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

Percentage Accurate: 85.8% → 99.2%

Time: 10.1s

Alternatives: 13

Speedup: 0.6×

Specification

Math

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

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 * Float64(z - 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 * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.8% accurate, 1.0× speedup

Math

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

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 * Float64(z - 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 * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+256}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 -5e+256)
     (fma (/ y (- z a)) (- z t) x)
     (if (<= t_1 2e+263)
       (- x (/ (* y (- t z)) (- z a)))
       (+ x (/ (- z t) (/ (- z a) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -5e+256) {
		tmp = fma((y / (z - a)), (z - t), x);
	} else if (t_1 <= 2e+263) {
		tmp = x - ((y * (t - z)) / (z - a));
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+256)
		tmp = fma(Float64(y / Float64(z - a)), Float64(z - t), x);
	elseif (t_1 <= 2e+263)
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+256], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+263], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -5.00000000000000015e256

   1. Initial program 46.7%

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

      1. +-commutative 46.7%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   if -5.00000000000000015e256 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000003e263

   1. Initial program 99.6%

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

   if 2.00000000000000003e263 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -5 \cdot 10^{+256}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+263}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+305} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+263}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -2e+305) (not (<= t_1 2e+263)))
     (+ x (/ (- z t) (/ (- z a) y)))
     (- x (/ (* y (- t z)) (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -2e+305) || !(t_1 <= 2e+263)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x - ((y * (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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (z - a)
    if ((t_1 <= (-2d+305)) .or. (.not. (t_1 <= 2d+263))) then
        tmp = x + ((z - t) / ((z - a) / y))
    else
        tmp = x - ((y * (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 t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -2e+305) || !(t_1 <= 2e+263)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x - ((y * (t - z)) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -2e+305) or not (t_1 <= 2e+263):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = x - ((y * (t - z)) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -2e+305) || !(t_1 <= 2e+263))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -2e+305) || ~((t_1 <= 2e+263)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = x - ((y * (t - z)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+305], N[Not[LessEqual[t$95$1, 2e+263]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -1.9999999999999999e305 or 2.00000000000000003e263 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 43.1%

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

      1. *-commutative 43.1%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -1.9999999999999999e305 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000003e263

   1. Initial program 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -2 \cdot 10^{+305} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+263}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+79} \lor \neg \left(z \leq 1.85 \cdot 10^{+113}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e+79) (not (<= z 1.85e+113)))
   (+ x (/ y (/ (- z a) z)))
   (- x (/ (* y (- t z)) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+79) || !(z <= 1.85e+113)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - ((y * (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 ((z <= (-7d+79)) .or. (.not. (z <= 1.85d+113))) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x - ((y * (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 ((z <= -7e+79) || !(z <= 1.85e+113)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - ((y * (t - z)) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e+79) or not (z <= 1.85e+113):
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x - ((y * (t - z)) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e+79) || !(z <= 1.85e+113))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7e+79) || ~((z <= 1.85e+113)))
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x - ((y * (t - z)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7e+79], N[Not[LessEqual[z, 1.85e+113]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999961e79 or 1.8499999999999999e113 < z

   1. Initial program 62.0%

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

      1. +-commutative 62.0%

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

      2. associate-*l/ 95.1%

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

      3. fma-def 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t around 0 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-/l* 95.9%

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

   7. Simplified 95.9%

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

   if -6.99999999999999961e79 < z < 1.8499999999999999e113

   1. Initial program 96.8%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+79} \lor \neg \left(z \leq 1.85 \cdot 10^{+113}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -32000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -32000000.0) (not (<= z 2.35e+111)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -32000000.0) || !(z <= 2.35e+111)) {
		tmp = x + (y * (1.0 - (t / z)));
	} 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 <= (-32000000.0d0)) .or. (.not. (z <= 2.35d+111))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    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 <= -32000000.0) || !(z <= 2.35e+111)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -32000000.0) or not (z <= 2.35e+111):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -32000000.0) || !(z <= 2.35e+111))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	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 <= -32000000.0) || ~((z <= 2.35e+111)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -32000000.0], N[Not[LessEqual[z, 2.35e+111]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e7 or 2.35000000000000004e111 < z

   1. Initial program 66.4%

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

      1. +-commutative 66.4%

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

      2. associate-*l/ 95.8%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in a around 0 61.5%

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

      1. +-commutative 61.5%

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

      2. associate-/l* 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

      3. associate-*r/ 92.1%

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

   10. Simplified 92.1%

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

   11. Taylor expanded in y around 0 92.1%

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

   if -3.2e7 < z < 2.35000000000000004e111

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 79.3%

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

      3. associate-/r/ 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -32000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.445 \lor \neg \left(z \leq 2.9 \cdot 10^{+28}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.445) (not (<= z 2.9e+28)))
   (+ x (/ y (/ (- z a) z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.445) || !(z <= 2.9e+28)) {
		tmp = x + (y / ((z - a) / z));
	} 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 <= (-0.445d0)) .or. (.not. (z <= 2.9d+28))) then
        tmp = x + (y / ((z - a) / z))
    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 <= -0.445) || !(z <= 2.9e+28)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.445) or not (z <= 2.9e+28):
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.445) || !(z <= 2.9e+28))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	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 <= -0.445) || ~((z <= 2.9e+28)))
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.445], N[Not[LessEqual[z, 2.9e+28]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.445000000000000007 or 2.9000000000000001e28 < z

   1. Initial program 70.8%

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

      1. +-commutative 70.8%

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

      2. associate-*l/ 96.4%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. associate-/l* 92.1%

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

   7. Simplified 92.1%

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

   if -0.445000000000000007 < z < 2.9000000000000001e28

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-*l/ 96.4%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-/l* 79.4%

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

      3. associate-/r/ 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.445 \lor \neg \left(z \leq 2.9 \cdot 10^{+28}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.9 \cdot 10^{+39} \lor \neg \left(z \leq 1.02 \cdot 10^{+113}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.9e+39) (not (<= z 1.02e+113)))
   (+ x (/ y (/ (- z a) z)))
   (- x (* t (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.9e+39) || !(z <= 1.02e+113)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - (t * (y / (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 ((z <= (-9.9d+39)) .or. (.not. (z <= 1.02d+113))) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x - (t * (y / (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 ((z <= -9.9e+39) || !(z <= 1.02e+113)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.9e+39) or not (z <= 1.02e+113):
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.9e+39) || !(z <= 1.02e+113))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.9e+39) || ~((z <= 1.02e+113)))
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.9e+39], N[Not[LessEqual[z, 1.02e+113]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9e39 or 1.02000000000000002e113 < z

   1. Initial program 65.2%

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

      1. +-commutative 65.2%

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

      2. associate-*l/ 95.5%

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

      3. fma-def 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around 0 65.6%

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

      1. +-commutative 65.6%

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

      2. associate-/l* 96.3%

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

   7. Simplified 96.3%

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

   if -9.9e39 < z < 1.02000000000000002e113

   1. Initial program 96.6%

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

   3. Taylor expanded in t around inf 86.6%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

      3. distribute-lft-neg-in 87.0%

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

      4. *-commutative 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.9 \cdot 10^{+39} \lor \neg \left(z \leq 1.02 \cdot 10^{+113}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -38000000:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -38000000.0)
   (+ x (- y (* t (/ y z))))
   (if (<= z 2.35e+111) (+ x (* y (/ t a))) (+ x (* y (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -38000000.0) {
		tmp = x + (y - (t * (y / z)));
	} else if (z <= 2.35e+111) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * (1.0 - (t / 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 <= (-38000000.0d0)) then
        tmp = x + (y - (t * (y / z)))
    else if (z <= 2.35d+111) then
        tmp = x + (y * (t / a))
    else
        tmp = x + (y * (1.0d0 - (t / 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 <= -38000000.0) {
		tmp = x + (y - (t * (y / z)));
	} else if (z <= 2.35e+111) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -38000000.0:
		tmp = x + (y - (t * (y / z)))
	elif z <= 2.35e+111:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -38000000.0)
		tmp = Float64(x + Float64(y - Float64(t * Float64(y / z))));
	elseif (z <= 2.35e+111)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -38000000.0)
		tmp = x + (y - (t * (y / z)));
	elseif (z <= 2.35e+111)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -38000000.0], N[(x + N[(y - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+111], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e7

   1. Initial program 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-*l/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. associate-/l* 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

      3. associate-*r/ 88.7%

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

   10. Simplified 88.7%

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

   if -3.8e7 < z < 2.35000000000000004e111

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 79.3%

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

      3. associate-/r/ 81.0%

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

   7. Simplified 81.0%

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

   if 2.35000000000000004e111 < z

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*l/ 91.3%

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

      3. fma-def 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in a around 0 59.7%

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

      1. +-commutative 59.7%

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

      2. associate-/l* 96.0%

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

   7. Simplified 96.0%

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

   8. Taylor expanded in z around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

      3. associate-*r/ 95.9%

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

   10. Simplified 95.9%

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

   11. Taylor expanded in y around 0 96.0%

       \[\leadsto \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -38000000:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -140000000:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -140000000.0)
   (+ x (- y (* t (/ y z))))
   (if (<= z 4.2e+18) (+ x (* (/ y a) (- t z))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -140000000.0) {
		tmp = x + (y - (t * (y / z)));
	} else if (z <= 4.2e+18) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x + (y / ((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 (z <= (-140000000.0d0)) then
        tmp = x + (y - (t * (y / z)))
    else if (z <= 4.2d+18) then
        tmp = x + ((y / a) * (t - z))
    else
        tmp = x + (y / ((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 (z <= -140000000.0) {
		tmp = x + (y - (t * (y / z)));
	} else if (z <= 4.2e+18) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -140000000.0:
		tmp = x + (y - (t * (y / z)))
	elif z <= 4.2e+18:
		tmp = x + ((y / a) * (t - z))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -140000000.0)
		tmp = Float64(x + Float64(y - Float64(t * Float64(y / z))));
	elseif (z <= 4.2e+18)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -140000000.0)
		tmp = x + (y - (t * (y / z)));
	elseif (z <= 4.2e+18)
		tmp = x + ((y / a) * (t - z));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -140000000.0], N[(x + N[(y - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+18], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e8

   1. Initial program 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-*l/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. associate-/l* 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

      3. associate-*r/ 88.7%

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

   10. Simplified 88.7%

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

   if -1.4e8 < z < 4.2e18

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-*l/ 96.4%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

      3. associate-/l* 84.6%

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

      4. associate-/r/ 83.9%

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

   7. Simplified 83.9%

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

   if 4.2e18 < z

   1. Initial program 72.2%

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

      1. +-commutative 72.2%

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

      2. associate-*l/ 93.7%

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

      3. fma-def 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around 0 72.2%

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

      1. +-commutative 72.2%

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

      2. associate-/l* 94.1%

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

   7. Simplified 94.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140000000:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -32000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -32000000.0) (not (<= z 2.35e+111)))
   (+ y x)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -32000000.0) || !(z <= 2.35e+111)) {
		tmp = y + x;
	} 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 <= (-32000000.0d0)) .or. (.not. (z <= 2.35d+111))) then
        tmp = y + x
    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 <= -32000000.0) || !(z <= 2.35e+111)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -32000000.0) or not (z <= 2.35e+111):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -32000000.0) || !(z <= 2.35e+111))
		tmp = Float64(y + x);
	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 <= -32000000.0) || ~((z <= 2.35e+111)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -32000000.0], N[Not[LessEqual[z, 2.35e+111]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e7 or 2.35000000000000004e111 < z

   1. Initial program 66.4%

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

      1. +-commutative 66.4%

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

      2. associate-*l/ 95.8%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 85.9%

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

      1. +-commutative 85.9%

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

   7. Simplified 85.9%

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

   if -3.2e7 < z < 2.35000000000000004e111

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 79.3%

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

      3. associate-/r/ 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in t around 0 79.1%

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

      1. associate-*r/ 79.2%

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

   10. Simplified 79.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -32000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -80000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -80000000.0) (not (<= z 2.35e+111)))
   (+ y x)
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -80000000.0) || !(z <= 2.35e+111)) {
		tmp = y + 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 <= (-80000000.0d0)) .or. (.not. (z <= 2.35d+111))) then
        tmp = y + 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 <= -80000000.0) || !(z <= 2.35e+111)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -80000000.0) or not (z <= 2.35e+111):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -80000000.0) || !(z <= 2.35e+111))
		tmp = Float64(y + 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 <= -80000000.0) || ~((z <= 2.35e+111)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -80000000.0], N[Not[LessEqual[z, 2.35e+111]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e7 or 2.35000000000000004e111 < z

   1. Initial program 66.4%

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

      1. +-commutative 66.4%

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

      2. associate-*l/ 95.8%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 85.9%

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

      1. +-commutative 85.9%

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

   7. Simplified 85.9%

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

   if -8e7 < z < 2.35000000000000004e111

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 79.3%

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

      3. associate-/r/ 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -80000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -35000000:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -35000000.0)
   (+ x (/ (- z t) (/ z y)))
   (if (<= z 2.35e+111) (+ x (* y (/ t a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -35000000.0) {
		tmp = x + ((z - t) / (z / y));
	} else if (z <= 2.35e+111) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + 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 <= (-35000000.0d0)) then
        tmp = x + ((z - t) / (z / y))
    else if (z <= 2.35d+111) then
        tmp = x + (y * (t / a))
    else
        tmp = y + 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 <= -35000000.0) {
		tmp = x + ((z - t) / (z / y));
	} else if (z <= 2.35e+111) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -35000000.0:
		tmp = x + ((z - t) / (z / y))
	elif z <= 2.35e+111:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -35000000.0)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	elseif (z <= 2.35e+111)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -35000000.0)
		tmp = x + ((z - t) / (z / y));
	elseif (z <= 2.35e+111)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -35000000.0], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+111], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e7

   1. Initial program 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 88.5%

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

   if -3.5e7 < z < 2.35000000000000004e111

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 79.3%

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

      3. associate-/r/ 81.0%

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

   7. Simplified 81.0%

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

   if 2.35000000000000004e111 < z

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*l/ 91.3%

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

      3. fma-def 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 93.9%

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

      1. +-commutative 93.9%

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

   7. Simplified 93.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -35000000:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -8.8e+91) x (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+91) {
		tmp = x;
	} else {
		tmp = y + 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 <= (-8.8d+91)) then
        tmp = x
    else
        tmp = y + 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 <= -8.8e+91) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.8e+91:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.8e+91)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.8e+91)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.8e+91], x, N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.79999999999999998e91

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-*l/ 97.7%

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

      3. fma-def 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around 0 73.2%

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

   if -8.79999999999999998e91 < a

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-*l/ 96.2%

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

      3. fma-def 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around inf 60.6%

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

      1. +-commutative 60.6%

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

   7. Simplified 60.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.7% 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 85.2%

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

   1. +-commutative 85.2%

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

   2. associate-*l/ 96.4%

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

   3. fma-def 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in y around 0 51.9%

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

6. Final simplification 51.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))