || !(z <= 1.2e+54))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	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 <= -4.8e+16) || ~((z <= 1.2e+54)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+16], N[Not[LessEqual[z, 1.2e+54]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e16 or 1.19999999999999999e54 < z

   1. Initial program 70.2%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 88.5%

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

      1. associate-*r/ 88.5%

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

      2. neg-mul-1 88.5%

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

   6. Simplified 88.5%

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

   7. Taylor expanded in y around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. unsub-neg 88.5%

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

   9. Simplified 88.5%

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

   if -4.8e16 < z < 1.19999999999999999e54

   1. Initial program 94.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 87.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+16} \lor \neg \left(z \leq 1.2 \cdot 10^{+54}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 7: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+51}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.42e+16)
   (+ x (* t (- 1.0 (/ y z))))
   (if (<= z 3e+51) (+ x (* t (/ y (- a z)))) (+ x (- t (/ t (/ z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.42e+16) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 3e+51) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t - (t / (z / 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 <= (-1.42d+16)) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else if (z <= 3d+51) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (t - (t / (z / 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 <= -1.42e+16) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 3e+51) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t - (t / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.42e+16:
		tmp = x + (t * (1.0 - (y / z)))
	elif z <= 3e+51:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (t - (t / (z / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.42e+16)
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	elseif (z <= 3e+51)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t - Float64(t / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.42e+16)
		tmp = x + (t * (1.0 - (y / z)));
	elseif (z <= 3e+51)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (t - (t / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.42e+16], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+51], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.42e16

   1. Initial program 73.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 89.7%

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

      1. associate-*r/ 89.7%

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

      2. neg-mul-1 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in y around 0 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   9. Simplified 89.7%

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

   if -1.42e16 < z < 3e51

   1. Initial program 94.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 87.3%

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

   if 3e51 < z

   1. Initial program 66.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   6. Simplified 87.1%

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

   7. Taylor expanded in y around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

      3. associate-/l* 87.2%

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

   9. Simplified 87.2%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+51}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \]

Alternative 8: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.42e+16)
   (+ x (* t (- 1.0 (/ y z))))
   (if (<= z 3.8e+52) (+ x (/ t (/ (- a z) y))) (+ x (- t (/ t (/ z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.42e+16) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 3.8e+52) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (t - (t / (z / 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 <= (-1.42d+16)) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else if (z <= 3.8d+52) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x + (t - (t / (z / 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 <= -1.42e+16) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 3.8e+52) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (t - (t / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.42e+16:
		tmp = x + (t * (1.0 - (y / z)))
	elif z <= 3.8e+52:
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x + (t - (t / (z / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.42e+16)
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	elseif (z <= 3.8e+52)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x + Float64(t - Float64(t / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.42e+16)
		tmp = x + (t * (1.0 - (y / z)));
	elseif (z <= 3.8e+52)
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x + (t - (t / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.42e+16], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+52], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.42e16

   1. Initial program 73.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 89.7%

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

      1. associate-*r/ 89.7%

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

      2. neg-mul-1 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in y around 0 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   9. Simplified 89.7%

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

   if -1.42e16 < z < 3.8e52

   1. Initial program 94.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 86.8%

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

      1. associate-/l* 87.3%

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

   6. Simplified 87.3%

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

   if 3.8e52 < z

   1. Initial program 66.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   6. Simplified 87.1%

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

   7. Taylor expanded in y around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

      3. associate-/l* 87.2%

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

   9. Simplified 87.2%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - \frac{t}{\frac{z}{y}}\right)\\ \end{array} \]

Alternative 9: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+16)
   (+ x (* t (- 1.0 (/ y z))))
   (if (<= z 8.5e+17) (+ x (/ t (/ (- a z) y))) (- x (* z (/ t (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+16) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 8.5e+17) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (z * (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 <= (-9.2d+16)) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else if (z <= 8.5d+17) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x - (z * (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 <= -9.2e+16) {
		tmp = x + (t * (1.0 - (y / z)));
	} else if (z <= 8.5e+17) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (z * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+16:
		tmp = x + (t * (1.0 - (y / z)))
	elif z <= 8.5e+17:
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x - (z * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+16)
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	elseif (z <= 8.5e+17)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x - Float64(z * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+16)
		tmp = x + (t * (1.0 - (y / z)));
	elseif (z <= 8.5e+17)
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x - (z * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+16], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+17], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2e16

   1. Initial program 73.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 89.7%

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

      1. associate-*r/ 89.7%

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

      2. neg-mul-1 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in y around 0 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   9. Simplified 89.7%

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

   if -9.2e16 < z < 8.5e17

   1. Initial program 94.9%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 87.0%

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

      1. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

   if 8.5e17 < z

   1. Initial program 67.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-/r/ 94.8%

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

   5. Applied egg-rr 94.8%

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

      1. div-inv 94.7%

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

      2. clear-num 95.1%

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

   7. Applied egg-rr 95.1%

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

   8. Taylor expanded in y around 0 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

      3. *-commutative 64.2%

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

      4. associate-*r/ 87.2%

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

   10. Simplified 87.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 10: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0008:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+23}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.0008)
   (+ x (* t (/ y (- a z))))
   (if (<= y 2.1e+23) (- x (* t (/ z (- a z)))) (+ x (/ t (/ (- a z) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.0008) {
		tmp = x + (t * (y / (a - z)));
	} else if (y <= 2.1e+23) {
		tmp = x - (t * (z / (a - z)));
	} else {
		tmp = x + (t / ((a - z) / 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 (y <= (-0.0008d0)) then
        tmp = x + (t * (y / (a - z)))
    else if (y <= 2.1d+23) then
        tmp = x - (t * (z / (a - z)))
    else
        tmp = x + (t / ((a - z) / 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 (y <= -0.0008) {
		tmp = x + (t * (y / (a - z)));
	} else if (y <= 2.1e+23) {
		tmp = x - (t * (z / (a - z)));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.0008:
		tmp = x + (t * (y / (a - z)))
	elif y <= 2.1e+23:
		tmp = x - (t * (z / (a - z)))
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.0008)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (y <= 2.1e+23)
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.0008)
		tmp = x + (t * (y / (a - z)));
	elseif (y <= 2.1e+23)
		tmp = x - (t * (z / (a - z)));
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.0008], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+23], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000038e-4

   1. Initial program 82.7%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 85.3%

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

   if -8.00000000000000038e-4 < y < 2.1000000000000001e23

   1. Initial program 82.7%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

      3. *-commutative 76.8%

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

      4. associate-*l/ 93.2%

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

   6. Simplified 93.2%

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

   if 2.1000000000000001e23 < y

   1. Initial program 86.5%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 79.0%

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

      1. associate-/l* 85.5%

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

   6. Simplified 85.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0008:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+23}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 11: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-176}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5e-176)
   (+ x (* (- y z) (/ t (- a z))))
   (+ x (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5e-176) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5d-176)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else
        tmp = x + (t * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5e-176) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5e-176:
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5e-176)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5e-176)
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = x + (t * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5e-176], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5e-176

   1. Initial program 79.0%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. div-inv 99.8%

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

      2. clear-num 99.8%

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

   7. Applied egg-rr 99.8%

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

   if -5e-176 < x

   1. Initial program 86.3%

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

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-176}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 12: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-175}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.15e-175)
   (+ x (/ (- y z) (/ (- a z) t)))
   (+ x (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.15e-175) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.15d-175)) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = x + (t * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.15e-175) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.15e-175:
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.15e-175)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.15e-175)
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = x + (t * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.15e-175], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e-175

   1. Initial program 79.0%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -1.15e-175 < x

   1. Initial program 86.3%

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

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-175}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 13: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+14) (+ x t) (if (<= z 2.2e+50) (+ x (* t (/ y a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+14) {
		tmp = x + t;
	} else if (z <= 2.2e+50) {
		tmp = x + (t * (y / 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 <= (-8d+14)) then
        tmp = x + t
    else if (z <= 2.2d+50) then
        tmp = x + (t * (y / 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 <= -8e+14) {
		tmp = x + t;
	} else if (z <= 2.2e+50) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+14:
		tmp = x + t
	elif z <= 2.2e+50:
		tmp = x + (t * (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+14)
		tmp = Float64(x + t);
	elseif (z <= 2.2e+50)
		tmp = Float64(x + Float64(t * Float64(y / 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 <= -8e+14)
		tmp = x + t;
	elseif (z <= 2.2e+50)
		tmp = x + (t * (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+14], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.2e+50], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8e14 or 2.20000000000000017e50 < z

   1. Initial program 70.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 77.2%

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

   if -8e14 < z < 2.20000000000000017e50

   1. Initial program 94.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 79.4%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 14: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+15}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+15) (+ x t) (if (<= z 3.2e+54) (+ x (/ t (/ a y))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+15) {
		tmp = x + t;
	} else if (z <= 3.2e+54) {
		tmp = x + (t / (a / y));
	} 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 <= (-1.65d+15)) then
        tmp = x + t
    else if (z <= 3.2d+54) then
        tmp = x + (t / (a / y))
    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 <= -1.65e+15) {
		tmp = x + t;
	} else if (z <= 3.2e+54) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+15:
		tmp = x + t
	elif z <= 3.2e+54:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+15)
		tmp = Float64(x + t);
	elseif (z <= 3.2e+54)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+15)
		tmp = x + t;
	elseif (z <= 3.2e+54)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+15], N[(x + t), $MachinePrecision], If[LessEqual[z, 3.2e+54], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e15 or 3.2e54 < z

   1. Initial program 70.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 77.2%

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

   if -1.65e15 < z < 3.2e54

   1. Initial program 94.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+15}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 15: 95.9% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 83.7%

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

   1. associate-*l/ 97.6%

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

3. Simplified 97.6%

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

   1. associate-/r/ 96.8%

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

5. Applied egg-rr 96.8%

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

   1. div-inv 96.4%

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

   2. clear-num 96.6%

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

7. Applied egg-rr 96.6%

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

8. Final simplification 96.6%

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

Alternative 16: 63.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+125}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.45e+129) x (if (<= a 2e+125) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e+129) {
		tmp = x;
	} else if (a <= 2e+125) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.45d+129)) then
        tmp = x
    else if (a <= 2d+125) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e+129) {
		tmp = x;
	} else if (a <= 2e+125) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.45e+129:
		tmp = x
	elif a <= 2e+125:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.45e+129)
		tmp = x;
	elseif (a <= 2e+125)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.45e+129)
		tmp = x;
	elseif (a <= 2e+125)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.45e+129], x, If[LessEqual[a, 2e+125], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.45e129 or 1.9999999999999998e125 < a

   1. Initial program 82.5%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around inf 68.5%

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

   if -2.45e129 < a < 1.9999999999999998e125

   1. Initial program 84.2%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 61.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+125}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 49.9% 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 83.7%

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

   1. associate-*l/ 97.6%

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

3. Simplified 97.6%

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

4. Taylor expanded in x around inf 46.9%

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

5. Final simplification 46.9%

   \[\leadsto x \]

Developer target: 99.2% 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 2023275 
(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))))