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

Percentage Accurate: 86.0% → 98.3%

Time: 9.8s

Alternatives: 14

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: 86.0% 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: 98.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot t}{a - z} \leq -1 \cdot 10^{-26}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* (- y z) t) (- a z))) -1e-26)
   (+ 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 + (((y - z) * t) / (a - z))) <= -1e-26) {
		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 + (((y - z) * t) / (a - z))) <= (-1d-26)) 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 + (((y - z) * t) / (a - z))) <= -1e-26) {
		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 + (((y - z) * t) / (a - z))) <= -1e-26:
		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 (Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z))) <= -1e-26)
		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 + (((y - z) * t) / (a - z))) <= -1e-26)
		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[N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1e-26], 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 (+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))) < -1e-26

   1. Initial program 84.7%

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

      1. associate-/l* 99.8%

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

      2. clear-num 99.8%

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

      3. associate-/r/ 99.8%

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

      4. clear-num 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -1e-26 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

   1. Initial program 89.7%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot t}{a - z} \leq -1 \cdot 10^{-26}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-15}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{t}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e-15)
   (+ x t)
   (if (<= z 5.2e-85)
     (+ x (/ y (/ a t)))
     (if (<= z 6.5e+95) (+ x (/ t (/ (- z) y))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e-15) {
		tmp = x + t;
	} else if (z <= 5.2e-85) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.5e+95) {
		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 <= (-1.25d-15)) then
        tmp = x + t
    else if (z <= 5.2d-85) then
        tmp = x + (y / (a / t))
    else if (z <= 6.5d+95) 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 <= -1.25e-15) {
		tmp = x + t;
	} else if (z <= 5.2e-85) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.5e+95) {
		tmp = x + (t / (-z / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e-15:
		tmp = x + t
	elif z <= 5.2e-85:
		tmp = x + (y / (a / t))
	elif z <= 6.5e+95:
		tmp = x + (t / (-z / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e-15)
		tmp = Float64(x + t);
	elseif (z <= 5.2e-85)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 6.5e+95)
		tmp = Float64(x + Float64(t / Float64(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 <= -1.25e-15)
		tmp = x + t;
	elseif (z <= 5.2e-85)
		tmp = x + (y / (a / t));
	elseif (z <= 6.5e+95)
		tmp = x + (t / (-z / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e-15], N[(x + t), $MachinePrecision], If[LessEqual[z, 5.2e-85], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+95], N[(x + N[(t / N[((-z) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e-15 or 6.5e95 < z

   1. Initial program 80.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.7%

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

   if -1.25e-15 < z < 5.20000000000000023e-85

   1. Initial program 93.2%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 83.6%

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

      1. associate-*l/ 81.4%

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

      2. associate-/l* 85.5%

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

   7. Applied egg-rr 85.5%

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

   if 5.20000000000000023e-85 < z < 6.5e95

   1. Initial program 92.5%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around inf 76.3%

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

      1. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in a around 0 76.0%

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

      1. neg-mul-1 76.0%

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

      2. distribute-neg-frac 76.0%

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

   10. Simplified 76.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-15}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{t}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-14}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+91}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e-14)
   (+ x t)
   (if (<= z 5.6e-85)
     (+ x (/ y (/ a t)))
     (if (<= z 8e+91) (- x (* y (/ t z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-14) {
		tmp = x + t;
	} else if (z <= 5.6e-85) {
		tmp = x + (y / (a / t));
	} else if (z <= 8e+91) {
		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 <= (-2.2d-14)) then
        tmp = x + t
    else if (z <= 5.6d-85) then
        tmp = x + (y / (a / t))
    else if (z <= 8d+91) 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 <= -2.2e-14) {
		tmp = x + t;
	} else if (z <= 5.6e-85) {
		tmp = x + (y / (a / t));
	} else if (z <= 8e+91) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e-14:
		tmp = x + t
	elif z <= 5.6e-85:
		tmp = x + (y / (a / t))
	elif z <= 8e+91:
		tmp = x - (y * (t / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e-14)
		tmp = Float64(x + t);
	elseif (z <= 5.6e-85)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 8e+91)
		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 <= -2.2e-14)
		tmp = x + t;
	elseif (z <= 5.6e-85)
		tmp = x + (y / (a / t));
	elseif (z <= 8e+91)
		tmp = x - (y * (t / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e-14], N[(x + t), $MachinePrecision], If[LessEqual[z, 5.6e-85], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+91], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e-14 or 8.00000000000000064e91 < z

   1. Initial program 81.2%

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

   5. Taylor expanded in z around inf 83.2%

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

   if -2.2000000000000001e-14 < z < 5.60000000000000033e-85

   1. Initial program 93.2%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 83.6%

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

      1. associate-*l/ 81.4%

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

      2. associate-/l* 85.5%

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

   7. Applied egg-rr 85.5%

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

   if 5.60000000000000033e-85 < z < 8.00000000000000064e91

   1. Initial program 92.1%

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

   5. Taylor expanded in y around inf 74.9%

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

      1. associate-/l* 77.5%

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

      2. associate-/r/ 77.7%

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

   7. Applied egg-rr 77.7%

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

   8. Taylor expanded in a around 0 74.8%

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

      1. associate-*r/ 74.8%

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

      2. neg-mul-1 74.8%

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

   10. Simplified 74.8%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-14}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+91}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-14}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+96}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.32e-14)
   (+ x t)
   (if (<= z 2.55e-85)
     (+ x (/ y (/ a t)))
     (if (<= z 1.3e+96) (- x (/ (* y t) z)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.32e-14) {
		tmp = x + t;
	} else if (z <= 2.55e-85) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.3e+96) {
		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 <= (-1.32d-14)) then
        tmp = x + t
    else if (z <= 2.55d-85) then
        tmp = x + (y / (a / t))
    else if (z <= 1.3d+96) 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 <= -1.32e-14) {
		tmp = x + t;
	} else if (z <= 2.55e-85) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.3e+96) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.32e-14:
		tmp = x + t
	elif z <= 2.55e-85:
		tmp = x + (y / (a / t))
	elif z <= 1.3e+96:
		tmp = x - ((y * t) / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.32e-14)
		tmp = Float64(x + t);
	elseif (z <= 2.55e-85)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.3e+96)
		tmp = Float64(x - Float64(Float64(y * 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 <= -1.32e-14)
		tmp = x + t;
	elseif (z <= 2.55e-85)
		tmp = x + (y / (a / t));
	elseif (z <= 1.3e+96)
		tmp = x - ((y * t) / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.32e-14], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.55e-85], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+96], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32e-14 or 1.3e96 < z

   1. Initial program 80.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.7%

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

   if -1.32e-14 < z < 2.5500000000000001e-85

   1. Initial program 93.2%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 83.6%

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

      1. associate-*l/ 81.4%

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

      2. associate-/l* 85.5%

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

   7. Applied egg-rr 85.5%

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

   if 2.5500000000000001e-85 < z < 1.3e96

   1. Initial program 92.5%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around inf 76.3%

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

   6. Taylor expanded in a around 0 76.1%

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

      1. associate-*r/ 76.1%

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

      2. mul-1-neg 76.1%

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

      3. distribute-rgt-neg-out 76.1%

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

   8. Simplified 76.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-14}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+96}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+125} \lor \neg \left(z \leq 1.02 \cdot 10^{+93}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e+125) (not (<= z 1.02e+93)))
   (+ x t)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e+125) || !(z <= 1.02e+93)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6d+125)) .or. (.not. (z <= 1.02d+93))) then
        tmp = x + t
    else
        tmp = x + (y * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e+125) || !(z <= 1.02e+93)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6e+125) or not (z <= 1.02e+93):
		tmp = x + t
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e+125) || !(z <= 1.02e+93))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6e+125) || ~((z <= 1.02e+93)))
		tmp = x + t;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e+125], N[Not[LessEqual[z, 1.02e+93]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000003e125 or 1.0200000000000001e93 < z

   1. Initial program 78.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 88.9%

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

   if -6.0000000000000003e125 < z < 1.0200000000000001e93

   1. Initial program 92.4%

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

   5. Taylor expanded in y around inf 84.1%

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

      1. associate-/l* 85.8%

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

      2. associate-/r/ 88.6%

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

   7. Applied egg-rr 88.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+125} \lor \neg \left(z \leq 1.02 \cdot 10^{+93}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+37} \lor \neg \left(z \leq 4.7 \cdot 10^{+91}\right):\\ \;\;\;\;x - z \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- a z))))
   (if (or (<= z -1.1e+37) (not (<= z 4.7e+91)))
     (- x (* z t_1))
     (+ x (* y t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a - z);
	double tmp;
	if ((z <= -1.1e+37) || !(z <= 4.7e+91)) {
		tmp = x - (z * t_1);
	} else {
		tmp = x + (y * 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 = t / (a - z)
    if ((z <= (-1.1d+37)) .or. (.not. (z <= 4.7d+91))) then
        tmp = x - (z * t_1)
    else
        tmp = x + (y * 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 = t / (a - z);
	double tmp;
	if ((z <= -1.1e+37) || !(z <= 4.7e+91)) {
		tmp = x - (z * t_1);
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a - z)
	tmp = 0
	if (z <= -1.1e+37) or not (z <= 4.7e+91):
		tmp = x - (z * t_1)
	else:
		tmp = x + (y * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a - z))
	tmp = 0.0
	if ((z <= -1.1e+37) || !(z <= 4.7e+91))
		tmp = Float64(x - Float64(z * t_1));
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a - z);
	tmp = 0.0;
	if ((z <= -1.1e+37) || ~((z <= 4.7e+91)))
		tmp = x - (z * t_1);
	else
		tmp = x + (y * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.1e+37], N[Not[LessEqual[z, 4.7e+91]], $MachinePrecision]], N[(x - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e37 or 4.6999999999999997e91 < z

   1. Initial program 80.0%

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

   5. Taylor expanded in y around 0 91.8%

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

      1. neg-mul-1 91.8%

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

      2. distribute-neg-frac 91.8%

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

   7. Simplified 91.8%

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

   8. Taylor expanded in x around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

      3. associate-/l* 91.7%

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

      4. associate-/r/ 87.9%

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

   10. Simplified 87.9%

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

   if -1.1e37 < z < 4.6999999999999997e91

   1. Initial program 93.2%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around inf 86.8%

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

      1. associate-/l* 87.9%

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

      2. associate-/r/ 91.0%

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

   7. Applied egg-rr 91.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+37} \lor \neg \left(z \leq 4.7 \cdot 10^{+91}\right):\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+36}:\\ \;\;\;\;x - z \cdot t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(\frac{y}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- a z))))
   (if (<= z -2.15e+36)
     (- x (* z t_1))
     (if (<= z 5.6e-85) (+ x (* y t_1)) (- x (* t (+ (/ y z) -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a - z);
	double tmp;
	if (z <= -2.15e+36) {
		tmp = x - (z * t_1);
	} else if (z <= 5.6e-85) {
		tmp = x + (y * t_1);
	} else {
		tmp = x - (t * ((y / z) + -1.0));
	}
	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 = t / (a - z)
    if (z <= (-2.15d+36)) then
        tmp = x - (z * t_1)
    else if (z <= 5.6d-85) then
        tmp = x + (y * t_1)
    else
        tmp = x - (t * ((y / z) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a - z);
	double tmp;
	if (z <= -2.15e+36) {
		tmp = x - (z * t_1);
	} else if (z <= 5.6e-85) {
		tmp = x + (y * t_1);
	} else {
		tmp = x - (t * ((y / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a - z)
	tmp = 0
	if z <= -2.15e+36:
		tmp = x - (z * t_1)
	elif z <= 5.6e-85:
		tmp = x + (y * t_1)
	else:
		tmp = x - (t * ((y / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a - z))
	tmp = 0.0
	if (z <= -2.15e+36)
		tmp = Float64(x - Float64(z * t_1));
	elseif (z <= 5.6e-85)
		tmp = Float64(x + Float64(y * t_1));
	else
		tmp = Float64(x - Float64(t * Float64(Float64(y / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a - z);
	tmp = 0.0;
	if (z <= -2.15e+36)
		tmp = x - (z * t_1);
	elseif (z <= 5.6e-85)
		tmp = x + (y * t_1);
	else
		tmp = x - (t * ((y / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+36], N[(x - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-85], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15000000000000002e36

   1. Initial program 86.7%

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

   5. Taylor expanded in y around 0 91.5%

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

      1. neg-mul-1 91.5%

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

      2. distribute-neg-frac 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in x around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

      3. associate-/l* 91.5%

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

      4. associate-/r/ 85.2%

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

   10. Simplified 85.2%

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

   if -2.15000000000000002e36 < z < 5.60000000000000033e-85

   1. Initial program 93.6%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around inf 90.3%

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

      1. associate-/l* 91.0%

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

      2. associate-/r/ 95.0%

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

   7. Applied egg-rr 95.0%

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

   if 5.60000000000000033e-85 < z

   1. Initial program 80.6%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in a around 0 92.1%

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

      1. mul-1-neg 92.1%

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

      2. div-sub 92.1%

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

      3. sub-neg 92.1%

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

      4. *-inverses 92.1%

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

      5. metadata-eval 92.1%

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

   7. Simplified 92.1%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{y}{z} + -1\right)\right)} \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+36}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(\frac{y}{z} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(\frac{y}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+36)
   (- x (* t (/ z (- a z))))
   (if (<= z 5.6e-85) (+ x (* y (/ t (- a z)))) (- x (* t (+ (/ y z) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+36) {
		tmp = x - (t * (z / (a - z)));
	} else if (z <= 5.6e-85) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x - (t * ((y / z) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+36)) then
        tmp = x - (t * (z / (a - z)))
    else if (z <= 5.6d-85) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x - (t * ((y / z) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+36) {
		tmp = x - (t * (z / (a - z)));
	} else if (z <= 5.6e-85) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x - (t * ((y / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+36:
		tmp = x - (t * (z / (a - z)))
	elif z <= 5.6e-85:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x - (t * ((y / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+36)
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	elseif (z <= 5.6e-85)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t * Float64(Float64(y / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+36)
		tmp = x - (t * (z / (a - z)));
	elseif (z <= 5.6e-85)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x - (t * ((y / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+36], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-85], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000003e36

   1. Initial program 86.7%

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

   5. Taylor expanded in y around 0 91.5%

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

      1. neg-mul-1 91.5%

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

      2. distribute-neg-frac 91.5%

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

   7. Simplified 91.5%

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

   if -5.2000000000000003e36 < z < 5.60000000000000033e-85

   1. Initial program 93.6%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around inf 90.3%

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

      1. associate-/l* 91.0%

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

      2. associate-/r/ 95.0%

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

   7. Applied egg-rr 95.0%

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

   if 5.60000000000000033e-85 < z

   1. Initial program 80.6%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in a around 0 92.1%

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

      1. mul-1-neg 92.1%

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

      2. div-sub 92.1%

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

      3. sub-neg 92.1%

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

      4. *-inverses 92.1%

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

      5. metadata-eval 92.1%

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

   7. Simplified 92.1%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{y}{z} + -1\right)\right)} \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(\frac{y}{z} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-16} \lor \neg \left(z \leq 5.6 \cdot 10^{-85}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e-16) (not (<= z 5.6e-85))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-16) || !(z <= 5.6e-85)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.2d-16)) .or. (.not. (z <= 5.6d-85))) then
        tmp = x + t
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-16) || !(z <= 5.6e-85)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e-16) or not (z <= 5.6e-85):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e-16) || !(z <= 5.6e-85))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e-16) || ~((z <= 5.6e-85)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e-16], N[Not[LessEqual[z, 5.6e-85]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999965e-16 or 5.60000000000000033e-85 < z

   1. Initial program 83.9%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 76.4%

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

   if -7.19999999999999965e-16 < z < 5.60000000000000033e-85

   1. Initial program 93.2%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 83.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-16} \lor \neg \left(z \leq 5.6 \cdot 10^{-85}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-15} \lor \neg \left(z \leq 5.6 \cdot 10^{-85}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e-15) (not (<= z 5.6e-85))) (+ x t) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e-15) || !(z <= 5.6e-85)) {
		tmp = x + t;
	} 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 <= (-3.6d-15)) .or. (.not. (z <= 5.6d-85))) then
        tmp = x + t
    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 <= -3.6e-15) || !(z <= 5.6e-85)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e-15) or not (z <= 5.6e-85):
		tmp = x + t
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e-15) || !(z <= 5.6e-85))
		tmp = Float64(x + t);
	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 <= -3.6e-15) || ~((z <= 5.6e-85)))
		tmp = x + t;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e-15], N[Not[LessEqual[z, 5.6e-85]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6000000000000001e-15 or 5.60000000000000033e-85 < z

   1. Initial program 83.9%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 76.4%

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

   if -3.6000000000000001e-15 < z < 5.60000000000000033e-85

   1. Initial program 93.2%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 81.4%

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

      1. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-15} \lor \neg \left(z \leq 5.6 \cdot 10^{-85}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-14} \lor \neg \left(z \leq 5.6 \cdot 10^{-85}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e-14) (not (<= z 5.6e-85))) (+ x t) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e-14) || !(z <= 5.6e-85)) {
		tmp = x + t;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.65d-14)) .or. (.not. (z <= 5.6d-85))) then
        tmp = x + t
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e-14) || !(z <= 5.6e-85)) {
		tmp = x + t;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e-14) or not (z <= 5.6e-85):
		tmp = x + t
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e-14) || !(z <= 5.6e-85))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e-14) || ~((z <= 5.6e-85)))
		tmp = x + t;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e-14], N[Not[LessEqual[z, 5.6e-85]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e-14 or 5.60000000000000033e-85 < z

   1. Initial program 83.9%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 76.4%

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

   if -1.6499999999999999e-14 < z < 5.60000000000000033e-85

   1. Initial program 93.2%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 83.6%

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

      1. associate-*l/ 81.4%

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

      2. associate-/l* 85.5%

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

   7. Applied egg-rr 85.5%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-14} \lor \neg \left(z \leq 5.6 \cdot 10^{-85}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-16} \lor \neg \left(z \leq 8.2 \cdot 10^{-63}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e-16) (not (<= z 8.2e-63))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e-16) || !(z <= 8.2e-63)) {
		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 ((z <= (-4.4d-16)) .or. (.not. (z <= 8.2d-63))) 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 ((z <= -4.4e-16) || !(z <= 8.2e-63)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e-16) or not (z <= 8.2e-63):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e-16) || !(z <= 8.2e-63))
		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 ((z <= -4.4e-16) || ~((z <= 8.2e-63)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e-16], N[Not[LessEqual[z, 8.2e-63]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000001e-16 or 8.1999999999999995e-63 < z

   1. Initial program 83.2%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 78.2%

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

   if -4.40000000000000001e-16 < z < 8.1999999999999995e-63

   1. Initial program 93.5%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in z around 0 78.9%

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

      1. associate-/l* 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in x around inf 50.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-16} \lor \neg \left(z \leq 8.2 \cdot 10^{-63}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.8% 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 87.9%

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

   1. associate-/l* 96.3%

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

   2. clear-num 96.3%

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

   3. associate-/r/ 96.3%

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

   4. clear-num 96.8%

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

4. Applied egg-rr 96.8%

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

5. Final simplification 96.8%

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

Alternative 14: 51.7% 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 87.9%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

5. Taylor expanded in z around 0 61.0%

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

   1. associate-/l* 62.2%

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

7. Simplified 62.2%

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

8. Taylor expanded in x around inf 53.2%

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

9. Final simplification 53.2%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 99.1% accurate, 0.5× 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 2024020 
(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))))