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

Percentage Accurate: 85.4% → 96.0%

Time: 7.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% 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: 96.0% 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 83.7%

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

5. Final simplification 98.6%

   \[\leadsto x + \frac{y - z}{\frac{a - z}{t}} \]
6. Add Preprocessing

Alternative 2: 81.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+84}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-217}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 30000:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+84)
   (+ x t)
   (if (<= z -2.9e-217)
     (+ x (* t (/ y (- a z))))
     (if (<= z 30000.0) (+ x (/ (* (- y z) t) a)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+84) {
		tmp = x + t;
	} else if (z <= -2.9e-217) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= 30000.0) {
		tmp = x + (((y - z) * t) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+84)) then
        tmp = x + t
    else if (z <= (-2.9d-217)) then
        tmp = x + (t * (y / (a - z)))
    else if (z <= 30000.0d0) then
        tmp = x + (((y - z) * t) / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+84) {
		tmp = x + t;
	} else if (z <= -2.9e-217) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= 30000.0) {
		tmp = x + (((y - z) * t) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+84:
		tmp = x + t
	elif z <= -2.9e-217:
		tmp = x + (t * (y / (a - z)))
	elif z <= 30000.0:
		tmp = x + (((y - z) * t) / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+84)
		tmp = Float64(x + t);
	elseif (z <= -2.9e-217)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (z <= 30000.0)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+84)
		tmp = x + t;
	elseif (z <= -2.9e-217)
		tmp = x + (t * (y / (a - z)));
	elseif (z <= 30000.0)
		tmp = x + (((y - z) * t) / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+84], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.9e-217], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 30000.0], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e84 or 3e4 < z

   1. Initial program 69.9%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.2%

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

   if -1.35e84 < z < -2.89999999999999982e-217

   1. Initial program 95.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 87.1%

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

   if -2.89999999999999982e-217 < z < 3e4

   1. Initial program 96.2%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in a around inf 91.3%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+84}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-217}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 30000:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-213}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 11800:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e+84)
   (+ x t)
   (if (<= z -2.2e-213)
     (+ x (* t (/ y (- a z))))
     (if (<= z 11800.0) (+ x (/ (- y z) (/ a t))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+84) {
		tmp = x + t;
	} else if (z <= -2.2e-213) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= 11800.0) {
		tmp = x + ((y - z) / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.6d+84)) then
        tmp = x + t
    else if (z <= (-2.2d-213)) then
        tmp = x + (t * (y / (a - z)))
    else if (z <= 11800.0d0) then
        tmp = x + ((y - z) / (a / t))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+84) {
		tmp = x + t;
	} else if (z <= -2.2e-213) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= 11800.0) {
		tmp = x + ((y - z) / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e+84:
		tmp = x + t
	elif z <= -2.2e-213:
		tmp = x + (t * (y / (a - z)))
	elif z <= 11800.0:
		tmp = x + ((y - z) / (a / t))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e+84)
		tmp = Float64(x + t);
	elseif (z <= -2.2e-213)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (z <= 11800.0)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e+84)
		tmp = x + t;
	elseif (z <= -2.2e-213)
		tmp = x + (t * (y / (a - z)));
	elseif (z <= 11800.0)
		tmp = x + ((y - z) / (a / t));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e+84], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.2e-213], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 11800.0], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000005e84 or 11800 < z

   1. Initial program 69.9%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.2%

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

   if -1.60000000000000005e84 < z < -2.2000000000000001e-213

   1. Initial program 95.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 87.1%

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

   if -2.2000000000000001e-213 < z < 11800

   1. Initial program 96.2%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in a around inf 93.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-213}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 11800:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{-212}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 850:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (+ (/ a z) -1.0)))))
   (if (<= z -1.52e+16)
     t_1
     (if (<= z -3.85e-212)
       (+ x (* t (/ y (- a z))))
       (if (<= z 850.0) (+ x (/ (- y z) (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / ((a / z) + -1.0));
	double tmp;
	if (z <= -1.52e+16) {
		tmp = t_1;
	} else if (z <= -3.85e-212) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= 850.0) {
		tmp = x + ((y - z) / (a / t));
	} 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 - (t / ((a / z) + (-1.0d0)))
    if (z <= (-1.52d+16)) then
        tmp = t_1
    else if (z <= (-3.85d-212)) then
        tmp = x + (t * (y / (a - z)))
    else if (z <= 850.0d0) then
        tmp = x + ((y - z) / (a / t))
    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 - (t / ((a / z) + -1.0));
	double tmp;
	if (z <= -1.52e+16) {
		tmp = t_1;
	} else if (z <= -3.85e-212) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= 850.0) {
		tmp = x + ((y - z) / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / ((a / z) + -1.0))
	tmp = 0
	if z <= -1.52e+16:
		tmp = t_1
	elif z <= -3.85e-212:
		tmp = x + (t * (y / (a - z)))
	elif z <= 850.0:
		tmp = x + ((y - z) / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)))
	tmp = 0.0
	if (z <= -1.52e+16)
		tmp = t_1;
	elseif (z <= -3.85e-212)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (z <= 850.0)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / ((a / z) + -1.0));
	tmp = 0.0;
	if (z <= -1.52e+16)
		tmp = t_1;
	elseif (z <= -3.85e-212)
		tmp = x + (t * (y / (a - z)));
	elseif (z <= 850.0)
		tmp = x + ((y - z) / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.52e+16], t$95$1, If[LessEqual[z, -3.85e-212], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 850.0], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.52e16 or 850 < z

   1. Initial program 71.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unsub-neg 64.6%

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

      3. associate-/l* 88.6%

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

      4. div-sub 88.6%

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

      5. *-inverses 88.6%

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

   7. Simplified 88.6%

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

   if -1.52e16 < z < -3.8499999999999999e-212

   1. Initial program 97.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 92.1%

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

   if -3.8499999999999999e-212 < z < 850

   1. Initial program 96.2%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in a around inf 93.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{-212}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 850:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-214}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 0.0136:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+16)
   (- x (/ t (+ (/ a z) -1.0)))
   (if (<= z -4.9e-214)
     (+ x (* t (/ y (- a z))))
     (if (<= z 0.0136) (+ x (/ (- y z) (/ a t))) (- x (/ t (/ z (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+16) {
		tmp = x - (t / ((a / z) + -1.0));
	} else if (z <= -4.9e-214) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= 0.0136) {
		tmp = x + ((y - z) / (a / 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 <= (-4.6d+16)) then
        tmp = x - (t / ((a / z) + (-1.0d0)))
    else if (z <= (-4.9d-214)) then
        tmp = x + (t * (y / (a - z)))
    else if (z <= 0.0136d0) then
        tmp = x + ((y - z) / (a / 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 <= -4.6e+16) {
		tmp = x - (t / ((a / z) + -1.0));
	} else if (z <= -4.9e-214) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= 0.0136) {
		tmp = x + ((y - z) / (a / t));
	} else {
		tmp = x - (t / (z / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+16:
		tmp = x - (t / ((a / z) + -1.0))
	elif z <= -4.9e-214:
		tmp = x + (t * (y / (a - z)))
	elif z <= 0.0136:
		tmp = x + ((y - z) / (a / t))
	else:
		tmp = x - (t / (z / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+16)
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	elseif (z <= -4.9e-214)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (z <= 0.0136)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / 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 <= -4.6e+16)
		tmp = x - (t / ((a / z) + -1.0));
	elseif (z <= -4.9e-214)
		tmp = x + (t * (y / (a - z)));
	elseif (z <= 0.0136)
		tmp = x + ((y - z) / (a / t));
	else
		tmp = x - (t / (z / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+16], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e-214], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0136], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.6e16

   1. Initial program 66.9%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

      3. associate-/l* 92.2%

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

      4. div-sub 92.2%

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

      5. *-inverses 92.2%

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

   7. Simplified 92.2%

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

   if -4.6e16 < z < -4.89999999999999968e-214

   1. Initial program 97.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 92.1%

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

   if -4.89999999999999968e-214 < z < 0.0135999999999999992

   1. Initial program 96.1%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in a around inf 94.8%

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

   if 0.0135999999999999992 < z

   1. Initial program 76.7%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. associate-/l* 90.8%

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

   7. Simplified 90.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-214}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 0.0136:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{+84} \lor \neg \left(z \leq 3.3 \cdot 10^{+38}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.86e+84) (not (<= z 3.3e+38)))
   (+ x t)
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.86e+84) || !(z <= 3.3e+38)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.86d+84)) .or. (.not. (z <= 3.3d+38))) then
        tmp = x + t
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.86e+84) || !(z <= 3.3e+38)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.86e+84) or not (z <= 3.3e+38):
		tmp = x + t
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.86e+84) || !(z <= 3.3e+38))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.86e+84) || ~((z <= 3.3e+38)))
		tmp = x + t;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.86e+84], N[Not[LessEqual[z, 3.3e+38]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.86000000000000006e84 or 3.2999999999999999e38 < z

   1. Initial program 69.1%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 86.1%

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

   if -1.86000000000000006e84 < z < 3.2999999999999999e38

   1. Initial program 95.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in y around inf 84.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{+84} \lor \neg \left(z \leq 3.3 \cdot 10^{+38}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+140} \lor \neg \left(t \leq 4.1 \cdot 10^{+140}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e+140) (not (<= t 4.1e+140)))
   (* t (- 1.0 (/ y z)))
   (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e+140) || !(t <= 4.1e+140)) {
		tmp = t * (1.0 - (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 ((t <= (-1.45d+140)) .or. (.not. (t <= 4.1d+140))) then
        tmp = t * (1.0d0 - (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 ((t <= -1.45e+140) || !(t <= 4.1e+140)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e+140) or not (t <= 4.1e+140):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e+140) || !(t <= 4.1e+140))
		tmp = Float64(t * Float64(1.0 - 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 ((t <= -1.45e+140) || ~((t <= 4.1e+140)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e+140], N[Not[LessEqual[t, 4.1e+140]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4499999999999999e140 or 4.0999999999999999e140 < t

   1. Initial program 59.3%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in a around 0 29.3%

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

      1. mul-1-neg 29.3%

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

      2. unsub-neg 29.3%

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

      3. associate-/l* 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in t around inf 53.6%

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

   if -1.4499999999999999e140 < t < 4.0999999999999999e140

   1. Initial program 94.5%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around inf 72.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+140} \lor \neg \left(t \leq 4.1 \cdot 10^{+140}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 2.3 \cdot 10^{-17}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+83) (not (<= z 2.3e-17))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+83) || !(z <= 2.3e-17)) {
		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 <= (-8.8d+83)) .or. (.not. (z <= 2.3d-17))) 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 <= -8.8e+83) || !(z <= 2.3e-17)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+83) or not (z <= 2.3e-17):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+83) || !(z <= 2.3e-17))
		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 <= -8.8e+83) || ~((z <= 2.3e-17)))
		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, -8.8e+83], N[Not[LessEqual[z, 2.3e-17]], $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 < -8.79999999999999995e83 or 2.30000000000000009e-17 < z

   1. Initial program 71.1%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -8.79999999999999995e83 < z < 2.30000000000000009e-17

   1. Initial program 95.6%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 77.4%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 2.3 \cdot 10^{-17}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 460\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+83) (not (<= z 460.0))) (+ x t) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+83) || !(z <= 460.0)) {
		tmp = x + t;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.8d+83)) .or. (.not. (z <= 460.0d0))) then
        tmp = x + t
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+83) || !(z <= 460.0)) {
		tmp = x + t;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+83) or not (z <= 460.0):
		tmp = x + t
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+83) || !(z <= 460.0))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.8e+83) || ~((z <= 460.0)))
		tmp = x + t;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+83], N[Not[LessEqual[z, 460.0]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999995e83 or 460 < z

   1. Initial program 69.9%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.2%

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

   if -8.79999999999999995e83 < z < 460

   1. Initial program 95.8%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 77.6%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 460\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.1% 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 83.7%

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

   1. associate-*l/ 98.1%

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

3. Simplified 98.1%

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

5. Final simplification 98.1%

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

Alternative 11: 63.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-19} \lor \neg \left(z \leq 1.65 \cdot 10^{-27}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-19) (not (<= z 1.65e-27))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-19) || !(z <= 1.65e-27)) {
		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 <= (-2.7d-19)) .or. (.not. (z <= 1.65d-27))) 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 <= -2.7e-19) || !(z <= 1.65e-27)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-19) or not (z <= 1.65e-27):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-19) || !(z <= 1.65e-27))
		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 <= -2.7e-19) || ~((z <= 1.65e-27)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-19], N[Not[LessEqual[z, 1.65e-27]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.7000000000000001e-19 or 1.64999999999999999e-27 < z

   1. Initial program 74.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 77.1%

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

   if -2.7000000000000001e-19 < z < 1.64999999999999999e-27

   1. Initial program 97.2%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in x around inf 51.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-19} \lor \neg \left(z \leq 1.65 \cdot 10^{-27}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-124}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e-63) x (if (<= x 1.4e-124) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e-63) {
		tmp = x;
	} else if (x <= 1.4e-124) {
		tmp = 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 (x <= (-1.1d-63)) then
        tmp = x
    else if (x <= 1.4d-124) then
        tmp = 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 (x <= -1.1e-63) {
		tmp = x;
	} else if (x <= 1.4e-124) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e-63:
		tmp = x
	elif x <= 1.4e-124:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.1e-63)
		tmp = x;
	elseif (x <= 1.4e-124)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.1e-63)
		tmp = x;
	elseif (x <= 1.4e-124)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e-63], x, If[LessEqual[x, 1.4e-124], t, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e-63 or 1.39999999999999999e-124 < x

   1. Initial program 82.6%

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

   5. Taylor expanded in x around inf 67.0%

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

   if -1.1e-63 < x < 1.39999999999999999e-124

   1. Initial program 86.1%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in a around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

      3. associate-/l* 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in t around inf 52.5%

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

   9. Taylor expanded in y around 0 31.5%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-124}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 18.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.7%

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

   1. associate-*l/ 98.1%

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

3. Simplified 98.1%

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

5. Taylor expanded in a around 0 58.8%

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

   1. mul-1-neg 58.8%

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

   2. unsub-neg 58.8%

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

   3. associate-/l* 70.6%

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

7. Simplified 70.6%

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

8. Taylor expanded in t around inf 31.5%

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

9. Taylor expanded in y around 0 19.6%

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

10. Final simplification 19.6%

    \[\leadsto t \]
11. Add Preprocessing

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 2024010 
(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))))