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

Percentage Accurate: 85.9% → 99.7%

Time: 8.3s

Alternatives: 11

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: 85.9% 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z - a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+289}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t (- y z)) (- a z))))
   (if (<= t_1 (- INFINITY))
     (- x (* (- y z) (/ t (- z a))))
     (if (<= t_1 5e+289) (+ x t_1) (+ x (/ (- y z) (/ (- a z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - ((y - z) * (t / (z - a)));
	} else if (t_1 <= 5e+289) {
		tmp = x + t_1;
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - ((y - z) * (t / (z - a)));
	} else if (t_1 <= 5e+289) {
		tmp = x + t_1;
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * (y - z)) / (a - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - ((y - z) * (t / (z - a)))
	elif t_1 <= 5e+289:
		tmp = x + t_1
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(Float64(y - z) * Float64(t / Float64(z - a))));
	elseif (t_1 <= 5e+289)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * (y - z)) / (a - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - ((y - z) * (t / (z - a)));
	elseif (t_1 <= 5e+289)
		tmp = x + t_1;
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(N[(y - z), $MachinePrecision] * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+289], N[(x + t$95$1), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0

   1. Initial program 38.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 5.00000000000000031e289

   1. Initial program 99.9%

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

   if 5.00000000000000031e289 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 31.1%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z - a}\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+289}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t (- y z)) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+289)))
     (- x (* (- y z) (/ t (- z a))))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (y - z)) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+289)) {
		tmp = x - ((y - z) * (t / (z - a)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (y - z)) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+289)) {
		tmp = x - ((y - z) * (t / (z - a)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * (y - z)) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+289):
		tmp = x - ((y - z) * (t / (z - a)))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+289))
		tmp = Float64(x - Float64(Float64(y - z) * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * (y - z)) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+289)))
		tmp = x - ((y - z) * (t / (z - a)));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+289]], $MachinePrecision]], N[(x - N[(N[(y - z), $MachinePrecision] * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 5.00000000000000031e289 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 34.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 5.00000000000000031e289

   1. Initial program 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty \lor \neg \left(\frac{t \cdot \left(y - z\right)}{a - z} \leq 5 \cdot 10^{+289}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+87} \lor \neg \left(z \leq 9.8 \cdot 10^{+210}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+87) (not (<= z 9.8e+210)))
   (+ x t)
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+87) || !(z <= 9.8e+210)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.3d+87)) .or. (.not. (z <= 9.8d+210))) then
        tmp = x + t
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+87) || !(z <= 9.8e+210)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+87) or not (z <= 9.8e+210):
		tmp = x + t
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+87) || !(z <= 9.8e+210))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e+87) || ~((z <= 9.8e+210)))
		tmp = x + t;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+87], N[Not[LessEqual[z, 9.8e+210]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.29999999999999999e87 or 9.80000000000000013e210 < z

   1. Initial program 63.9%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 85.5%

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

   if -1.29999999999999999e87 < z < 9.80000000000000013e210

   1. Initial program 92.1%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around inf 81.5%

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

      1. associate-/l* 85.9%

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

   7. Simplified 85.9%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+87} \lor \neg \left(z \leq 9.8 \cdot 10^{+210}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-107} \lor \neg \left(y \leq 5 \cdot 10^{+46}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3e-107) (not (<= y 5e+46)))
   (+ x (* t (/ y (- a z))))
   (- x (* t (/ z (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e-107) || !(y <= 5e+46)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3d-107)) .or. (.not. (y <= 5d+46))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x - (t * (z / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e-107) || !(y <= 5e+46)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3e-107) or not (y <= 5e+46):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x - (t * (z / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3e-107) || !(y <= 5e+46))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3e-107) || ~((y <= 5e+46)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x - (t * (z / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3e-107], N[Not[LessEqual[y, 5e+46]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9999999999999997e-107 or 5.0000000000000002e46 < y

   1. Initial program 80.6%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around inf 76.7%

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

      1. associate-/l* 86.2%

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

   7. Simplified 86.2%

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

   if -2.9999999999999997e-107 < y < 5.0000000000000002e46

   1. Initial program 87.1%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

      3. associate-/l* 93.6%

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

   7. Simplified 93.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-107} \lor \neg \left(y \leq 5 \cdot 10^{+46}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46} \lor \neg \left(z \leq 3 \cdot 10^{-43}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+46) (not (<= z 3e-43))) (+ x t) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+46) || !(z <= 3e-43)) {
		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 <= (-5.2d+46)) .or. (.not. (z <= 3d-43))) 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 <= -5.2e+46) || !(z <= 3e-43)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+46) or not (z <= 3e-43):
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+46) || !(z <= 3e-43))
		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 <= -5.2e+46) || ~((z <= 3e-43)))
		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, -5.2e+46], N[Not[LessEqual[z, 3e-43]], $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 < -5.20000000000000027e46 or 3.00000000000000003e-43 < z

   1. Initial program 73.7%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around inf 78.2%

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

   if -5.20000000000000027e46 < z < 3.00000000000000003e-43

   1. Initial program 93.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46} \lor \neg \left(z \leq 3 \cdot 10^{-43}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+46} \lor \neg \left(z \leq 2.8 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+46) (not (<= z 2.8e-45))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+46) || !(z <= 2.8e-45)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.8d+46)) .or. (.not. (z <= 2.8d-45))) then
        tmp = x + t
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+46) || !(z <= 2.8e-45)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+46) or not (z <= 2.8e-45):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+46) || !(z <= 2.8e-45))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e+46) || ~((z <= 2.8e-45)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+46], N[Not[LessEqual[z, 2.8e-45]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000004e46 or 2.8000000000000001e-45 < z

   1. Initial program 73.7%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around inf 78.2%

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

   if -5.8000000000000004e46 < z < 2.8000000000000001e-45

   1. Initial program 93.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+46} \lor \neg \left(z \leq 2.8 \cdot 10^{-45}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+46} \lor \neg \left(z \leq 3.4 \cdot 10^{-43}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e+46) (not (<= z 3.4e-43))) (+ x t) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e+46) || !(z <= 3.4e-43)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.4d+46)) .or. (.not. (z <= 3.4d-43))) then
        tmp = x + t
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e+46) || !(z <= 3.4e-43)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.4e+46) or not (z <= 3.4e-43):
		tmp = x + t
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.4e+46) || !(z <= 3.4e-43))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.4e+46) || ~((z <= 3.4e-43)))
		tmp = x + t;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.4e+46], N[Not[LessEqual[z, 3.4e-43]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.3999999999999996e46 or 3.4000000000000001e-43 < z

   1. Initial program 73.7%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around inf 78.2%

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

   if -6.3999999999999996e46 < z < 3.4000000000000001e-43

   1. Initial program 93.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

      1. clear-num 74.0%

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

      2. un-div-inv 74.1%

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

   9. Applied egg-rr 74.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+46} \lor \neg \left(z \leq 3.4 \cdot 10^{-43}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+139}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e+50) x (if (<= a 2.3e+139) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+50) {
		tmp = x;
	} else if (a <= 2.3e+139) {
		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 (a <= (-4.8d+50)) then
        tmp = x
    else if (a <= 2.3d+139) 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 (a <= -4.8e+50) {
		tmp = x;
	} else if (a <= 2.3e+139) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e+50:
		tmp = x
	elif a <= 2.3e+139:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e+50)
		tmp = x;
	elseif (a <= 2.3e+139)
		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 (a <= -4.8e+50)
		tmp = x;
	elseif (a <= 2.3e+139)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e+50], x, If[LessEqual[a, 2.3e+139], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8000000000000004e50 or 2.3e139 < a

   1. Initial program 78.1%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 66.5%

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

   if -4.8000000000000004e50 < a < 2.3e139

   1. Initial program 86.2%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around inf 61.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+139}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + t \cdot \left(\frac{-1}{z - a} \cdot \left(y - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* t (* (/ -1.0 (- z a)) (- y z)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (t * ((-1.0 / (z - a)) * (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 * (((-1.0d0) / (z - a)) * (y - z)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (t * ((-1.0 / (z - a)) * (y - z)));
}

Python

def code(x, y, z, t, a):
	return x + (t * ((-1.0 / (z - a)) * (y - z)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(t * Float64(Float64(-1.0 / Float64(z - a)) * Float64(y - z))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (t * ((-1.0 / (z - a)) * (y - z)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(t * N[(N[(-1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.5%

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

   1. associate-*r/ 94.8%

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

   2. *-commutative 94.8%

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

   3. div-inv 94.7%

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

   4. associate-*l* 98.3%

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

4. Applied egg-rr 98.3%

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

5. Final simplification 98.3%

   \[\leadsto x + t \cdot \left(\frac{-1}{z - a} \cdot \left(y - z\right)\right) \]
6. Add Preprocessing

Alternative 10: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.5%

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

   1. associate-/l* 94.8%

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

3. Simplified 94.8%

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

5. Final simplification 94.8%

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

Alternative 11: 51.4% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.5%

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

   1. associate-/l* 94.8%

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

3. Simplified 94.8%

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

5. Taylor expanded in x around inf 50.4%

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

6. Final simplification 50.4%

   \[\leadsto x \]
7. 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 2024077 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (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))))