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

Percentage Accurate: 85.5% → 98.4%

Time: 9.3s

Alternatives: 10

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: 85.5% 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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. *-commutative 98.4%

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

   2. clear-num 98.4%

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

   3. un-div-inv 98.5%

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

6. Applied egg-rr 98.5%

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

7. Final simplification 98.5%

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

Alternative 2: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+35} \lor \neg \left(z \leq 3.45 \cdot 10^{+152}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+35) (not (<= z 3.45e+152)))
   (+ x t)
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+35) || !(z <= 3.45e+152)) {
		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 <= (-3.8d+35)) .or. (.not. (z <= 3.45d+152))) 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 <= -3.8e+35) || !(z <= 3.45e+152)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+35) or not (z <= 3.45e+152):
		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 <= -3.8e+35) || !(z <= 3.45e+152))
		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 <= -3.8e+35) || ~((z <= 3.45e+152)))
		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, -3.8e+35], N[Not[LessEqual[z, 3.45e+152]], $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 < -3.8e35 or 3.45e152 < z

   1. Initial program 74.5%

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

   5. Taylor expanded in z around inf 88.0%

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

   if -3.8e35 < z < 3.45e152

   1. Initial program 94.7%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf 88.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+35} \lor \neg \left(z \leq 3.45 \cdot 10^{+152}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -180000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -180000000.0) (not (<= z 2.35e+111)))
   (+ x (- t (* y (/ t z))))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -180000000.0) || !(z <= 2.35e+111)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-180000000.0d0)) .or. (.not. (z <= 2.35d+111))) then
        tmp = x + (t - (y * (t / z)))
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -180000000.0) || !(z <= 2.35e+111)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -180000000.0) or not (z <= 2.35e+111):
		tmp = x + (t - (y * (t / z)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -180000000.0) || !(z <= 2.35e+111))
		tmp = Float64(x + Float64(t - Float64(y * Float64(t / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -180000000.0) || ~((z <= 2.35e+111)))
		tmp = x + (t - (y * (t / z)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -180000000.0], N[Not[LessEqual[z, 2.35e+111]], $MachinePrecision]], N[(x + N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e8 or 2.35000000000000004e111 < z

   1. Initial program 74.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-/l* 92.1%

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

      3. distribute-neg-frac 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

      3. associate-*l/ 93.1%

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

      4. *-commutative 93.1%

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

   10. Simplified 93.1%

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

   if -1.8e8 < z < 2.35000000000000004e111

   1. Initial program 96.1%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 89.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -180000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000000 \lor \neg \left(z \leq 6 \cdot 10^{+111}\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -105000000.0) (not (<= z 6e+111)))
   (+ x (- t (* y (/ t z))))
   (+ x (/ t (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -105000000.0) || !(z <= 6e+111)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-105000000.0d0)) .or. (.not. (z <= 6d+111))) then
        tmp = x + (t - (y * (t / z)))
    else
        tmp = x + (t / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -105000000.0) || !(z <= 6e+111)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -105000000.0) or not (z <= 6e+111):
		tmp = x + (t - (y * (t / z)))
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -105000000.0) || !(z <= 6e+111))
		tmp = Float64(x + Float64(t - Float64(y * Float64(t / z))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -105000000.0) || ~((z <= 6e+111)))
		tmp = x + (t - (y * (t / z)));
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -105000000.0], N[Not[LessEqual[z, 6e+111]], $MachinePrecision]], N[(x + N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e8 or 6e111 < z

   1. Initial program 74.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-/l* 92.1%

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

      3. distribute-neg-frac 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

      3. associate-*l/ 93.1%

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

      4. *-commutative 93.1%

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

   10. Simplified 93.1%

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

   if -1.05e8 < z < 6e111

   1. Initial program 96.1%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 89.3%

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

      1. associate-/l* 89.5%

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

   7. Simplified 89.5%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -105000000 \lor \neg \left(z \leq 6 \cdot 10^{+111}\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000000 \lor \neg \left(z \leq 2.4 \cdot 10^{+111}\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -105000000.0) (not (<= z 2.4e+111)))
   (+ x (- t (* y (/ t z))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -105000000.0) || !(z <= 2.4e+111)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-105000000.0d0)) .or. (.not. (z <= 2.4d+111))) then
        tmp = x + (t - (y * (t / z)))
    else
        tmp = x + (y / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -105000000.0) || !(z <= 2.4e+111)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -105000000.0) or not (z <= 2.4e+111):
		tmp = x + (t - (y * (t / z)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -105000000.0) || !(z <= 2.4e+111))
		tmp = Float64(x + Float64(t - Float64(y * Float64(t / z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -105000000.0) || ~((z <= 2.4e+111)))
		tmp = x + (t - (y * (t / z)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -105000000.0], N[Not[LessEqual[z, 2.4e+111]], $MachinePrecision]], N[(x + N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e8 or 2.40000000000000006e111 < z

   1. Initial program 74.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-/l* 92.1%

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

      3. distribute-neg-frac 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

      3. associate-*l/ 93.1%

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

      4. *-commutative 93.1%

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

   10. Simplified 93.1%

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

   if -1.05e8 < z < 2.40000000000000006e111

   1. Initial program 96.1%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

      1. *-commutative 97.4%

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

      2. clear-num 97.4%

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

      3. un-div-inv 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around inf 89.3%

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

      1. associate-*r/ 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-/r/ 90.6%

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

   9. Simplified 90.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -105000000 \lor \neg \left(z \leq 2.4 \cdot 10^{+111}\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-103}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.8e+93)
   (+ x (/ y (/ (- a z) t)))
   (if (<= y 3.4e-103)
     (- x (/ t (+ (/ a z) -1.0)))
     (+ x (/ t (/ (- a z) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.8e+93) {
		tmp = x + (y / ((a - z) / t));
	} else if (y <= 3.4e-103) {
		tmp = x - (t / ((a / z) + -1.0));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.8d+93)) then
        tmp = x + (y / ((a - z) / t))
    else if (y <= 3.4d-103) then
        tmp = x - (t / ((a / z) + (-1.0d0)))
    else
        tmp = x + (t / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.8e+93) {
		tmp = x + (y / ((a - z) / t));
	} else if (y <= 3.4e-103) {
		tmp = x - (t / ((a / z) + -1.0));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.8e+93:
		tmp = x + (y / ((a - z) / t))
	elif y <= 3.4e-103:
		tmp = x - (t / ((a / z) + -1.0))
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.8e+93)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	elseif (y <= 3.4e-103)
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.8e+93)
		tmp = x + (y / ((a - z) / t));
	elseif (y <= 3.4e-103)
		tmp = x - (t / ((a / z) + -1.0));
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.8e+93], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-103], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999989e93

   1. Initial program 87.7%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

      1. *-commutative 93.7%

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

      2. clear-num 93.7%

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

      3. un-div-inv 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in y around inf 87.6%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. associate-/r/ 95.6%

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

   9. Simplified 95.6%

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

   if -2.79999999999999989e93 < y < 3.40000000000000003e-103

   1. Initial program 87.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-/l* 92.9%

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

      3. distribute-neg-frac 92.9%

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

      4. div-sub 92.9%

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

      5. *-inverses 92.9%

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

   7. Simplified 92.9%

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

      1. distribute-frac-neg 92.9%

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

      2. unsub-neg 92.9%

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

      3. sub-neg 92.9%

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

      4. metadata-eval 92.9%

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

   9. Applied egg-rr 92.9%

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

   if 3.40000000000000003e-103 < y

   1. Initial program 88.1%

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

   5. Taylor expanded in y around inf 86.2%

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

      1. associate-/l* 92.3%

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

   7. Simplified 92.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-103}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -230000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -230000000.0) (not (<= z 2.35e+111)))
   (+ x t)
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -230000000.0) || !(z <= 2.35e+111)) {
		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 <= (-230000000.0d0)) .or. (.not. (z <= 2.35d+111))) 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 <= -230000000.0) || !(z <= 2.35e+111)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -230000000.0) or not (z <= 2.35e+111):
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -230000000.0) || !(z <= 2.35e+111))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -230000000.0) || ~((z <= 2.35e+111)))
		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, -230000000.0], N[Not[LessEqual[z, 2.35e+111]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e8 or 2.35000000000000004e111 < z

   1. Initial program 74.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.7%

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

   if -2.3e8 < z < 2.35000000000000004e111

   1. Initial program 96.1%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

      1. associate-/r/ 98.0%

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

      2. clear-num 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in z around 0 80.4%

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

      1. associate-*l/ 81.7%

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

   9. Simplified 81.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -230000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-27} \lor \neg \left(z \leq 2.5 \cdot 10^{+111}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e-27) (not (<= z 2.5e+111))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e-27) || !(z <= 2.5e+111)) {
		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 <= (-1.45d-27)) .or. (.not. (z <= 2.5d+111))) 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 <= -1.45e-27) || !(z <= 2.5e+111)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e-27) or not (z <= 2.5e+111):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e-27) || !(z <= 2.5e+111))
		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 <= -1.45e-27) || ~((z <= 2.5e+111)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e-27], N[Not[LessEqual[z, 2.5e+111]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000002e-27 or 2.4999999999999998e111 < z

   1. Initial program 76.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.5%

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

   if -1.45000000000000002e-27 < z < 2.4999999999999998e111

   1. Initial program 96.5%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around inf 84.1%

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

   6. Taylor expanded in x around inf 53.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-27} \lor \neg \left(z \leq 2.5 \cdot 10^{+111}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

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

Alternative 10: 50.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. associate-*l/ 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 a around inf 63.5%

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

6. Taylor expanded in x around inf 53.9%

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

7. Final simplification 53.9%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024036 
(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))))