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

Percentage Accurate: 85.2% → 99.6%

Time: 14.9s

Alternatives: 23

Speedup: 0.5×

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: 85.2% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{z - a} + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- z t) (/ y (- z a))))
     (if (<= t_1 4e+307) (+ x t_1) (* y (+ (/ (- z t) (- z a)) (/ x 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 <= -((double) INFINITY)) {
		tmp = x + ((z - t) * (y / (z - a)));
	} else if (t_1 <= 4e+307) {
		tmp = x + t_1;
	} else {
		tmp = y * (((z - t) / (z - a)) + (x / y));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((z - t) * (y / (z - a)));
	} else if (t_1 <= 4e+307) {
		tmp = x + t_1;
	} else {
		tmp = y * (((z - t) / (z - a)) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - t) * (y / (z - a)))
	elif t_1 <= 4e+307:
		tmp = x + t_1
	else:
		tmp = y * (((z - t) / (z - a)) + (x / 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 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(z - a))));
	elseif (t_1 <= 4e+307)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(z - a)) + Float64(x / y)));
	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 <= -Inf)
		tmp = x + ((z - t) * (y / (z - a)));
	elseif (t_1 <= 4e+307)
		tmp = x + t_1;
	else
		tmp = y * (((z - t) / (z - a)) + (x / y));
	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[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+307], N[(x + t$95$1), $MachinePrecision], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 36.0%

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

      1. +-commutative 36.0%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

      1. fma-undefine 99.7%

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

      2. associate-/l* 36.0%

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

      3. div-inv 36.0%

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

      4. *-commutative 36.0%

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

      5. associate-*r* 99.9%

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

      6. div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 3.99999999999999994e307

   1. Initial program 98.7%

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

   if 3.99999999999999994e307 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 40.0%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{z - a} + \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 83.6%

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

   1. +-commutative 83.6%

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

   2. associate-/l* 97.3%

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

   3. fma-define 97.3%

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

3. Simplified 97.3%

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

5. Final simplification 97.3%

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

Alternative 3: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+300} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -5e+300) (not (<= t_1 4e+307)))
     (/ y (/ (- z a) (- z t)))
     (+ x t_1))))

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+300) || !(t_1 <= 4e+307)) {
		tmp = y / ((z - a) / (z - t));
	} else {
		tmp = x + 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 = (y * (z - t)) / (z - a)
    if ((t_1 <= (-5d+300)) .or. (.not. (t_1 <= 4d+307))) then
        tmp = y / ((z - a) / (z - t))
    else
        tmp = x + 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 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -5e+300) || !(t_1 <= 4e+307)) {
		tmp = y / ((z - a) / (z - t));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -5e+300) or not (t_1 <= 4e+307):
		tmp = y / ((z - a) / (z - t))
	else:
		tmp = x + t_1
	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+300) || !(t_1 <= 4e+307))
		tmp = Float64(y / Float64(Float64(z - a) / Float64(z - t)));
	else
		tmp = Float64(x + t_1);
	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 <= -5e+300) || ~((t_1 <= 4e+307)))
		tmp = y / ((z - a) / (z - t));
	else
		tmp = x + t_1;
	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, -5e+300], N[Not[LessEqual[t$95$1, 4e+307]], $MachinePrecision]], N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -5.00000000000000026e300 or 3.99999999999999994e307 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 40.1%

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

   3. Taylor expanded in y around inf 90.0%

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

      1. sub-div 90.0%

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

      2. clear-num 90.0%

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

      3. un-div-inv 90.1%

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

   5. Applied egg-rr 90.1%

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

   if -5.00000000000000026e300 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 3.99999999999999994e307

   1. Initial program 98.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -5 \cdot 10^{+300} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+307)))
     (+ x (* (- z t) (/ y (- z a))))
     (+ x t_1))))

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 <= -((double) INFINITY)) || !(t_1 <= 4e+307)) {
		tmp = x + ((z - t) * (y / (z - a)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+307)) {
		tmp = x + ((z - t) * (y / (z - a)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+307):
		tmp = x + ((z - t) * (y / (z - a)))
	else:
		tmp = x + t_1
	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 <= Float64(-Inf)) || !(t_1 <= 4e+307))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+307)))
		tmp = x + ((z - t) * (y / (z - a)));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+307]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 3.99999999999999994e307 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 38.2%

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

      1. +-commutative 38.2%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

      1. fma-undefine 99.8%

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

      2. associate-/l* 38.2%

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

      3. div-inv 38.2%

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

      4. *-commutative 38.2%

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

      5. associate-*r* 99.8%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 3.99999999999999994e307

   1. Initial program 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e-18)
   (+ y x)
   (if (<= z -1.05e-253)
     x
     (if (<= z 5.8e-278)
       (/ (* y t) a)
       (if (<= z 1.12e-153)
         x
         (if (<= z 1.15e-133)
           (* y (/ (- t) z))
           (if (<= z 1.48e-118) x (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e-18) {
		tmp = y + x;
	} else if (z <= -1.05e-253) {
		tmp = x;
	} else if (z <= 5.8e-278) {
		tmp = (y * t) / a;
	} else if (z <= 1.12e-153) {
		tmp = x;
	} else if (z <= 1.15e-133) {
		tmp = y * (-t / z);
	} else if (z <= 1.48e-118) {
		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 (z <= (-5.2d-18)) then
        tmp = y + x
    else if (z <= (-1.05d-253)) then
        tmp = x
    else if (z <= 5.8d-278) then
        tmp = (y * t) / a
    else if (z <= 1.12d-153) then
        tmp = x
    else if (z <= 1.15d-133) then
        tmp = y * (-t / z)
    else if (z <= 1.48d-118) 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 (z <= -5.2e-18) {
		tmp = y + x;
	} else if (z <= -1.05e-253) {
		tmp = x;
	} else if (z <= 5.8e-278) {
		tmp = (y * t) / a;
	} else if (z <= 1.12e-153) {
		tmp = x;
	} else if (z <= 1.15e-133) {
		tmp = y * (-t / z);
	} else if (z <= 1.48e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e-18:
		tmp = y + x
	elif z <= -1.05e-253:
		tmp = x
	elif z <= 5.8e-278:
		tmp = (y * t) / a
	elif z <= 1.12e-153:
		tmp = x
	elif z <= 1.15e-133:
		tmp = y * (-t / z)
	elif z <= 1.48e-118:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e-18)
		tmp = Float64(y + x);
	elseif (z <= -1.05e-253)
		tmp = x;
	elseif (z <= 5.8e-278)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.12e-153)
		tmp = x;
	elseif (z <= 1.15e-133)
		tmp = Float64(y * Float64(Float64(-t) / z));
	elseif (z <= 1.48e-118)
		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 (z <= -5.2e-18)
		tmp = y + x;
	elseif (z <= -1.05e-253)
		tmp = x;
	elseif (z <= 5.8e-278)
		tmp = (y * t) / a;
	elseif (z <= 1.12e-153)
		tmp = x;
	elseif (z <= 1.15e-133)
		tmp = y * (-t / z);
	elseif (z <= 1.48e-118)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e-18], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.05e-253], x, If[LessEqual[z, 5.8e-278], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.12e-153], x, If[LessEqual[z, 1.15e-133], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.48e-118], x, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2000000000000001e-18 or 1.4800000000000001e-118 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -5.2000000000000001e-18 < z < -1.0499999999999999e-253 or 5.8e-278 < z < 1.12000000000000005e-153 or 1.15e-133 < z < 1.4800000000000001e-118

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 57.7%

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

   if -1.0499999999999999e-253 < z < 5.8e-278

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-/l* 82.1%

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

      3. fma-define 82.1%

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

   3. Simplified 82.1%

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

      1. clear-num 82.2%

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

      2. associate-/r/ 82.1%

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

   6. Applied egg-rr 82.1%

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

   7. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-frac-neg2 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-/l* 69.6%

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

      5. sub-neg 69.6%

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

      6. mul-1-neg 69.6%

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

      7. distribute-neg-in 69.6%

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

      8. mul-1-neg 69.6%

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

      9. remove-double-neg 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in z around 0 76.4%

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

   if 1.12000000000000005e-153 < z < 1.15e-133

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. distribute-frac-neg2 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-/l* 79.1%

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

      5. sub-neg 79.1%

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

      6. mul-1-neg 79.1%

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

      7. distribute-neg-in 79.1%

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

      8. mul-1-neg 79.1%

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

      9. remove-double-neg 79.1%

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

   9. Simplified 79.1%

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

   10. Taylor expanded in z around inf 68.8%

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

       1. associate-*r/ 68.8%

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

       2. neg-mul-1 68.8%

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

   12. Simplified 68.8%

       \[\leadsto y \cdot \color{blue}{\frac{-t}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-271}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-132}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq 1.88 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e-18)
   (+ y x)
   (if (<= z -9.2e-254)
     x
     (if (<= z 3.2e-271)
       (/ (* y t) a)
       (if (<= z 1.32e-154)
         x
         (if (<= z 1.85e-132)
           (/ (* y (- t)) z)
           (if (<= z 1.88e-118) x (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e-18) {
		tmp = y + x;
	} else if (z <= -9.2e-254) {
		tmp = x;
	} else if (z <= 3.2e-271) {
		tmp = (y * t) / a;
	} else if (z <= 1.32e-154) {
		tmp = x;
	} else if (z <= 1.85e-132) {
		tmp = (y * -t) / z;
	} else if (z <= 1.88e-118) {
		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 (z <= (-1.9d-18)) then
        tmp = y + x
    else if (z <= (-9.2d-254)) then
        tmp = x
    else if (z <= 3.2d-271) then
        tmp = (y * t) / a
    else if (z <= 1.32d-154) then
        tmp = x
    else if (z <= 1.85d-132) then
        tmp = (y * -t) / z
    else if (z <= 1.88d-118) 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 (z <= -1.9e-18) {
		tmp = y + x;
	} else if (z <= -9.2e-254) {
		tmp = x;
	} else if (z <= 3.2e-271) {
		tmp = (y * t) / a;
	} else if (z <= 1.32e-154) {
		tmp = x;
	} else if (z <= 1.85e-132) {
		tmp = (y * -t) / z;
	} else if (z <= 1.88e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e-18:
		tmp = y + x
	elif z <= -9.2e-254:
		tmp = x
	elif z <= 3.2e-271:
		tmp = (y * t) / a
	elif z <= 1.32e-154:
		tmp = x
	elif z <= 1.85e-132:
		tmp = (y * -t) / z
	elif z <= 1.88e-118:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e-18)
		tmp = Float64(y + x);
	elseif (z <= -9.2e-254)
		tmp = x;
	elseif (z <= 3.2e-271)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.32e-154)
		tmp = x;
	elseif (z <= 1.85e-132)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (z <= 1.88e-118)
		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 (z <= -1.9e-18)
		tmp = y + x;
	elseif (z <= -9.2e-254)
		tmp = x;
	elseif (z <= 3.2e-271)
		tmp = (y * t) / a;
	elseif (z <= 1.32e-154)
		tmp = x;
	elseif (z <= 1.85e-132)
		tmp = (y * -t) / z;
	elseif (z <= 1.88e-118)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e-18], N[(y + x), $MachinePrecision], If[LessEqual[z, -9.2e-254], x, If[LessEqual[z, 3.2e-271], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.32e-154], x, If[LessEqual[z, 1.85e-132], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.88e-118], x, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8999999999999999e-18 or 1.88000000000000001e-118 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -1.8999999999999999e-18 < z < -9.1999999999999995e-254 or 3.19999999999999978e-271 < z < 1.31999999999999994e-154 or 1.8500000000000001e-132 < z < 1.88000000000000001e-118

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 57.7%

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

   if -9.1999999999999995e-254 < z < 3.19999999999999978e-271

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-/l* 82.1%

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

      3. fma-define 82.1%

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

   3. Simplified 82.1%

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

      1. clear-num 82.2%

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

      2. associate-/r/ 82.1%

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

   6. Applied egg-rr 82.1%

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

   7. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-frac-neg2 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-/l* 69.6%

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

      5. sub-neg 69.6%

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

      6. mul-1-neg 69.6%

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

      7. distribute-neg-in 69.6%

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

      8. mul-1-neg 69.6%

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

      9. remove-double-neg 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in z around 0 76.4%

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

   if 1.31999999999999994e-154 < z < 1.8500000000000001e-132

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. distribute-frac-neg2 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-/l* 79.1%

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

      5. sub-neg 79.1%

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

      6. mul-1-neg 79.1%

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

      7. distribute-neg-in 79.1%

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

      8. mul-1-neg 79.1%

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

      9. remove-double-neg 79.1%

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

   9. Simplified 79.1%

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

   10. Taylor expanded in z around inf 68.9%

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

       1. associate-*r/ 68.9%

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

       2. *-commutative 68.9%

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

       3. neg-mul-1 68.9%

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

       4. distribute-rgt-neg-in 68.9%

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

   12. Simplified 68.9%

       \[\leadsto \color{blue}{\frac{y \cdot \left(-t\right)}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-271}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-132}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq 1.88 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ t_2 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{-141}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ t z)))) (t_2 (* t (/ y (- a z)))))
   (if (<= x -1.02e-141)
     (+ y x)
     (if (<= x -5.4e-186)
       t_2
       (if (<= x -2.3e-254)
         t_1
         (if (<= x 5.5e-231) t_2 (if (<= x 5e-14) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double t_2 = t * (y / (a - z));
	double tmp;
	if (x <= -1.02e-141) {
		tmp = y + x;
	} else if (x <= -5.4e-186) {
		tmp = t_2;
	} else if (x <= -2.3e-254) {
		tmp = t_1;
	} else if (x <= 5.5e-231) {
		tmp = t_2;
	} else if (x <= 5e-14) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (1.0d0 - (t / z))
    t_2 = t * (y / (a - z))
    if (x <= (-1.02d-141)) then
        tmp = y + x
    else if (x <= (-5.4d-186)) then
        tmp = t_2
    else if (x <= (-2.3d-254)) then
        tmp = t_1
    else if (x <= 5.5d-231) then
        tmp = t_2
    else if (x <= 5d-14) then
        tmp = t_1
    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 t_1 = y * (1.0 - (t / z));
	double t_2 = t * (y / (a - z));
	double tmp;
	if (x <= -1.02e-141) {
		tmp = y + x;
	} else if (x <= -5.4e-186) {
		tmp = t_2;
	} else if (x <= -2.3e-254) {
		tmp = t_1;
	} else if (x <= 5.5e-231) {
		tmp = t_2;
	} else if (x <= 5e-14) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (t / z))
	t_2 = t * (y / (a - z))
	tmp = 0
	if x <= -1.02e-141:
		tmp = y + x
	elif x <= -5.4e-186:
		tmp = t_2
	elif x <= -2.3e-254:
		tmp = t_1
	elif x <= 5.5e-231:
		tmp = t_2
	elif x <= 5e-14:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(t / z)))
	t_2 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (x <= -1.02e-141)
		tmp = Float64(y + x);
	elseif (x <= -5.4e-186)
		tmp = t_2;
	elseif (x <= -2.3e-254)
		tmp = t_1;
	elseif (x <= 5.5e-231)
		tmp = t_2;
	elseif (x <= 5e-14)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (t / z));
	t_2 = t * (y / (a - z));
	tmp = 0.0;
	if (x <= -1.02e-141)
		tmp = y + x;
	elseif (x <= -5.4e-186)
		tmp = t_2;
	elseif (x <= -2.3e-254)
		tmp = t_1;
	elseif (x <= 5.5e-231)
		tmp = t_2;
	elseif (x <= 5e-14)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e-141], N[(y + x), $MachinePrecision], If[LessEqual[x, -5.4e-186], t$95$2, If[LessEqual[x, -2.3e-254], t$95$1, If[LessEqual[x, 5.5e-231], t$95$2, If[LessEqual[x, 5e-14], t$95$1, N[(y + x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e-141 or 5.0000000000000002e-14 < x

   1. Initial program 86.3%

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

   3. Taylor expanded in z around inf 74.7%

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

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -1.02e-141 < x < -5.3999999999999998e-186 or -2.2999999999999999e-254 < x < 5.49999999999999951e-231

   1. Initial program 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/l* 95.1%

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

      3. fma-define 95.1%

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

   3. Simplified 95.1%

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

      1. clear-num 93.8%

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

      2. associate-/r/ 94.8%

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

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in t around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. distribute-frac-neg2 51.4%

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

      3. *-commutative 51.4%

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

      4. associate-/l* 60.6%

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

      5. sub-neg 60.6%

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

      6. mul-1-neg 60.6%

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

      7. distribute-neg-in 60.6%

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

      8. mul-1-neg 60.6%

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

      9. remove-double-neg 60.6%

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

   9. Simplified 60.6%

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

   10. Taylor expanded in y around 0 51.4%

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

       1. associate-/l* 60.2%

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

   12. Simplified 60.2%

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

   if -5.3999999999999998e-186 < x < -2.2999999999999999e-254 or 5.49999999999999951e-231 < x < 5.0000000000000002e-14

   1. Initial program 78.4%

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

   3. Taylor expanded in y around inf 76.3%

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

   4. Taylor expanded in a around 0 61.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-141}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= z -1.02e-8)
     (+ y x)
     (if (<= z -2.9e-254)
       x
       (if (<= z 1.22e-265)
         t_1
         (if (<= z 6.2e-165) x (if (<= z 7.2e-133) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -1.02e-8) {
		tmp = y + x;
	} else if (z <= -2.9e-254) {
		tmp = x;
	} else if (z <= 1.22e-265) {
		tmp = t_1;
	} else if (z <= 6.2e-165) {
		tmp = x;
	} else if (z <= 7.2e-133) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (z <= (-1.02d-8)) then
        tmp = y + x
    else if (z <= (-2.9d-254)) then
        tmp = x
    else if (z <= 1.22d-265) then
        tmp = t_1
    else if (z <= 6.2d-165) then
        tmp = x
    else if (z <= 7.2d-133) then
        tmp = t_1
    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 t_1 = y * (t / a);
	double tmp;
	if (z <= -1.02e-8) {
		tmp = y + x;
	} else if (z <= -2.9e-254) {
		tmp = x;
	} else if (z <= 1.22e-265) {
		tmp = t_1;
	} else if (z <= 6.2e-165) {
		tmp = x;
	} else if (z <= 7.2e-133) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if z <= -1.02e-8:
		tmp = y + x
	elif z <= -2.9e-254:
		tmp = x
	elif z <= 1.22e-265:
		tmp = t_1
	elif z <= 6.2e-165:
		tmp = x
	elif z <= 7.2e-133:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (z <= -1.02e-8)
		tmp = Float64(y + x);
	elseif (z <= -2.9e-254)
		tmp = x;
	elseif (z <= 1.22e-265)
		tmp = t_1;
	elseif (z <= 6.2e-165)
		tmp = x;
	elseif (z <= 7.2e-133)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (z <= -1.02e-8)
		tmp = y + x;
	elseif (z <= -2.9e-254)
		tmp = x;
	elseif (z <= 1.22e-265)
		tmp = t_1;
	elseif (z <= 6.2e-165)
		tmp = x;
	elseif (z <= 7.2e-133)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e-8], N[(y + x), $MachinePrecision], If[LessEqual[z, -2.9e-254], x, If[LessEqual[z, 1.22e-265], t$95$1, If[LessEqual[z, 6.2e-165], x, If[LessEqual[z, 7.2e-133], t$95$1, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02000000000000003e-8 or 7.2000000000000008e-133 < z

   1. Initial program 77.1%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. +-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -1.02000000000000003e-8 < z < -2.9e-254 or 1.22e-265 < z < 6.19999999999999992e-165

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 54.8%

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

   if -2.9e-254 < z < 1.22e-265 or 6.19999999999999992e-165 < z < 7.2000000000000008e-133

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-/l* 91.8%

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

      3. fma-define 91.8%

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

   3. Simplified 91.8%

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

      1. clear-num 91.9%

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

      2. associate-/r/ 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in t around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. distribute-frac-neg2 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-/l* 75.9%

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

      5. sub-neg 75.9%

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

      6. mul-1-neg 75.9%

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

      7. distribute-neg-in 75.9%

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

      8. mul-1-neg 75.9%

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

      9. remove-double-neg 75.9%

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

   9. Simplified 75.9%

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

   10. Taylor expanded in z around 0 66.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-265}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-142} \lor \neg \left(x \leq 4.8 \cdot 10^{-196}\right) \land \left(x \leq 1.4 \cdot 10^{-151} \lor \neg \left(x \leq 1.02 \cdot 10^{-116}\right)\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.3e-142)
         (and (not (<= x 4.8e-196))
              (or (<= x 1.4e-151) (not (<= x 1.02e-116)))))
   (+ x (* z (/ y (- z a))))
   (* y (/ (- z t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.3e-142) || (!(x <= 4.8e-196) && ((x <= 1.4e-151) || !(x <= 1.02e-116)))) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = y * ((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 ((x <= (-1.3d-142)) .or. (.not. (x <= 4.8d-196)) .and. (x <= 1.4d-151) .or. (.not. (x <= 1.02d-116))) then
        tmp = x + (z * (y / (z - a)))
    else
        tmp = y * ((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 ((x <= -1.3e-142) || (!(x <= 4.8e-196) && ((x <= 1.4e-151) || !(x <= 1.02e-116)))) {
		tmp = x + (z * (y / (z - a)));
	} else {
		tmp = y * ((z - t) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.3e-142) or (not (x <= 4.8e-196) and ((x <= 1.4e-151) or not (x <= 1.02e-116))):
		tmp = x + (z * (y / (z - a)))
	else:
		tmp = y * ((z - t) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.3e-142) || (!(x <= 4.8e-196) && ((x <= 1.4e-151) || !(x <= 1.02e-116))))
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.3e-142) || (~((x <= 4.8e-196)) && ((x <= 1.4e-151) || ~((x <= 1.02e-116)))))
		tmp = x + (z * (y / (z - a)));
	else
		tmp = y * ((z - t) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.3e-142], And[N[Not[LessEqual[x, 4.8e-196]], $MachinePrecision], Or[LessEqual[x, 1.4e-151], N[Not[LessEqual[x, 1.02e-116]], $MachinePrecision]]]], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e-142 or 4.80000000000000041e-196 < x < 1.4e-151 or 1.02e-116 < x

   1. Initial program 86.9%

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

      1. +-commutative 86.9%

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

      2. associate-/l* 97.8%

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

      3. fma-define 97.8%

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

   3. Simplified 97.8%

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

      1. clear-num 97.8%

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

      2. associate-/r/ 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in t around 0 73.0%

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

      1. associate-*l/ 82.1%

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

      2. *-commutative 82.1%

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

   9. Simplified 82.1%

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

   if -1.3e-142 < x < 4.80000000000000041e-196 or 1.4e-151 < x < 1.02e-116

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-/l* 96.1%

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

      3. fma-define 96.1%

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

   3. Simplified 96.1%

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

      1. clear-num 95.1%

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

      2. associate-/r/ 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around inf 83.3%

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

      1. div-sub 83.3%

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

   9. Simplified 83.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-142} \lor \neg \left(x \leq 4.8 \cdot 10^{-196}\right) \land \left(x \leq 1.4 \cdot 10^{-151} \lor \neg \left(x \leq 1.02 \cdot 10^{-116}\right)\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-196} \lor \neg \left(x \leq 5.3 \cdot 10^{-153}\right) \land x \leq 3.3 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.3e-141)
   (+ x (/ z (/ (- z a) y)))
   (if (or (<= x 4.8e-196) (and (not (<= x 5.3e-153)) (<= x 3.3e-115)))
     (* y (/ (- z t) (- z a)))
     (+ x (* z (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.3e-141) {
		tmp = x + (z / ((z - a) / y));
	} else if ((x <= 4.8e-196) || (!(x <= 5.3e-153) && (x <= 3.3e-115))) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (z * (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 (x <= (-4.3d-141)) then
        tmp = x + (z / ((z - a) / y))
    else if ((x <= 4.8d-196) .or. (.not. (x <= 5.3d-153)) .and. (x <= 3.3d-115)) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = x + (z * (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 (x <= -4.3e-141) {
		tmp = x + (z / ((z - a) / y));
	} else if ((x <= 4.8e-196) || (!(x <= 5.3e-153) && (x <= 3.3e-115))) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.3e-141:
		tmp = x + (z / ((z - a) / y))
	elif (x <= 4.8e-196) or (not (x <= 5.3e-153) and (x <= 3.3e-115)):
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.3e-141)
		tmp = Float64(x + Float64(z / Float64(Float64(z - a) / y)));
	elseif ((x <= 4.8e-196) || (!(x <= 5.3e-153) && (x <= 3.3e-115)))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.3e-141)
		tmp = x + (z / ((z - a) / y));
	elseif ((x <= 4.8e-196) || (~((x <= 5.3e-153)) && (x <= 3.3e-115)))
		tmp = y * ((z - t) / (z - a));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.3e-141], N[(x + N[(z / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4.8e-196], And[N[Not[LessEqual[x, 5.3e-153]], $MachinePrecision], LessEqual[x, 3.3e-115]]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.29999999999999974e-141

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. associate-/l* 98.9%

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

      3. fma-define 98.9%

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

   3. Simplified 98.9%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in t around 0 72.9%

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

      1. associate-*l/ 82.9%

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

      2. *-commutative 82.9%

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

   9. Simplified 82.9%

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

       1. clear-num 82.9%

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

       2. un-div-inv 82.9%

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

   11. Applied egg-rr 82.9%

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

   if -4.29999999999999974e-141 < x < 4.80000000000000041e-196 or 5.2999999999999997e-153 < x < 3.2999999999999999e-115

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-/l* 96.1%

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

      3. fma-define 96.1%

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

   3. Simplified 96.1%

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

      1. clear-num 95.1%

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

      2. associate-/r/ 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around inf 83.3%

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

      1. div-sub 83.3%

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

   9. Simplified 83.3%

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

   if 4.80000000000000041e-196 < x < 5.2999999999999997e-153 or 3.2999999999999999e-115 < x

   1. Initial program 87.3%

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

      1. +-commutative 87.3%

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

      2. associate-/l* 96.5%

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

      3. fma-define 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.5%

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

      2. associate-/r/ 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in t around 0 73.1%

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

      1. associate-*l/ 81.1%

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

      2. *-commutative 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-196} \lor \neg \left(x \leq 5.3 \cdot 10^{-153}\right) \land x \leq 3.3 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-13}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ (- z a) y)))))
   (if (<= a -4.1e+61)
     t_1
     (if (<= a 2.1e-13)
       (- x (* y (/ (- t z) z)))
       (if (<= a 7.6e+61)
         (* y (/ (- z t) (- z a)))
         (if (<= a 9e+216) t_1 (+ x (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / ((z - a) / y));
	double tmp;
	if (a <= -4.1e+61) {
		tmp = t_1;
	} else if (a <= 2.1e-13) {
		tmp = x - (y * ((t - z) / z));
	} else if (a <= 7.6e+61) {
		tmp = y * ((z - t) / (z - a));
	} else if (a <= 9e+216) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z / ((z - a) / y))
    if (a <= (-4.1d+61)) then
        tmp = t_1
    else if (a <= 2.1d-13) then
        tmp = x - (y * ((t - z) / z))
    else if (a <= 7.6d+61) then
        tmp = y * ((z - t) / (z - a))
    else if (a <= 9d+216) then
        tmp = t_1
    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 t_1 = x + (z / ((z - a) / y));
	double tmp;
	if (a <= -4.1e+61) {
		tmp = t_1;
	} else if (a <= 2.1e-13) {
		tmp = x - (y * ((t - z) / z));
	} else if (a <= 7.6e+61) {
		tmp = y * ((z - t) / (z - a));
	} else if (a <= 9e+216) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / ((z - a) / y))
	tmp = 0
	if a <= -4.1e+61:
		tmp = t_1
	elif a <= 2.1e-13:
		tmp = x - (y * ((t - z) / z))
	elif a <= 7.6e+61:
		tmp = y * ((z - t) / (z - a))
	elif a <= 9e+216:
		tmp = t_1
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(Float64(z - a) / y)))
	tmp = 0.0
	if (a <= -4.1e+61)
		tmp = t_1;
	elseif (a <= 2.1e-13)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	elseif (a <= 7.6e+61)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	elseif (a <= 9e+216)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / ((z - a) / y));
	tmp = 0.0;
	if (a <= -4.1e+61)
		tmp = t_1;
	elseif (a <= 2.1e-13)
		tmp = x - (y * ((t - z) / z));
	elseif (a <= 7.6e+61)
		tmp = y * ((z - t) / (z - a));
	elseif (a <= 9e+216)
		tmp = t_1;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+61], t$95$1, If[LessEqual[a, 2.1e-13], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+61], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+216], t$95$1, N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.09999999999999972e61 or 7.5999999999999999e61 < a < 9.0000000000000005e216

   1. Initial program 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 97.5%

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

      3. fma-define 97.5%

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

   3. Simplified 97.5%

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

      1. clear-num 96.6%

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

      2. associate-/r/ 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in t around 0 73.1%

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

      1. associate-*l/ 82.8%

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

      2. *-commutative 82.8%

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

   9. Simplified 82.8%

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

       1. clear-num 82.8%

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

       2. un-div-inv 82.8%

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

   11. Applied egg-rr 82.8%

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

   if -4.09999999999999972e61 < a < 2.09999999999999989e-13

   1. Initial program 86.2%

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

   3. Taylor expanded in a around 0 74.6%

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

      1. +-commutative 74.6%

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

      2. associate-/l* 86.1%

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

   5. Simplified 86.1%

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

   if 2.09999999999999989e-13 < a < 7.5999999999999999e61

   1. Initial program 79.8%

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

      1. +-commutative 79.8%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in y around inf 85.7%

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

      1. div-sub 85.7%

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

   9. Simplified 85.7%

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

   if 9.0000000000000005e216 < a

   1. Initial program 77.8%

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

   3. Taylor expanded in z around 0 85.5%

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

      1. +-commutative 85.5%

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

      2. associate-/l* 93.0%

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

   5. Simplified 93.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-13}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+216}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-142} \lor \neg \left(x \leq 6.8 \cdot 10^{-215}\right) \land \left(x \leq 5.3 \cdot 10^{-186} \lor \neg \left(x \leq 1.3 \cdot 10^{-72}\right)\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.36e-142)
         (and (not (<= x 6.8e-215)) (or (<= x 5.3e-186) (not (<= x 1.3e-72)))))
   (+ y x)
   (* t (/ y (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.36e-142) || (!(x <= 6.8e-215) && ((x <= 5.3e-186) || !(x <= 1.3e-72)))) {
		tmp = y + x;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.36d-142)) .or. (.not. (x <= 6.8d-215)) .and. (x <= 5.3d-186) .or. (.not. (x <= 1.3d-72))) then
        tmp = y + x
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.36e-142) || (!(x <= 6.8e-215) && ((x <= 5.3e-186) || !(x <= 1.3e-72)))) {
		tmp = y + x;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.36e-142) or (not (x <= 6.8e-215) and ((x <= 5.3e-186) or not (x <= 1.3e-72))):
		tmp = y + x
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.36e-142) || (!(x <= 6.8e-215) && ((x <= 5.3e-186) || !(x <= 1.3e-72))))
		tmp = Float64(y + x);
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.36e-142) || (~((x <= 6.8e-215)) && ((x <= 5.3e-186) || ~((x <= 1.3e-72)))))
		tmp = y + x;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.36e-142], And[N[Not[LessEqual[x, 6.8e-215]], $MachinePrecision], Or[LessEqual[x, 5.3e-186], N[Not[LessEqual[x, 1.3e-72]], $MachinePrecision]]]], N[(y + x), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35999999999999993e-142 or 6.80000000000000003e-215 < x < 5.30000000000000022e-186 or 1.29999999999999998e-72 < x

   1. Initial program 84.0%

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

   3. Taylor expanded in z around inf 75.6%

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

      1. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   if -1.35999999999999993e-142 < x < 6.80000000000000003e-215 or 5.30000000000000022e-186 < x < 1.29999999999999998e-72

   1. Initial program 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-/l* 93.7%

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

      3. fma-define 93.7%

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

   3. Simplified 93.7%

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

      1. clear-num 92.8%

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

      2. associate-/r/ 93.5%

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

   6. Applied egg-rr 93.5%

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

   7. Taylor expanded in t around inf 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-frac-neg2 45.3%

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

      3. *-commutative 45.3%

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

      4. associate-/l* 51.1%

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

      5. sub-neg 51.1%

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

      6. mul-1-neg 51.1%

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

      7. distribute-neg-in 51.1%

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

      8. mul-1-neg 51.1%

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

      9. remove-double-neg 51.1%

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

   9. Simplified 51.1%

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

   10. Taylor expanded in y around 0 45.3%

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

       1. associate-/l* 52.7%

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

   12. Simplified 52.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-142} \lor \neg \left(x \leq 6.8 \cdot 10^{-215}\right) \land \left(x \leq 5.3 \cdot 10^{-186} \lor \neg \left(x \leq 1.3 \cdot 10^{-72}\right)\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+187}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+187)
   (- x (* y (/ (- t z) z)))
   (if (<= z -9e-8)
     (+ x (* z (/ y (- z a))))
     (if (<= z 4.1e+27) (+ x (/ t (/ (- a z) y))) (- x (/ y (/ z (- t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+187) {
		tmp = x - (y * ((t - z) / z));
	} else if (z <= -9e-8) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 4.1e+27) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (y / (z / (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 <= (-9.8d+187)) then
        tmp = x - (y * ((t - z) / z))
    else if (z <= (-9d-8)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 4.1d+27) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x - (y / (z / (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 <= -9.8e+187) {
		tmp = x - (y * ((t - z) / z));
	} else if (z <= -9e-8) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 4.1e+27) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (y / (z / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+187:
		tmp = x - (y * ((t - z) / z))
	elif z <= -9e-8:
		tmp = x + (z * (y / (z - a)))
	elif z <= 4.1e+27:
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x - (y / (z / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+187)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	elseif (z <= -9e-8)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 4.1e+27)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x - Float64(y / Float64(z / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+187)
		tmp = x - (y * ((t - z) / z));
	elseif (z <= -9e-8)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 4.1e+27)
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x - (y / (z / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+187], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-8], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+27], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.8000000000000006e187

   1. Initial program 57.6%

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

   3. Taylor expanded in a around 0 57.8%

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

      1. +-commutative 57.8%

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

      2. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   if -9.8000000000000006e187 < z < -8.99999999999999986e-8

   1. Initial program 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 78.0%

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

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

   9. Simplified 89.8%

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

   if -8.99999999999999986e-8 < z < 4.1000000000000002e27

   1. Initial program 93.9%

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

   3. Taylor expanded in t around inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. associate-/l* 87.5%

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

      3. distribute-rgt-neg-in 87.5%

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

      4. distribute-frac-neg 87.5%

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

   5. Simplified 87.5%

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

      1. *-commutative 87.5%

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

      2. div-inv 87.5%

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

      3. div-inv 87.5%

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

      4. add-sqr-sqrt 45.5%

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

      5. sqrt-unprod 60.3%

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

      6. sqr-neg 60.3%

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

      7. sqrt-unprod 23.7%

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

      8. add-sqr-sqrt 45.9%

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

      9. cancel-sign-sub 45.9%

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

      10. distribute-frac-neg 45.9%

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

      11. *-commutative 45.9%

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

      12. clear-num 45.9%

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

      13. un-div-inv 45.9%

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

      14. add-sqr-sqrt 22.2%

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

      15. sqrt-unprod 56.8%

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

      16. sqr-neg 56.8%

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

      17. sqrt-unprod 42.0%

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

      18. add-sqr-sqrt 87.5%

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

   7. Applied egg-rr 87.5%

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

   if 4.1000000000000002e27 < z

   1. Initial program 70.0%

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

   3. Taylor expanded in a around 0 66.8%

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

      1. +-commutative 66.8%

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

      2. associate-/l* 92.1%

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

   5. Simplified 92.1%

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

      1. clear-num 92.1%

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

      2. un-div-inv 92.2%

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

   7. Applied egg-rr 92.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+187}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-15}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e-15)
   (+ y x)
   (if (<= z -1.18e-253)
     x
     (if (<= z 3.6e-275) (* t (/ y a)) (if (<= z 2.7e-118) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e-15) {
		tmp = y + x;
	} else if (z <= -1.18e-253) {
		tmp = x;
	} else if (z <= 3.6e-275) {
		tmp = t * (y / a);
	} else if (z <= 2.7e-118) {
		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 (z <= (-4d-15)) then
        tmp = y + x
    else if (z <= (-1.18d-253)) then
        tmp = x
    else if (z <= 3.6d-275) then
        tmp = t * (y / a)
    else if (z <= 2.7d-118) 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 (z <= -4e-15) {
		tmp = y + x;
	} else if (z <= -1.18e-253) {
		tmp = x;
	} else if (z <= 3.6e-275) {
		tmp = t * (y / a);
	} else if (z <= 2.7e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e-15:
		tmp = y + x
	elif z <= -1.18e-253:
		tmp = x
	elif z <= 3.6e-275:
		tmp = t * (y / a)
	elif z <= 2.7e-118:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e-15)
		tmp = Float64(y + x);
	elseif (z <= -1.18e-253)
		tmp = x;
	elseif (z <= 3.6e-275)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 2.7e-118)
		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 (z <= -4e-15)
		tmp = y + x;
	elseif (z <= -1.18e-253)
		tmp = x;
	elseif (z <= 3.6e-275)
		tmp = t * (y / a);
	elseif (z <= 2.7e-118)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e-15], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.18e-253], x, If[LessEqual[z, 3.6e-275], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-118], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000003e-15 or 2.69999999999999994e-118 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -4.0000000000000003e-15 < z < -1.1799999999999999e-253 or 3.5999999999999997e-275 < z < 2.69999999999999994e-118

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 53.4%

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

   if -1.1799999999999999e-253 < z < 3.5999999999999997e-275

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-/l* 82.1%

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

      3. fma-define 82.1%

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

   3. Simplified 82.1%

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

      1. clear-num 82.2%

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

      2. associate-/r/ 82.1%

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

   6. Applied egg-rr 82.1%

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

   7. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-frac-neg2 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-/l* 69.6%

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

      5. sub-neg 69.6%

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

      6. mul-1-neg 69.6%

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

      7. distribute-neg-in 69.6%

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

      8. mul-1-neg 69.6%

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

      9. remove-double-neg 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in z around 0 76.4%

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

       1. associate-/l* 63.1%

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

   12. Simplified 63.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-15}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-12}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-275}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.88 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e-12)
   (+ y x)
   (if (<= z -1.6e-251)
     x
     (if (<= z 2.15e-275) (/ (* y t) a) (if (<= z 1.88e-118) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e-12) {
		tmp = y + x;
	} else if (z <= -1.6e-251) {
		tmp = x;
	} else if (z <= 2.15e-275) {
		tmp = (y * t) / a;
	} else if (z <= 1.88e-118) {
		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 (z <= (-3.15d-12)) then
        tmp = y + x
    else if (z <= (-1.6d-251)) then
        tmp = x
    else if (z <= 2.15d-275) then
        tmp = (y * t) / a
    else if (z <= 1.88d-118) 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 (z <= -3.15e-12) {
		tmp = y + x;
	} else if (z <= -1.6e-251) {
		tmp = x;
	} else if (z <= 2.15e-275) {
		tmp = (y * t) / a;
	} else if (z <= 1.88e-118) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e-12:
		tmp = y + x
	elif z <= -1.6e-251:
		tmp = x
	elif z <= 2.15e-275:
		tmp = (y * t) / a
	elif z <= 1.88e-118:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e-12)
		tmp = Float64(y + x);
	elseif (z <= -1.6e-251)
		tmp = x;
	elseif (z <= 2.15e-275)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.88e-118)
		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 (z <= -3.15e-12)
		tmp = y + x;
	elseif (z <= -1.6e-251)
		tmp = x;
	elseif (z <= 2.15e-275)
		tmp = (y * t) / a;
	elseif (z <= 1.88e-118)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e-12], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.6e-251], x, If[LessEqual[z, 2.15e-275], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.88e-118], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1500000000000001e-12 or 1.88000000000000001e-118 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -3.1500000000000001e-12 < z < -1.59999999999999991e-251 or 2.14999999999999988e-275 < z < 1.88000000000000001e-118

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 53.4%

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

   if -1.59999999999999991e-251 < z < 2.14999999999999988e-275

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-/l* 82.1%

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

      3. fma-define 82.1%

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

   3. Simplified 82.1%

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

      1. clear-num 82.2%

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

      2. associate-/r/ 82.1%

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

   6. Applied egg-rr 82.1%

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

   7. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-frac-neg2 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-/l* 69.6%

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

      5. sub-neg 69.6%

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

      6. mul-1-neg 69.6%

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

      7. distribute-neg-in 69.6%

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

      8. mul-1-neg 69.6%

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

      9. remove-double-neg 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in z around 0 76.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-12}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-275}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.88 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.92 \cdot 10^{+84} \lor \neg \left(y \leq 22\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.92e+84) (not (<= y 22.0))) (* y (/ (- z t) (- z a))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.92e+84) || !(y <= 22.0)) {
		tmp = y * ((z - t) / (z - a));
	} 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 ((y <= (-1.92d+84)) .or. (.not. (y <= 22.0d0))) then
        tmp = y * ((z - t) / (z - a))
    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 ((y <= -1.92e+84) || !(y <= 22.0)) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.92e+84) or not (y <= 22.0):
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.92e+84) || !(y <= 22.0))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.92e+84) || ~((y <= 22.0)))
		tmp = y * ((z - t) / (z - a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.92e+84], N[Not[LessEqual[y, 22.0]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.91999999999999993e84 or 22 < y

   1. Initial program 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 97.3%

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

      3. fma-define 97.3%

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

   3. Simplified 97.3%

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

      1. clear-num 96.7%

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

      2. associate-/r/ 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around inf 79.5%

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

      1. div-sub 79.5%

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

   9. Simplified 79.5%

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

   if -1.91999999999999993e84 < y < 22

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 73.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.92 \cdot 10^{+84} \lor \neg \left(y \leq 22\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+61} \lor \neg \left(a \leq 1060\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9e+61) (not (<= a 1060.0)))
   (- x (* y (/ (- z t) a)))
   (- x (* y (/ (- t z) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9e+61) || !(a <= 1060.0)) {
		tmp = x - (y * ((z - t) / a));
	} else {
		tmp = x - (y * ((t - z) / 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 ((a <= (-9d+61)) .or. (.not. (a <= 1060.0d0))) then
        tmp = x - (y * ((z - t) / a))
    else
        tmp = x - (y * ((t - z) / 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 ((a <= -9e+61) || !(a <= 1060.0)) {
		tmp = x - (y * ((z - t) / a));
	} else {
		tmp = x - (y * ((t - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9e+61) or not (a <= 1060.0):
		tmp = x - (y * ((z - t) / a))
	else:
		tmp = x - (y * ((t - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9e+61) || !(a <= 1060.0))
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9e+61) || ~((a <= 1060.0)))
		tmp = x - (y * ((z - t) / a));
	else
		tmp = x - (y * ((t - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9e+61], N[Not[LessEqual[a, 1060.0]], $MachinePrecision]], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9e61 or 1060 < a

   1. Initial program 80.7%

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

   3. Taylor expanded in a around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   if -9e61 < a < 1060

   1. Initial program 85.9%

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

   3. Taylor expanded in a around 0 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+61} \lor \neg \left(a \leq 1060\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -410000 \lor \neg \left(z \leq 8.6 \cdot 10^{-53}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -410000.0) (not (<= z 8.6e-53))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -410000.0) || !(z <= 8.6e-53)) {
		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 <= (-410000.0d0)) .or. (.not. (z <= 8.6d-53))) 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 <= -410000.0) || !(z <= 8.6e-53)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -410000.0) or not (z <= 8.6e-53):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -410000.0) || !(z <= 8.6e-53))
		tmp = Float64(y + 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 <= -410000.0) || ~((z <= 8.6e-53)))
		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, -410000.0], N[Not[LessEqual[z, 8.6e-53]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e5 or 8.5999999999999999e-53 < z

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf 75.6%

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

      1. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   if -4.1e5 < z < 8.5999999999999999e-53

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 73.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -410000 \lor \neg \left(z \leq 8.6 \cdot 10^{-53}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -24.5 \lor \neg \left(z \leq 3.5 \cdot 10^{-6}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -24.5) (not (<= z 3.5e-6))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -24.5) || !(z <= 3.5e-6)) {
		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 <= (-24.5d0)) .or. (.not. (z <= 3.5d-6))) 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 <= -24.5) || !(z <= 3.5e-6)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -24.5) or not (z <= 3.5e-6):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -24.5) || !(z <= 3.5e-6))
		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 <= -24.5) || ~((z <= 3.5e-6)))
		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, -24.5], N[Not[LessEqual[z, 3.5e-6]], $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 < -24.5 or 3.49999999999999995e-6 < z

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -24.5 < z < 3.49999999999999995e-6

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-/l* 73.5%

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

   5. Simplified 73.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24.5 \lor \neg \left(z \leq 3.5 \cdot 10^{-6}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3300 \lor \neg \left(z \leq 1.3 \cdot 10^{-5}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3300.0) (not (<= z 1.3e-5))) (+ y x) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3300.0) || !(z <= 1.3e-5)) {
		tmp = y + x;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3300.0d0)) .or. (.not. (z <= 1.3d-5))) then
        tmp = y + x
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3300.0) || !(z <= 1.3e-5)) {
		tmp = y + x;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3300.0) or not (z <= 1.3e-5):
		tmp = y + x
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3300.0) || !(z <= 1.3e-5))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3300.0) || ~((z <= 1.3e-5)))
		tmp = y + x;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3300.0], N[Not[LessEqual[z, 1.3e-5]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3300 or 1.29999999999999992e-5 < z

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -3300 < z < 1.29999999999999992e-5

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-/l* 73.5%

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

   5. Simplified 73.5%

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

      1. clear-num 73.5%

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

      2. un-div-inv 73.6%

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

   7. Applied egg-rr 73.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3300 \lor \neg \left(z \leq 1.3 \cdot 10^{-5}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-13} \lor \neg \left(z \leq 1.55 \cdot 10^{-118}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e-13) (not (<= z 1.55e-118))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e-13) || !(z <= 1.55e-118)) {
		tmp = y + 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 ((z <= (-8d-13)) .or. (.not. (z <= 1.55d-118))) then
        tmp = y + 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 ((z <= -8e-13) || !(z <= 1.55e-118)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e-13) or not (z <= 1.55e-118):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e-13) || !(z <= 1.55e-118))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e-13) || ~((z <= 1.55e-118)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e-13], N[Not[LessEqual[z, 1.55e-118]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000002e-13 or 1.5500000000000001e-118 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -8.0000000000000002e-13 < z < 1.5500000000000001e-118

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 47.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-13} \lor \neg \left(z \leq 1.55 \cdot 10^{-118}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+163}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.1e+163) y (if (<= y 1.48e+156) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.1e+163) {
		tmp = y;
	} else if (y <= 1.48e+156) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.1d+163)) then
        tmp = y
    else if (y <= 1.48d+156) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.1e+163) {
		tmp = y;
	} else if (y <= 1.48e+156) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.1e+163:
		tmp = y
	elif y <= 1.48e+156:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.1e+163)
		tmp = y;
	elseif (y <= 1.48e+156)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.1e+163)
		tmp = y;
	elseif (y <= 1.48e+156)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.1e+163], y, If[LessEqual[y, 1.48e+156], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000029e163 or 1.4799999999999999e156 < y

   1. Initial program 59.8%

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

   3. Taylor expanded in y around inf 87.4%

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

   4. Taylor expanded in z around inf 35.3%

      \[\leadsto y \cdot \color{blue}{1} \]

   if -3.10000000000000029e163 < y < 1.4799999999999999e156

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 62.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+163}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 49.7% 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 83.6%

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

3. Taylor expanded in x around inf 47.5%

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

4. Final simplification 47.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.4% 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 2024067 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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