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

Percentage Accurate: 85.7% → 99.3%

Time: 10.0s

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: 85.7% 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: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+214}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+214)))
     (- x (/ (- y z) (/ (- z a) t)))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+214)) {
		tmp = x - ((y - z) / ((z - a) / t));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+214)) {
		tmp = x - ((y - z) / ((z - a) / t));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+214):
		tmp = x - ((y - z) / ((z - a) / t))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+214))
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(z - a) / t)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+214)))
		tmp = x - ((y - z) / ((z - a) / t));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+214]], $MachinePrecision]], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 4.99999999999999953e214 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 38.5%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999953e214

   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 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 5 \cdot 10^{+214}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{z - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+230}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+230)))
     (+ x (* (- y z) (/ t (- a z))))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+230)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+230)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+230):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+230))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+230)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+230]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 1.0000000000000001e230 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 35.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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)) < 1.0000000000000001e230

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+230}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+35} \lor \neg \left(z \leq 1.35 \cdot 10^{+149}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+35) (not (<= z 1.35e+149)))
   (+ t x)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+35) || !(z <= 1.35e+149)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.1d+35)) .or. (.not. (z <= 1.35d+149))) then
        tmp = t + x
    else
        tmp = x + (y * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+35) || !(z <= 1.35e+149)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+35) or not (z <= 1.35e+149):
		tmp = t + x
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+35) || !(z <= 1.35e+149))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e+35) || ~((z <= 1.35e+149)))
		tmp = t + x;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+35], N[Not[LessEqual[z, 1.35e+149]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0999999999999999e35 or 1.35e149 < z

   1. Initial program 69.7%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 87.2%

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

   if -2.0999999999999999e35 < z < 1.35e149

   1. Initial program 97.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 88.0%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+35} \lor \neg \left(z \leq 1.35 \cdot 10^{+149}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+17} \lor \neg \left(y \leq 10^{+17}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.6e+17) (not (<= y 1e+17)))
   (+ x (* y (/ t (- a z))))
   (+ x (* z (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.6e+17) || !(y <= 1e+17)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (z * (t / (z - 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 ((y <= (-5.6d+17)) .or. (.not. (y <= 1d+17))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (z * (t / (z - 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 ((y <= -5.6e+17) || !(y <= 1e+17)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (z * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.6e+17) or not (y <= 1e+17):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (z * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.6e+17) || !(y <= 1e+17))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.6e+17) || ~((y <= 1e+17)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (z * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.6e+17], N[Not[LessEqual[y, 1e+17]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e17 or 1e17 < y

   1. Initial program 86.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around inf 83.4%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

   7. Simplified 88.2%

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

   if -5.6e17 < y < 1e17

   1. Initial program 90.8%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. mul-1-neg 82.3%

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

      3. distribute-rgt-neg-out 82.3%

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

      4. associate-*l/ 88.4%

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

   7. Simplified 88.4%

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

      1. associate-*l/ 82.3%

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

      2. frac-2neg 82.3%

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

      3. add-sqr-sqrt 43.4%

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

      4. sqrt-unprod 57.5%

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

      5. sqr-neg 57.5%

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

      6. sqrt-unprod 26.9%

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

      7. add-sqr-sqrt 58.5%

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

      8. distribute-rgt-neg-out 58.5%

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

      9. *-commutative 58.5%

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

      10. add-sqr-sqrt 31.6%

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

      11. sqrt-unprod 53.9%

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

      12. sqr-neg 53.9%

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

      13. sqrt-unprod 38.8%

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

      14. add-sqr-sqrt 82.3%

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

      15. sub-neg 82.3%

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

      16. distribute-neg-in 82.3%

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

      17. add-sqr-sqrt 43.4%

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

      18. sqrt-unprod 71.1%

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

      19. sqr-neg 71.1%

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

      20. sqrt-unprod 29.1%

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

      21. add-sqr-sqrt 64.7%

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

      22. add-sqr-sqrt 35.6%

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

      23. sqrt-unprod 68.5%

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

      24. sqr-neg 68.5%

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

   9. Applied egg-rr 82.3%

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

       1. associate-/l* 88.4%

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

       2. +-commutative 88.4%

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

       3. unsub-neg 88.4%

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

   11. Simplified 88.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+17} \lor \neg \left(y \leq 10^{+17}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+19} \lor \neg \left(y \leq 5.2 \cdot 10^{+17}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.4e+19) (not (<= y 5.2e+17)))
   (+ x (* y (/ t (- a z))))
   (+ x (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.4e+19) || !(y <= 5.2e+17)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * (z / (z - 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 ((y <= (-6.4d+19)) .or. (.not. (y <= 5.2d+17))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (t * (z / (z - 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 ((y <= -6.4e+19) || !(y <= 5.2e+17)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.4e+19) or not (y <= 5.2e+17):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (t * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.4e+19) || !(y <= 5.2e+17))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.4e+19) || ~((y <= 5.2e+17)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (t * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.4e+19], N[Not[LessEqual[y, 5.2e+17]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e19 or 5.2e17 < y

   1. Initial program 86.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around inf 83.4%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

   7. Simplified 88.2%

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

   if -6.4e19 < y < 5.2e17

   1. Initial program 90.8%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

      3. associate-/l* 90.7%

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

   7. Simplified 90.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+19} \lor \neg \left(y \leq 5.2 \cdot 10^{+17}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-33} \lor \neg \left(z \leq 9.8 \cdot 10^{-32}\right):\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e-33) (not (<= z 9.8e-32)))
   (+ x (* t (/ (- z y) z)))
   (+ x (/ (* y t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e-33) || !(z <= 9.8e-32)) {
		tmp = x + (t * ((z - y) / z));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.55d-33)) .or. (.not. (z <= 9.8d-32))) then
        tmp = x + (t * ((z - y) / z))
    else
        tmp = x + ((y * t) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e-33) || !(z <= 9.8e-32)) {
		tmp = x + (t * ((z - y) / z));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e-33) or not (z <= 9.8e-32):
		tmp = x + (t * ((z - y) / z))
	else:
		tmp = x + ((y * t) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e-33) || !(z <= 9.8e-32))
		tmp = Float64(x + Float64(t * Float64(Float64(z - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.55e-33) || ~((z <= 9.8e-32)))
		tmp = x + (t * ((z - y) / z));
	else
		tmp = x + ((y * t) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e-33], N[Not[LessEqual[z, 9.8e-32]], $MachinePrecision]], N[(x + N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999998e-33 or 9.7999999999999996e-32 < z

   1. Initial program 79.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in a around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. associate-/l* 90.0%

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

   7. Simplified 90.0%

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

   if -1.54999999999999998e-33 < z < 9.7999999999999996e-32

   1. Initial program 99.0%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 92.7%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-33} \lor \neg \left(z \leq 9.8 \cdot 10^{-32}\right):\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-33} \lor \neg \left(z \leq 7.5 \cdot 10^{-32}\right):\\ \;\;\;\;x + \frac{t}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e-33) (not (<= z 7.5e-32)))
   (+ x (/ t (/ z (- z y))))
   (+ x (/ (* y t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e-33) || !(z <= 7.5e-32)) {
		tmp = x + (t / (z / (z - y)));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.55d-33)) .or. (.not. (z <= 7.5d-32))) then
        tmp = x + (t / (z / (z - y)))
    else
        tmp = x + ((y * t) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e-33) || !(z <= 7.5e-32)) {
		tmp = x + (t / (z / (z - y)));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e-33) or not (z <= 7.5e-32):
		tmp = x + (t / (z / (z - y)))
	else:
		tmp = x + ((y * t) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e-33) || !(z <= 7.5e-32))
		tmp = Float64(x + Float64(t / Float64(z / Float64(z - y))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.55e-33) || ~((z <= 7.5e-32)))
		tmp = x + (t / (z / (z - y)));
	else
		tmp = x + ((y * t) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e-33], N[Not[LessEqual[z, 7.5e-32]], $MachinePrecision]], N[(x + N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999998e-33 or 7.49999999999999953e-32 < z

   1. Initial program 79.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in a around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. associate-/l* 90.0%

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

   7. Simplified 90.0%

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

      1. clear-num 90.0%

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

      2. un-div-inv 90.0%

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

   9. Applied egg-rr 90.0%

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

   if -1.54999999999999998e-33 < z < 7.49999999999999953e-32

   1. Initial program 99.0%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 92.7%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-33} \lor \neg \left(z \leq 7.5 \cdot 10^{-32}\right):\\ \;\;\;\;x + \frac{t}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-34} \lor \neg \left(z \leq 4.6 \cdot 10^{-32}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.4e-34) (not (<= z 4.6e-32))) (+ t x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.4e-34) || !(z <= 4.6e-32)) {
		tmp = t + x;
	} 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 <= (-7.4d-34)) .or. (.not. (z <= 4.6d-32))) then
        tmp = t + x
    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 <= -7.4e-34) || !(z <= 4.6e-32)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.4e-34) or not (z <= 4.6e-32):
		tmp = t + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.4e-34) || !(z <= 4.6e-32))
		tmp = Float64(t + x);
	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 <= -7.4e-34) || ~((z <= 4.6e-32)))
		tmp = t + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.4e-34], N[Not[LessEqual[z, 4.6e-32]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.39999999999999976e-34 or 4.6000000000000001e-32 < z

   1. Initial program 79.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 76.9%

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

   if -7.39999999999999976e-34 < z < 4.6000000000000001e-32

   1. Initial program 99.0%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

      1. clear-num 95.8%

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

      2. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in z around 0 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*r/ 80.6%

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

   9. Simplified 80.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-34} \lor \neg \left(z \leq 4.6 \cdot 10^{-32}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-34} \lor \neg \left(z \leq 7.5 \cdot 10^{-32}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.55e-34) (not (<= z 7.5e-32))) (+ t x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.55e-34) || !(z <= 7.5e-32)) {
		tmp = t + x;
	} 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 <= (-3.55d-34)) .or. (.not. (z <= 7.5d-32))) then
        tmp = t + x
    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 <= -3.55e-34) || !(z <= 7.5e-32)) {
		tmp = t + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.55e-34) or not (z <= 7.5e-32):
		tmp = t + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.55e-34) || !(z <= 7.5e-32))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.55e-34) || ~((z <= 7.5e-32)))
		tmp = t + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.55e-34], N[Not[LessEqual[z, 7.5e-32]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.55000000000000018e-34 or 7.49999999999999953e-32 < z

   1. Initial program 79.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 76.9%

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

   if -3.55000000000000018e-34 < z < 7.49999999999999953e-32

   1. Initial program 99.0%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around 0 82.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-34} \lor \neg \left(z \leq 7.5 \cdot 10^{-32}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.96 \cdot 10^{+182}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.45e+197) x (if (<= a 1.96e+182) (+ t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e+197) {
		tmp = x;
	} else if (a <= 1.96e+182) {
		tmp = t + x;
	} 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 <= (-2.45d+197)) then
        tmp = x
    else if (a <= 1.96d+182) then
        tmp = t + x
    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 <= -2.45e+197) {
		tmp = x;
	} else if (a <= 1.96e+182) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.45e+197:
		tmp = x
	elif a <= 1.96e+182:
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.45e+197)
		tmp = x;
	elseif (a <= 1.96e+182)
		tmp = Float64(t + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.45e+197)
		tmp = x;
	elseif (a <= 1.96e+182)
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.45e+197], x, If[LessEqual[a, 1.96e+182], N[(t + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.45000000000000013e197 or 1.95999999999999993e182 < a

   1. Initial program 91.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.1%

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

   if -2.45000000000000013e197 < a < 1.95999999999999993e182

   1. Initial program 88.0%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around inf 65.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.96 \cdot 10^{+182}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

   1. associate-/l* 96.1%

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

3. Simplified 96.1%

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

5. Final simplification 96.1%

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

Alternative 12: 50.5% 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 88.6%

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

   1. associate-/l* 96.1%

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

3. Simplified 96.1%

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

5. Taylor expanded in x around inf 53.0%

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

6. Final simplification 53.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% 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 2024053 
(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))))