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

Percentage Accurate: 85.7% → 95.8%

Time: 11.6s

Alternatives: 18

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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) / Float64(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[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.8%

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

   1. associate-/l* 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 77.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+16}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 550000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+214}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.75e+16)
   (+ x t)
   (if (<= z 550000000000.0)
     (+ x (* y (/ t a)))
     (if (<= z 6.3e+214) (- x (* y (/ t z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.75e+16) {
		tmp = x + t;
	} else if (z <= 550000000000.0) {
		tmp = x + (y * (t / a));
	} else if (z <= 6.3e+214) {
		tmp = x - (y * (t / 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 (z <= (-2.75d+16)) then
        tmp = x + t
    else if (z <= 550000000000.0d0) then
        tmp = x + (y * (t / a))
    else if (z <= 6.3d+214) then
        tmp = x - (y * (t / 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 (z <= -2.75e+16) {
		tmp = x + t;
	} else if (z <= 550000000000.0) {
		tmp = x + (y * (t / a));
	} else if (z <= 6.3e+214) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.75e+16:
		tmp = x + t
	elif z <= 550000000000.0:
		tmp = x + (y * (t / a))
	elif z <= 6.3e+214:
		tmp = x - (y * (t / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.75e+16)
		tmp = Float64(x + t);
	elseif (z <= 550000000000.0)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 6.3e+214)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.75e+16)
		tmp = x + t;
	elseif (z <= 550000000000.0)
		tmp = x + (y * (t / a));
	elseif (z <= 6.3e+214)
		tmp = x - (y * (t / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.75e+16], N[(x + t), $MachinePrecision], If[LessEqual[z, 550000000000.0], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.3e+214], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.75e16 or 6.3e214 < z

   1. Initial program 70.3%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 77.0%

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

   if -2.75e16 < z < 5.5e11

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around 0 80.0%

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

      1. associate-*r/ 87.1%

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

   8. Simplified 87.1%

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

   if 5.5e11 < z < 6.3e214

   1. Initial program 88.1%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in y around inf 70.6%

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

      1. associate-/l* 76.0%

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

      2. associate-/r/ 80.0%

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

   6. Simplified 80.0%

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

   7. Taylor expanded in a around 0 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. associate-*r/ 73.6%

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

   9. Simplified 73.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+16}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 550000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+214}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3: 77.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+214}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+15)
   (+ x t)
   (if (<= z 1.25e+15)
     (+ x (* y (/ t a)))
     (if (<= z 8.5e+214) (- x (/ t (/ z y))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+15) {
		tmp = x + t;
	} else if (z <= 1.25e+15) {
		tmp = x + (y * (t / a));
	} else if (z <= 8.5e+214) {
		tmp = x - (t / (z / 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 <= (-3.8d+15)) then
        tmp = x + t
    else if (z <= 1.25d+15) then
        tmp = x + (y * (t / a))
    else if (z <= 8.5d+214) then
        tmp = x - (t / (z / 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 <= -3.8e+15) {
		tmp = x + t;
	} else if (z <= 1.25e+15) {
		tmp = x + (y * (t / a));
	} else if (z <= 8.5e+214) {
		tmp = x - (t / (z / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+15:
		tmp = x + t
	elif z <= 1.25e+15:
		tmp = x + (y * (t / a))
	elif z <= 8.5e+214:
		tmp = x - (t / (z / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+15)
		tmp = Float64(x + t);
	elseif (z <= 1.25e+15)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 8.5e+214)
		tmp = Float64(x - Float64(t / Float64(z / 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 <= -3.8e+15)
		tmp = x + t;
	elseif (z <= 1.25e+15)
		tmp = x + (y * (t / a));
	elseif (z <= 8.5e+214)
		tmp = x - (t / (z / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+15], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.25e+15], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+214], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e15 or 8.50000000000000045e214 < z

   1. Initial program 70.3%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 77.0%

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

   if -3.8e15 < z < 1.25e15

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around 0 80.0%

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

      1. associate-*r/ 87.1%

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

   8. Simplified 87.1%

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

   if 1.25e15 < z < 8.50000000000000045e214

   1. Initial program 88.1%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in a around 0 73.6%

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

      1. +-commutative 73.6%

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

      2. mul-1-neg 73.6%

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

      3. unsub-neg 73.6%

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

      4. associate-/l* 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in z around 0 75.3%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+214}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4: 77.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -95000000000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7200:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+216}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -95000000000000.0)
   (+ x t)
   (if (<= z 7200.0)
     (+ x (* y (/ t a)))
     (if (<= z 1.1e+216) (- x (* t (/ y z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -95000000000000.0) {
		tmp = x + t;
	} else if (z <= 7200.0) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.1e+216) {
		tmp = x - (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 (z <= (-95000000000000.0d0)) then
        tmp = x + t
    else if (z <= 7200.0d0) then
        tmp = x + (y * (t / a))
    else if (z <= 1.1d+216) then
        tmp = x - (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 (z <= -95000000000000.0) {
		tmp = x + t;
	} else if (z <= 7200.0) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.1e+216) {
		tmp = x - (t * (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -95000000000000.0:
		tmp = x + t
	elif z <= 7200.0:
		tmp = x + (y * (t / a))
	elif z <= 1.1e+216:
		tmp = x - (t * (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -95000000000000.0)
		tmp = Float64(x + t);
	elseif (z <= 7200.0)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.1e+216)
		tmp = Float64(x - Float64(t * 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 (z <= -95000000000000.0)
		tmp = x + t;
	elseif (z <= 7200.0)
		tmp = x + (y * (t / a));
	elseif (z <= 1.1e+216)
		tmp = x - (t * (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -95000000000000.0], N[(x + t), $MachinePrecision], If[LessEqual[z, 7200.0], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+216], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5e13 or 1.1e216 < z

   1. Initial program 70.3%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 77.0%

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

   if -9.5e13 < z < 7200

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around 0 80.0%

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

      1. associate-*r/ 87.1%

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

   8. Simplified 87.1%

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

   if 7200 < z < 1.1e216

   1. Initial program 88.1%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in y around inf 70.6%

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

      1. associate-/l* 76.0%

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

      2. associate-/r/ 80.0%

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

   6. Simplified 80.0%

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

   7. Taylor expanded in a around 0 75.3%

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

      1. associate-*r/ 75.3%

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

      2. neg-mul-1 75.3%

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

   9. Simplified 75.3%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -95000000000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7200:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+216}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 5: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+20} \lor \neg \left(z \leq 13500000000\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+20) (not (<= z 13500000000.0)))
   (+ x (- t (* y (/ t z))))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+20) || !(z <= 13500000000.0)) {
		tmp = x + (t - (y * (t / 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 <= (-1.85d+20)) .or. (.not. (z <= 13500000000.0d0))) then
        tmp = x + (t - (y * (t / 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 <= -1.85e+20) || !(z <= 13500000000.0)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+20) or not (z <= 13500000000.0):
		tmp = x + (t - (y * (t / z)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+20) || !(z <= 13500000000.0))
		tmp = Float64(x + Float64(t - Float64(y * Float64(t / 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 <= -1.85e+20) || ~((z <= 13500000000.0)))
		tmp = x + (t - (y * (t / z)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+20], N[Not[LessEqual[z, 13500000000.0]], $MachinePrecision]], N[(x + N[(t - N[(y * N[(t / 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 < -1.85e20 or 1.35e10 < z

   1. Initial program 75.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in a around 0 86.1%

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

      1. neg-mul-1 86.1%

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

      2. distribute-neg-frac 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in y around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-*r/ 87.5%

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

   9. Simplified 87.5%

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

   if -1.85e20 < z < 1.35e10

   1. Initial program 92.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 86.6%

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

      1. associate-/l* 94.5%

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

      2. associate-/r/ 91.4%

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

   6. Simplified 91.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+20} \lor \neg \left(z \leq 13500000000\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 6: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.19 \lor \neg \left(z \leq 4.2 \cdot 10^{+15}\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.19) (not (<= z 4.2e+15)))
   (+ x (- t (* y (/ t z))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.19) || !(z <= 4.2e+15)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (y / ((a - z) / 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 <= (-0.19d0)) .or. (.not. (z <= 4.2d+15))) then
        tmp = x + (t - (y * (t / z)))
    else
        tmp = x + (y / ((a - z) / 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 <= -0.19) || !(z <= 4.2e+15)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.19) or not (z <= 4.2e+15):
		tmp = x + (t - (y * (t / z)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.19) || !(z <= 4.2e+15))
		tmp = Float64(x + Float64(t - Float64(y * Float64(t / z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.19) || ~((z <= 4.2e+15)))
		tmp = x + (t - (y * (t / z)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.19], N[Not[LessEqual[z, 4.2e+15]], $MachinePrecision]], N[(x + N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.19 or 4.2e15 < z

   1. Initial program 75.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in a around 0 86.1%

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

      1. neg-mul-1 86.1%

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

      2. distribute-neg-frac 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in y around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-*r/ 87.5%

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

   9. Simplified 87.5%

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

   if -0.19 < z < 4.2e15

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 86.6%

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

      1. associate-/l* 94.5%

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

   8. Simplified 94.5%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.19 \lor \neg \left(z \leq 4.2 \cdot 10^{+15}\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 7: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+20} \lor \neg \left(z \leq 2.65 \cdot 10^{+17}\right):\\ \;\;\;\;x + \left(t - \frac{y}{\frac{z}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+20) (not (<= z 2.65e+17)))
   (+ x (- t (/ y (/ z t))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+20) || !(z <= 2.65e+17)) {
		tmp = x + (t - (y / (z / t)));
	} else {
		tmp = x + (y / ((a - z) / 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 <= (-2.1d+20)) .or. (.not. (z <= 2.65d+17))) then
        tmp = x + (t - (y / (z / t)))
    else
        tmp = x + (y / ((a - z) / 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 <= -2.1e+20) || !(z <= 2.65e+17)) {
		tmp = x + (t - (y / (z / t)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+20) or not (z <= 2.65e+17):
		tmp = x + (t - (y / (z / t)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+20) || !(z <= 2.65e+17))
		tmp = Float64(x + Float64(t - Float64(y / Float64(z / t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e+20) || ~((z <= 2.65e+17)))
		tmp = x + (t - (y / (z / t)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+20], N[Not[LessEqual[z, 2.65e+17]], $MachinePrecision]], N[(x + N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e20 or 2.65e17 < z

   1. Initial program 75.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in a around 0 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

      4. associate-/l* 88.3%

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

   6. Simplified 88.3%

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

   7. Taylor expanded in z around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-/l* 87.6%

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

   9. Simplified 87.6%

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

   if -2.1e20 < z < 2.65e17

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 86.6%

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

      1. associate-/l* 94.5%

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

   8. Simplified 94.5%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+20} \lor \neg \left(z \leq 2.65 \cdot 10^{+17}\right):\\ \;\;\;\;x + \left(t - \frac{y}{\frac{z}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 8: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - z}{t}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+25} \lor \neg \left(y \leq 1.46 \cdot 10^{-80}\right):\\ \;\;\;\;x + \frac{y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- a z) t)))
   (if (or (<= y -1.25e+25) (not (<= y 1.46e-80)))
     (+ x (/ y t_1))
     (- x (/ z t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - z) / t;
	double tmp;
	if ((y <= -1.25e+25) || !(y <= 1.46e-80)) {
		tmp = x + (y / t_1);
	} else {
		tmp = x - (z / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - z) / t
    if ((y <= (-1.25d+25)) .or. (.not. (y <= 1.46d-80))) then
        tmp = x + (y / t_1)
    else
        tmp = x - (z / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - z) / t;
	double tmp;
	if ((y <= -1.25e+25) || !(y <= 1.46e-80)) {
		tmp = x + (y / t_1);
	} else {
		tmp = x - (z / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a - z) / t
	tmp = 0
	if (y <= -1.25e+25) or not (y <= 1.46e-80):
		tmp = x + (y / t_1)
	else:
		tmp = x - (z / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a - z) / t)
	tmp = 0.0
	if ((y <= -1.25e+25) || !(y <= 1.46e-80))
		tmp = Float64(x + Float64(y / t_1));
	else
		tmp = Float64(x - Float64(z / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a - z) / t;
	tmp = 0.0;
	if ((y <= -1.25e+25) || ~((y <= 1.46e-80)))
		tmp = x + (y / t_1);
	else
		tmp = x - (z / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]}, If[Or[LessEqual[y, -1.25e+25], N[Not[LessEqual[y, 1.46e-80]], $MachinePrecision]], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000006e25 or 1.46e-80 < y

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-*r/ 97.8%

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

      3. fma-def 97.8%

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

   3. Simplified 97.8%

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

      1. fma-udef 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in y around inf 80.1%

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

      1. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

   if -1.25000000000000006e25 < y < 1.46e-80

   1. Initial program 88.6%

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

      1. associate-*l/ 88.6%

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

      2. clear-num 88.5%

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

   5. Applied egg-rr 88.5%

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

   6. Taylor expanded in y around 0 84.6%

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

      1. fma-def 84.6%

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

      2. *-commutative 84.6%

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

      3. fma-def 84.6%

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

      4. neg-mul-1 84.6%

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

      5. +-commutative 84.6%

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

      6. sub-neg 84.6%

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

      7. associate-/l* 94.4%

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

   8. Simplified 94.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+25} \lor \neg \left(y \leq 1.46 \cdot 10^{-80}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 9: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+14} \lor \neg \left(y \leq 1.55 \cdot 10^{-80}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.2e+14) (not (<= y 1.55e-80)))
   (+ x (/ y (/ (- a z) t)))
   (- x (* z (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.2e+14) || !(y <= 1.55e-80)) {
		tmp = x + (y / ((a - z) / t));
	} 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 ((y <= (-7.2d+14)) .or. (.not. (y <= 1.55d-80))) then
        tmp = x + (y / ((a - z) / t))
    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 ((y <= -7.2e+14) || !(y <= 1.55e-80)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (z * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7.2e+14) or not (y <= 1.55e-80):
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x - (z * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7.2e+14) || !(y <= 1.55e-80))
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	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 ((y <= -7.2e+14) || ~((y <= 1.55e-80)))
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x - (z * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7.2e+14], N[Not[LessEqual[y, 1.55e-80]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e14 or 1.55000000000000008e-80 < y

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-*r/ 97.8%

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

      3. fma-def 97.8%

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

   3. Simplified 97.8%

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

      1. fma-udef 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in y around inf 80.1%

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

      1. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

   if -7.2e14 < y < 1.55000000000000008e-80

   1. Initial program 88.6%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. *-commutative 84.6%

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

      3. associate-*r/ 94.4%

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

      4. *-commutative 94.4%

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

      5. distribute-rgt-neg-in 94.4%

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

   6. Simplified 94.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+14} \lor \neg \left(y \leq 1.55 \cdot 10^{-80}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 10: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+20} \lor \neg \left(y \leq 8 \cdot 10^{-81}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.45e+20) (not (<= y 8e-81)))
   (+ x (/ y (/ (- a z) t)))
   (- x (/ t (/ (- a z) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.45e+20) || !(y <= 8e-81)) {
		tmp = x + (y / ((a - z) / t));
	} 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 <= (-1.45d+20)) .or. (.not. (y <= 8d-81))) then
        tmp = x + (y / ((a - z) / t))
    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 <= -1.45e+20) || !(y <= 8e-81)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t / ((a - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.45e+20) or not (y <= 8e-81):
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x - (t / ((a - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.45e+20) || !(y <= 8e-81))
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	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 <= -1.45e+20) || ~((y <= 8e-81)))
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x - (t / ((a - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.45e+20], N[Not[LessEqual[y, 8e-81]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $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 < -1.45e20 or 7.9999999999999997e-81 < y

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-*r/ 97.8%

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

      3. fma-def 97.8%

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

   3. Simplified 97.8%

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

      1. fma-udef 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in y around inf 80.1%

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

      1. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

   if -1.45e20 < y < 7.9999999999999997e-81

   1. Initial program 88.6%

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

      1. +-commutative 88.6%

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

      2. associate-*r/ 99.0%

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

      3. fma-def 99.0%

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

   3. Simplified 99.0%

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

      1. fma-udef 99.0%

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

   5. Applied egg-rr 99.0%

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

   6. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. associate-/l* 95.3%

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

   8. Simplified 95.3%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+20} \lor \neg \left(y \leq 8 \cdot 10^{-81}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \end{array} \]

Alternative 11: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+181}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+214}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+181)
   (+ x t)
   (if (<= z 7.4e+214) (+ x (* t (/ y (- a z)))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+181) {
		tmp = x + t;
	} else if (z <= 7.4e+214) {
		tmp = x + (t * (y / (a - 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 (z <= (-9d+181)) then
        tmp = x + t
    else if (z <= 7.4d+214) then
        tmp = x + (t * (y / (a - 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 (z <= -9e+181) {
		tmp = x + t;
	} else if (z <= 7.4e+214) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+181:
		tmp = x + t
	elif z <= 7.4e+214:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+181)
		tmp = Float64(x + t);
	elseif (z <= 7.4e+214)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e+181)
		tmp = x + t;
	elseif (z <= 7.4e+214)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+181], N[(x + t), $MachinePrecision], If[LessEqual[z, 7.4e+214], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9e181 or 7.39999999999999962e214 < z

   1. Initial program 51.5%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in z around inf 89.6%

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

   if -9e181 < z < 7.39999999999999962e214

   1. Initial program 91.8%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around inf 79.8%

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

      1. associate-/l* 85.7%

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

      2. associate-/r/ 84.6%

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

   6. Simplified 84.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+181}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+214}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 12: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;x + \left(t - \frac{y}{\frac{z}{t}}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+17)
   (+ x (- t (/ y (/ z t))))
   (if (<= z 2.8e+17) (+ x (/ y (/ (- a z) t))) (- x (/ t (/ z (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+17) {
		tmp = x + (t - (y / (z / t)));
	} else if (z <= 2.8e+17) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t / (z / (y - 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 <= (-2.4d+17)) then
        tmp = x + (t - (y / (z / t)))
    else if (z <= 2.8d+17) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x - (t / (z / (y - 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 <= -2.4e+17) {
		tmp = x + (t - (y / (z / t)));
	} else if (z <= 2.8e+17) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t / (z / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+17:
		tmp = x + (t - (y / (z / t)))
	elif z <= 2.8e+17:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x - (t / (z / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+17)
		tmp = Float64(x + Float64(t - Float64(y / Float64(z / t))));
	elseif (z <= 2.8e+17)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x - Float64(t / Float64(z / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+17)
		tmp = x + (t - (y / (z / t)));
	elseif (z <= 2.8e+17)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x - (t / (z / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+17], N[(x + N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+17], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e17

   1. Initial program 78.4%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

      4. associate-/l* 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

      4. associate-/l* 89.6%

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

   9. Simplified 89.6%

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

   if -2.4e17 < z < 2.8e17

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 86.6%

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

      1. associate-/l* 94.5%

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

   8. Simplified 94.5%

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

   if 2.8e17 < z

   1. Initial program 73.1%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in a around 0 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. associate-/l* 87.0%

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

   6. Simplified 87.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;x + \left(t - \frac{y}{\frac{z}{t}}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 13: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+257} \lor \neg \left(y \leq 3.5 \cdot 10^{+195}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.12e+257) (not (<= y 3.5e+195))) (* t (/ (- y z) a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.12e+257) || !(y <= 3.5e+195)) {
		tmp = t * ((y - z) / 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 ((y <= (-1.12d+257)) .or. (.not. (y <= 3.5d+195))) then
        tmp = t * ((y - z) / 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 ((y <= -1.12e+257) || !(y <= 3.5e+195)) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.12e+257) or not (y <= 3.5e+195):
		tmp = t * ((y - z) / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.12e+257) || !(y <= 3.5e+195))
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.12e+257) || ~((y <= 3.5e+195)))
		tmp = t * ((y - z) / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.12e+257], N[Not[LessEqual[y, 3.5e+195]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.11999999999999995e257 or 3.5000000000000002e195 < y

   1. Initial program 76.0%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around inf 61.4%

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

   5. Taylor expanded in t around inf 55.7%

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

      1. div-sub 55.7%

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

   7. Simplified 55.7%

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

   if -1.11999999999999995e257 < y < 3.5000000000000002e195

   1. Initial program 84.9%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 63.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+257} \lor \neg \left(y \leq 3.5 \cdot 10^{+195}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 14: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -32500000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -32500000.0)
   (+ x t)
   (if (<= z 1.45e+17) (+ x (* t (/ y a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -32500000.0) {
		tmp = x + t;
	} else if (z <= 1.45e+17) {
		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 <= (-32500000.0d0)) then
        tmp = x + t
    else if (z <= 1.45d+17) 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 <= -32500000.0) {
		tmp = x + t;
	} else if (z <= 1.45e+17) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -32500000.0:
		tmp = x + t
	elif z <= 1.45e+17:
		tmp = x + (t * (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -32500000.0)
		tmp = Float64(x + t);
	elseif (z <= 1.45e+17)
		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 <= -32500000.0)
		tmp = x + t;
	elseif (z <= 1.45e+17)
		tmp = x + (t * (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -32500000.0], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.45e+17], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.25e7 or 1.45e17 < z

   1. Initial program 75.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around inf 69.9%

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

   if -3.25e7 < z < 1.45e17

   1. Initial program 92.0%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around 0 87.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -32500000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 15: 78.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.55e+23) (+ x t) (if (<= z 1.9e+17) (+ x (* y (/ t a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.55e+23) {
		tmp = x + t;
	} else if (z <= 1.9e+17) {
		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 <= (-2.55d+23)) then
        tmp = x + t
    else if (z <= 1.9d+17) 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 <= -2.55e+23) {
		tmp = x + t;
	} else if (z <= 1.9e+17) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.55e+23:
		tmp = x + t
	elif z <= 1.9e+17:
		tmp = x + (y * (t / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.55e+23)
		tmp = Float64(x + t);
	elseif (z <= 1.9e+17)
		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 <= -2.55e+23)
		tmp = x + t;
	elseif (z <= 1.9e+17)
		tmp = x + (y * (t / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.55e+23], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.9e+17], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5500000000000001e23 or 1.9e17 < z

   1. Initial program 75.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around inf 69.9%

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

   if -2.5500000000000001e23 < z < 1.9e17

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around 0 80.0%

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

      1. associate-*r/ 87.1%

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

   8. Simplified 87.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 16: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
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. Final simplification 98.4%

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

Alternative 17: 65.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e-57) (+ x t) (if (<= z 1.28e-61) x (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e-57) {
		tmp = x + t;
	} else if (z <= 1.28e-61) {
		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 <= (-4.2d-57)) then
        tmp = x + t
    else if (z <= 1.28d-61) 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 <= -4.2e-57) {
		tmp = x + t;
	} else if (z <= 1.28e-61) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e-57:
		tmp = x + t
	elif z <= 1.28e-61:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e-57)
		tmp = Float64(x + t);
	elseif (z <= 1.28e-61)
		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 <= -4.2e-57)
		tmp = x + t;
	elseif (z <= 1.28e-61)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e-57], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.28e-61], x, N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999999e-57 or 1.28000000000000009e-61 < z

   1. Initial program 79.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 68.9%

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

   if -4.1999999999999999e-57 < z < 1.28000000000000009e-61

   1. Initial program 91.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 54.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 18: 52.1% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. associate-/l* 98.4%

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

3. Simplified 98.4%

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

4. Taylor expanded in x around inf 51.7%

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

5. Final simplification 51.7%

   \[\leadsto x \]

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 2023195 
(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))))