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

Percentage Accurate: 85.4% → 98.1%

Time: 8.0s

Alternatives: 12

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: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. associate-*l/ 99.0%

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

3. Simplified 99.0%

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

4. Final simplification 99.0%

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

Alternative 2: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+42} \lor \neg \left(z \leq 1.25 \cdot 10^{+32}\right):\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+42) (not (<= z 1.25e+32)))
   (- x (/ t (/ z (- y z))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+42) || !(z <= 1.25e+32)) {
		tmp = x - (t / (z / (y - z)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.2d+42)) .or. (.not. (z <= 1.25d+32))) then
        tmp = x - (t / (z / (y - z)))
    else
        tmp = x + (y / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+42) || !(z <= 1.25e+32)) {
		tmp = x - (t / (z / (y - z)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+42) or not (z <= 1.25e+32):
		tmp = x - (t / (z / (y - z)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+42) || !(z <= 1.25e+32))
		tmp = Float64(x - Float64(t / Float64(z / Float64(y - z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+42) || ~((z <= 1.25e+32)))
		tmp = x - (t / (z / (y - z)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+42], N[Not[LessEqual[z, 1.25e+32]], $MachinePrecision]], N[(x - N[(t / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1999999999999999e42 or 1.2499999999999999e32 < z

   1. Initial program 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-*r/ 95.7%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. associate-/l* 90.7%

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

   6. Simplified 90.7%

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

   if -1.1999999999999999e42 < z < 1.2499999999999999e32

   1. Initial program 96.6%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 89.1%

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

   5. Taylor expanded in x around 0 87.6%

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

      1. associate-/l* 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+42} \lor \neg \left(z \leq 1.25 \cdot 10^{+32}\right):\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 3: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+42} \lor \neg \left(z \leq 6.2 \cdot 10^{-86}\right):\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.6e+42) (not (<= z 6.2e-86)))
   (- x (* t (/ z (- a z))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e+42) || !(z <= 6.2e-86)) {
		tmp = x - (t * (z / (a - z)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.6d+42)) .or. (.not. (z <= 6.2d-86))) then
        tmp = x - (t * (z / (a - z)))
    else
        tmp = x + (y / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e+42) || !(z <= 6.2e-86)) {
		tmp = x - (t * (z / (a - z)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.6e+42) or not (z <= 6.2e-86):
		tmp = x - (t * (z / (a - z)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.6e+42) || !(z <= 6.2e-86))
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.6e+42) || ~((z <= 6.2e-86)))
		tmp = x - (t * (z / (a - z)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.6e+42], N[Not[LessEqual[z, 6.2e-86]], $MachinePrecision]], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5999999999999996e42 or 6.19999999999999977e-86 < z

   1. Initial program 79.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in y around 0 91.1%

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

      1. neg-mul-1 91.1%

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

      2. distribute-neg-frac 91.1%

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

   6. Simplified 91.1%

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

   if -8.5999999999999996e42 < z < 6.19999999999999977e-86

   1. Initial program 96.0%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 90.9%

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

   5. Taylor expanded in x around 0 89.1%

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

      1. associate-/l* 92.1%

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

   7. Simplified 92.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+42} \lor \neg \left(z \leq 6.2 \cdot 10^{-86}\right):\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 4: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+44}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+44)
   (+ x t)
   (if (<= z 7.6e+64) (+ x (* t (/ y (- a z)))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+44) {
		tmp = x + t;
	} else if (z <= 7.6e+64) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d+44)) then
        tmp = x + t
    else if (z <= 7.6d+64) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+44) {
		tmp = x + t;
	} else if (z <= 7.6e+64) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+44:
		tmp = x + t
	elif z <= 7.6e+64:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+44)
		tmp = Float64(x + t);
	elseif (z <= 7.6e+64)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e+44)
		tmp = x + t;
	elseif (z <= 7.6e+64)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+44], N[(x + t), $MachinePrecision], If[LessEqual[z, 7.6e+64], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e44 or 7.6000000000000002e64 < z

   1. Initial program 76.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in z around inf 85.8%

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

   if -1.4e44 < z < 7.6000000000000002e64

   1. Initial program 95.0%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around inf 88.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+44}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 5: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t + \frac{a}{\frac{z}{t}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+42)
   (+ x t)
   (if (<= z 5e+64) (+ x (* t (/ y (- a z)))) (+ x (+ t (/ a (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+42) {
		tmp = x + t;
	} else if (z <= 5e+64) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t + (a / (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+42)) then
        tmp = x + t
    else if (z <= 5d+64) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (t + (a / (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+42) {
		tmp = x + t;
	} else if (z <= 5e+64) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t + (a / (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+42:
		tmp = x + t
	elif z <= 5e+64:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (t + (a / (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+42)
		tmp = Float64(x + t);
	elseif (z <= 5e+64)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t + Float64(a / Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+42)
		tmp = x + t;
	elseif (z <= 5e+64)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (t + (a / (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+42], N[(x + t), $MachinePrecision], If[LessEqual[z, 5e+64], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999997e42

   1. Initial program 76.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in z around inf 84.4%

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

   if -4.7999999999999997e42 < z < 5e64

   1. Initial program 95.0%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around inf 88.3%

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

   if 5e64 < z

   1. Initial program 77.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. associate-/l* 93.1%

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

      3. distribute-neg-frac 93.1%

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

   8. Simplified 93.1%

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

   9. Taylor expanded in a around 0 82.2%

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

       1. associate-/l* 87.5%

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

   11. Simplified 87.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t + \frac{a}{\frac{z}{t}}\right)\\ \end{array} \]

Alternative 6: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t + \frac{a}{\frac{z}{t}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e+44)
   (+ x t)
   (if (<= z 6.6e+65) (+ x (/ y (/ (- a z) t))) (+ x (+ t (/ a (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+44) {
		tmp = x + t;
	} else if (z <= 6.6e+65) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (t + (a / (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.55d+44)) then
        tmp = x + t
    else if (z <= 6.6d+65) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x + (t + (a / (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+44) {
		tmp = x + t;
	} else if (z <= 6.6e+65) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (t + (a / (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e+44:
		tmp = x + t
	elif z <= 6.6e+65:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (t + (a / (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e+44)
		tmp = Float64(x + t);
	elseif (z <= 6.6e+65)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(t + Float64(a / Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.55e+44)
		tmp = x + t;
	elseif (z <= 6.6e+65)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (t + (a / (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e+44], N[(x + t), $MachinePrecision], If[LessEqual[z, 6.6e+65], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999998e44

   1. Initial program 76.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in z around inf 84.4%

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

   if -1.54999999999999998e44 < z < 6.60000000000000046e65

   1. Initial program 95.0%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around inf 88.3%

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

   5. Taylor expanded in x around 0 85.6%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   if 6.60000000000000046e65 < z

   1. Initial program 77.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. associate-/l* 93.1%

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

      3. distribute-neg-frac 93.1%

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

   8. Simplified 93.1%

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

   9. Taylor expanded in a around 0 82.2%

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

       1. associate-/l* 87.5%

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

   11. Simplified 87.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t + \frac{a}{\frac{z}{t}}\right)\\ \end{array} \]

Alternative 7: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+41}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+41)
   (- x (* t (/ z (- a z))))
   (if (<= z 1.35e-85)
     (+ x (/ y (/ (- a z) t)))
     (- x (/ t (+ (/ a z) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+41) {
		tmp = x - (t * (z / (a - z)));
	} else if (z <= 1.35e-85) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t / ((a / 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 <= (-8d+41)) then
        tmp = x - (t * (z / (a - z)))
    else if (z <= 1.35d-85) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x - (t / ((a / 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 <= -8e+41) {
		tmp = x - (t * (z / (a - z)));
	} else if (z <= 1.35e-85) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+41:
		tmp = x - (t * (z / (a - z)))
	elif z <= 1.35e-85:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x - (t / ((a / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+41)
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	elseif (z <= 1.35e-85)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+41)
		tmp = x - (t * (z / (a - z)));
	elseif (z <= 1.35e-85)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x - (t / ((a / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+41], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-85], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.00000000000000005e41

   1. Initial program 76.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in y around 0 94.8%

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

      1. neg-mul-1 94.8%

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

      2. distribute-neg-frac 94.8%

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

   6. Simplified 94.8%

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

   if -8.00000000000000005e41 < z < 1.3500000000000001e-85

   1. Initial program 96.0%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 90.9%

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

   5. Taylor expanded in x around 0 89.1%

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

      1. associate-/l* 92.1%

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

   7. Simplified 92.1%

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

   if 1.3500000000000001e-85 < z

   1. Initial program 82.1%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-/l* 88.8%

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

      3. distribute-neg-frac 88.8%

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

   8. Simplified 88.8%

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

   9. Taylor expanded in a around 0 88.8%

      \[\leadsto x + \frac{-t}{\color{blue}{\frac{a}{z} - 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+41}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \]

Alternative 8: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-87}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-181}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e-87)
   (+ x t)
   (if (<= z -7.2e-181) (* t (/ (- y z) a)) (if (<= z 1.85e-71) x (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e-87) {
		tmp = x + t;
	} else if (z <= -7.2e-181) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.85e-71) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d-87)) then
        tmp = x + t
    else if (z <= (-7.2d-181)) then
        tmp = t * ((y - z) / a)
    else if (z <= 1.85d-71) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e-87) {
		tmp = x + t;
	} else if (z <= -7.2e-181) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.85e-71) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e-87:
		tmp = x + t
	elif z <= -7.2e-181:
		tmp = t * ((y - z) / a)
	elif z <= 1.85e-71:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e-87)
		tmp = Float64(x + t);
	elseif (z <= -7.2e-181)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 1.85e-71)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e-87)
		tmp = x + t;
	elseif (z <= -7.2e-181)
		tmp = t * ((y - z) / a);
	elseif (z <= 1.85e-71)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e-87], N[(x + t), $MachinePrecision], If[LessEqual[z, -7.2e-181], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-71], x, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004e-87 or 1.8499999999999998e-71 < z

   1. Initial program 80.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in z around inf 79.5%

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

   if -1.05000000000000004e-87 < z < -7.1999999999999998e-181

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-*r/ 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around inf 76.9%

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

   5. Taylor expanded in t around inf 64.6%

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

      1. div-sub 64.6%

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

   7. Simplified 64.6%

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

   if -7.1999999999999998e-181 < z < 1.8499999999999998e-71

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 97.5%

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

      3. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around 0 58.1%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-87}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-181}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 9: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 10^{-71}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+42) (+ x t) (if (<= z 1e-71) (+ x (* t (/ y a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+42) {
		tmp = x + t;
	} else if (z <= 1e-71) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.5d+42)) then
        tmp = x + t
    else if (z <= 1d-71) then
        tmp = x + (t * (y / a))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+42) {
		tmp = x + t;
	} else if (z <= 1e-71) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+42:
		tmp = x + t
	elif z <= 1e-71:
		tmp = x + (t * (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+42)
		tmp = Float64(x + t);
	elseif (z <= 1e-71)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+42)
		tmp = x + t;
	elseif (z <= 1e-71)
		tmp = x + (t * (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+42], N[(x + t), $MachinePrecision], If[LessEqual[z, 1e-71], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000014e42 or 9.9999999999999992e-72 < z

   1. Initial program 79.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 82.9%

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

   if -1.50000000000000014e42 < z < 9.9999999999999992e-72

   1. Initial program 96.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around 0 80.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 10^{-71}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 10: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+41}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+41) (+ x t) (if (<= z 2e-72) (+ x (/ y (/ a t))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+41) {
		tmp = x + t;
	} else if (z <= 2e-72) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+41)) then
        tmp = x + t
    else if (z <= 2d-72) then
        tmp = x + (y / (a / t))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+41) {
		tmp = x + t;
	} else if (z <= 2e-72) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+41:
		tmp = x + t
	elif z <= 2e-72:
		tmp = x + (y / (a / t))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+41)
		tmp = Float64(x + t);
	elseif (z <= 2e-72)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+41)
		tmp = x + t;
	elseif (z <= 2e-72)
		tmp = x + (y / (a / t));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+41], N[(x + t), $MachinePrecision], If[LessEqual[z, 2e-72], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999938e41 or 1.9999999999999999e-72 < z

   1. Initial program 79.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 82.9%

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

   if -8.49999999999999938e41 < z < 1.9999999999999999e-72

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-*r/ 98.3%

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

      3. fma-def 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 79.1%

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

      1. associate-/l* 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+41}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 11: 63.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-181}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e-181) (+ x t) (if (<= z 3e-71) x (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e-181) {
		tmp = x + t;
	} else if (z <= 3e-71) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d-181)) then
        tmp = x + t
    else if (z <= 3d-71) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e-181) {
		tmp = x + t;
	} else if (z <= 3e-71) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e-181:
		tmp = x + t
	elif z <= 3e-71:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e-181)
		tmp = Float64(x + t);
	elseif (z <= 3e-71)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e-181)
		tmp = x + t;
	elseif (z <= 3e-71)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e-181], N[(x + t), $MachinePrecision], If[LessEqual[z, 3e-71], x, N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000003e-181 or 3.0000000000000001e-71 < z

   1. Initial program 82.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in z around inf 75.4%

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

   if -8.2000000000000003e-181 < z < 3.0000000000000001e-71

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 97.5%

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

      3. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around 0 58.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-181}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 12: 50.8% 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 87.5%

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

   1. +-commutative 87.5%

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

   2. associate-*r/ 97.3%

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

   3. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in t around 0 51.2%

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

5. Final simplification 51.2%

   \[\leadsto x \]

Developer target: 99.1% 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 2023200 
(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))))