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

Percentage Accurate: 85.7% → 99.2%

Time: 10.3s

Alternatives: 15

Speedup: 0.8×

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: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+305} \lor \neg \left(t_1 \leq 2 \cdot 10^{+191}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -2e+305) (not (<= t_1 2e+191)))
     (+ x (/ (- z t) (/ (- z a) y)))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -2e+305) || !(t_1 <= 2e+191)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = t_1 + 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 * (z - t)) / (z - a)
    if ((t_1 <= (-2d+305)) .or. (.not. (t_1 <= 2d+191))) then
        tmp = x + ((z - t) / ((z - a) / y))
    else
        tmp = t_1 + 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 * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -2e+305) || !(t_1 <= 2e+191)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -2e+305) or not (t_1 <= 2e+191):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -2e+305) || !(t_1 <= 2e+191))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -2e+305) || ~((t_1 <= 2e+191)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+305], N[Not[LessEqual[t$95$1, 2e+191]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -1.9999999999999999e305 or 2.00000000000000015e191 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 41.3%

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

      1. *-commutative 41.3%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -1.9999999999999999e305 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000015e191

   1. Initial program 98.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -2 \cdot 10^{+305} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+191}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]

Alternative 2: 92.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{z}{t - a}}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+275}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 (- INFINITY))
     (+ x (- y (/ y (/ z (- t a)))))
     (if (<= t_1 2e+275) (+ t_1 x) (+ x (/ (- z t) (/ z 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 + (y - (y / (z / (t - a))));
	} else if (t_1 <= 2e+275) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((z - t) / (z / 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 + (y - (y / (z / (t - a))));
	} else if (t_1 <= 2e+275) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((z - t) / (z / 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 + (y - (y / (z / (t - a))))
	elif t_1 <= 2e+275:
		tmp = t_1 + x
	else:
		tmp = x + ((z - t) / (z / 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(y - Float64(y / Float64(z / Float64(t - a)))));
	elseif (t_1 <= 2e+275)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / 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 + (y - (y / (z / (t - a))));
	elseif (t_1 <= 2e+275)
		tmp = t_1 + x;
	else
		tmp = x + ((z - t) / (z / 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[(y - N[(y / N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+275], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / 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 37.5%

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

   2. Taylor expanded in z around inf 54.5%

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

      1. associate--l+ 54.5%

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

      2. distribute-lft-out-- 54.5%

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

      3. div-sub 54.5%

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

      4. mul-1-neg 54.5%

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

      5. unsub-neg 54.5%

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

      6. distribute-rgt-out-- 58.3%

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

      7. associate-/l* 85.8%

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

   4. Simplified 85.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.99999999999999992e275

   1. Initial program 98.9%

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

   if 1.99999999999999992e275 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 29.6%

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

      1. *-commutative 29.6%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 75.6%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{z}{t - a}}\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+275}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 3: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a}\\ t_2 := x - t \cdot t_1\\ \mathbf{if}\;t \leq -1.72 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-94}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+49}:\\ \;\;\;\;x + z \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- z a))) (t_2 (- x (* t t_1))))
   (if (<= t -1.72e-40)
     t_2
     (if (<= t -1.4e-94)
       (+ y x)
       (if (<= t -3e-128)
         (- x (/ y (/ a (- z t))))
         (if (<= t 2.6e+49) (+ x (* z t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - a);
	double t_2 = x - (t * t_1);
	double tmp;
	if (t <= -1.72e-40) {
		tmp = t_2;
	} else if (t <= -1.4e-94) {
		tmp = y + x;
	} else if (t <= -3e-128) {
		tmp = x - (y / (a / (z - t)));
	} else if (t <= 2.6e+49) {
		tmp = x + (z * t_1);
	} else {
		tmp = t_2;
	}
	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 / (z - a)
    t_2 = x - (t * t_1)
    if (t <= (-1.72d-40)) then
        tmp = t_2
    else if (t <= (-1.4d-94)) then
        tmp = y + x
    else if (t <= (-3d-128)) then
        tmp = x - (y / (a / (z - t)))
    else if (t <= 2.6d+49) then
        tmp = x + (z * t_1)
    else
        tmp = t_2
    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 - a);
	double t_2 = x - (t * t_1);
	double tmp;
	if (t <= -1.72e-40) {
		tmp = t_2;
	} else if (t <= -1.4e-94) {
		tmp = y + x;
	} else if (t <= -3e-128) {
		tmp = x - (y / (a / (z - t)));
	} else if (t <= 2.6e+49) {
		tmp = x + (z * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z - a)
	t_2 = x - (t * t_1)
	tmp = 0
	if t <= -1.72e-40:
		tmp = t_2
	elif t <= -1.4e-94:
		tmp = y + x
	elif t <= -3e-128:
		tmp = x - (y / (a / (z - t)))
	elif t <= 2.6e+49:
		tmp = x + (z * t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z - a))
	t_2 = Float64(x - Float64(t * t_1))
	tmp = 0.0
	if (t <= -1.72e-40)
		tmp = t_2;
	elseif (t <= -1.4e-94)
		tmp = Float64(y + x);
	elseif (t <= -3e-128)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	elseif (t <= 2.6e+49)
		tmp = Float64(x + Float64(z * t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z - a);
	t_2 = x - (t * t_1);
	tmp = 0.0;
	if (t <= -1.72e-40)
		tmp = t_2;
	elseif (t <= -1.4e-94)
		tmp = y + x;
	elseif (t <= -3e-128)
		tmp = x - (y / (a / (z - t)));
	elseif (t <= 2.6e+49)
		tmp = x + (z * t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.72e-40], t$95$2, If[LessEqual[t, -1.4e-94], N[(y + x), $MachinePrecision], If[LessEqual[t, -3e-128], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+49], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.7199999999999999e-40 or 2.59999999999999989e49 < t

   1. Initial program 81.6%

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

   2. Taylor expanded in z around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-lft-neg-out 78.6%

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

      3. *-commutative 78.6%

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

   4. Simplified 78.6%

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

      1. div-inv 78.6%

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

      2. add-sqr-sqrt 34.0%

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

      3. sqrt-unprod 31.8%

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

      4. sqr-neg 31.8%

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

      5. sqrt-unprod 21.6%

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

      6. add-sqr-sqrt 35.6%

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

      7. distribute-rgt-neg-in 35.6%

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

      8. cancel-sign-sub-inv 35.6%

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

      9. div-inv 35.6%

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

      10. associate-/l* 37.2%

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

      11. associate-/r/ 37.2%

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

      12. add-sqr-sqrt 23.2%

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

      13. sqrt-unprod 33.7%

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

      14. sqr-neg 33.7%

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

      15. sqrt-unprod 36.5%

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

      16. add-sqr-sqrt 85.9%

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

   6. Applied egg-rr 85.9%

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

   if -1.7199999999999999e-40 < t < -1.3999999999999999e-94

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-*l/ 85.6%

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

      3. fma-def 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in z around inf 92.9%

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

      1. +-commutative 92.9%

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

   6. Simplified 92.9%

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

   if -1.3999999999999999e-94 < t < -2.99999999999999978e-128

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in a around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -2.99999999999999978e-128 < t < 2.59999999999999989e49

   1. Initial program 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-*l/ 95.9%

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

      3. fma-def 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-*l/ 94.3%

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

      3. *-commutative 94.3%

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

   6. Simplified 94.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{-40}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-94}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+49}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 4: 77.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -0.38:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+76}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+131)
   (+ y x)
   (if (<= z -0.38)
     (+ x (/ (* y z) (- z a)))
     (if (<= z 3.6e-78)
       (+ x (* y (/ t a)))
       (if (<= z 3.3e+76) (- x (/ t (/ z y))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+131) {
		tmp = y + x;
	} else if (z <= -0.38) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= 3.6e-78) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.3e+76) {
		tmp = x - (t / (z / y));
	} 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 <= (-1.7d+131)) then
        tmp = y + x
    else if (z <= (-0.38d0)) then
        tmp = x + ((y * z) / (z - a))
    else if (z <= 3.6d-78) then
        tmp = x + (y * (t / a))
    else if (z <= 3.3d+76) then
        tmp = x - (t / (z / y))
    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 <= -1.7e+131) {
		tmp = y + x;
	} else if (z <= -0.38) {
		tmp = x + ((y * z) / (z - a));
	} else if (z <= 3.6e-78) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.3e+76) {
		tmp = x - (t / (z / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+131:
		tmp = y + x
	elif z <= -0.38:
		tmp = x + ((y * z) / (z - a))
	elif z <= 3.6e-78:
		tmp = x + (y * (t / a))
	elif z <= 3.3e+76:
		tmp = x - (t / (z / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+131)
		tmp = Float64(y + x);
	elseif (z <= -0.38)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(z - a)));
	elseif (z <= 3.6e-78)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 3.3e+76)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+131)
		tmp = y + x;
	elseif (z <= -0.38)
		tmp = x + ((y * z) / (z - a));
	elseif (z <= 3.6e-78)
		tmp = x + (y * (t / a));
	elseif (z <= 3.3e+76)
		tmp = x - (t / (z / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+131], N[(y + x), $MachinePrecision], If[LessEqual[z, -0.38], N[(x + N[(N[(y * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-78], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+76], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.69999999999999993e131 or 3.3000000000000001e76 < z

   1. Initial program 65.0%

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

      1. +-commutative 65.0%

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

      2. associate-*l/ 90.4%

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

      3. fma-def 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in z around inf 84.3%

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

      1. +-commutative 84.3%

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

   6. Simplified 84.3%

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

   if -1.69999999999999993e131 < z < -0.38

   1. Initial program 86.1%

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

   2. Taylor expanded in t around 0 71.1%

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

   if -0.38 < z < 3.6000000000000002e-78

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-*l/ 95.6%

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

      3. fma-def 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 79.5%

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

      3. associate-/r/ 82.3%

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

   6. Simplified 82.3%

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

   if 3.6000000000000002e-78 < z < 3.3000000000000001e76

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. associate-/l* 80.6%

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

      3. associate-/r/ 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in z around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. associate-/l* 78.8%

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

   9. Simplified 78.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -0.38:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+76}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+29}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+74}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.65e+29)
   (+ y x)
   (if (<= z 4e-78)
     (+ x (* y (/ t a)))
     (if (<= z 9e+74) (- x (* y (/ t z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.65e+29) {
		tmp = y + x;
	} else if (z <= 4e-78) {
		tmp = x + (y * (t / a));
	} else if (z <= 9e+74) {
		tmp = x - (y * (t / z));
	} 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 <= (-2.65d+29)) then
        tmp = y + x
    else if (z <= 4d-78) then
        tmp = x + (y * (t / a))
    else if (z <= 9d+74) then
        tmp = x - (y * (t / z))
    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 <= -2.65e+29) {
		tmp = y + x;
	} else if (z <= 4e-78) {
		tmp = x + (y * (t / a));
	} else if (z <= 9e+74) {
		tmp = x - (y * (t / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.65e+29:
		tmp = y + x
	elif z <= 4e-78:
		tmp = x + (y * (t / a))
	elif z <= 9e+74:
		tmp = x - (y * (t / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.65e+29)
		tmp = Float64(y + x);
	elseif (z <= 4e-78)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 9e+74)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.65e+29)
		tmp = y + x;
	elseif (z <= 4e-78)
		tmp = x + (y * (t / a));
	elseif (z <= 9e+74)
		tmp = x - (y * (t / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.65e+29], N[(y + x), $MachinePrecision], If[LessEqual[z, 4e-78], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+74], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.65e29 or 8.9999999999999999e74 < z

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 77.6%

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

      1. +-commutative 77.6%

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

   6. Simplified 77.6%

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

   if -2.65e29 < z < 4e-78

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*l/ 95.9%

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

      3. fma-def 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-/l* 77.9%

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

      3. associate-/r/ 80.5%

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

   6. Simplified 80.5%

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

   if 4e-78 < z < 8.9999999999999999e74

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. associate-/l* 80.6%

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

      3. associate-/r/ 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in z around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. associate-/l* 78.8%

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

   9. Simplified 78.8%

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

       1. +-commutative 78.8%

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

       2. unsub-neg 78.8%

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

       3. associate-/r/ 78.8%

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

       4. *-commutative 78.8%

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

   11. Applied egg-rr 78.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+29}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+74}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+27}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+77}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+27)
   (+ y x)
   (if (<= z 3.8e-78)
     (+ x (* y (/ t a)))
     (if (<= z 3.2e+77) (- x (/ t (/ z y))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+27) {
		tmp = y + x;
	} else if (z <= 3.8e-78) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.2e+77) {
		tmp = x - (t / (z / y));
	} 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 <= (-6d+27)) then
        tmp = y + x
    else if (z <= 3.8d-78) then
        tmp = x + (y * (t / a))
    else if (z <= 3.2d+77) then
        tmp = x - (t / (z / y))
    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 <= -6e+27) {
		tmp = y + x;
	} else if (z <= 3.8e-78) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.2e+77) {
		tmp = x - (t / (z / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+27:
		tmp = y + x
	elif z <= 3.8e-78:
		tmp = x + (y * (t / a))
	elif z <= 3.2e+77:
		tmp = x - (t / (z / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+27)
		tmp = Float64(y + x);
	elseif (z <= 3.8e-78)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 3.2e+77)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+27)
		tmp = y + x;
	elseif (z <= 3.8e-78)
		tmp = x + (y * (t / a));
	elseif (z <= 3.2e+77)
		tmp = x - (t / (z / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+27], N[(y + x), $MachinePrecision], If[LessEqual[z, 3.8e-78], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+77], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999953e27 or 3.2000000000000002e77 < z

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 77.6%

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

      1. +-commutative 77.6%

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

   6. Simplified 77.6%

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

   if -5.99999999999999953e27 < z < 3.7999999999999999e-78

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*l/ 95.9%

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

      3. fma-def 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-/l* 77.9%

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

      3. associate-/r/ 80.5%

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

   6. Simplified 80.5%

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

   if 3.7999999999999999e-78 < z < 3.2000000000000002e77

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. associate-/l* 80.6%

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

      3. associate-/r/ 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in z around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. associate-/l* 78.8%

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

   9. Simplified 78.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+27}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+77}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-74} \lor \neg \left(z \leq 3.1 \cdot 10^{-78}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e-74) (not (<= z 3.1e-78)))
   (+ x (/ (- z t) (/ z y)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e-74) || !(z <= 3.1e-78)) {
		tmp = x + ((z - t) / (z / y));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.3d-74)) .or. (.not. (z <= 3.1d-78))) then
        tmp = x + ((z - t) / (z / y))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e-74) || !(z <= 3.1e-78)) {
		tmp = x + ((z - t) / (z / y));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.3e-74) or not (z <= 3.1e-78):
		tmp = x + ((z - t) / (z / y))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.3e-74) || !(z <= 3.1e-78))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.3e-74) || ~((z <= 3.1e-78)))
		tmp = x + ((z - t) / (z / y));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.3e-74], N[Not[LessEqual[z, 3.1e-78]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.29999999999999996e-74 or 3.10000000000000018e-78 < z

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around inf 78.8%

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

   if -3.29999999999999996e-74 < z < 3.10000000000000018e-78

   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/ 94.9%

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

      3. fma-def 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. associate-/l* 82.9%

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

      3. associate-/r/ 86.2%

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

   6. Simplified 86.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-74} \lor \neg \left(z \leq 3.1 \cdot 10^{-78}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 8: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-71} \lor \neg \left(z \leq 1.6 \cdot 10^{-78}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e-71) (not (<= z 1.6e-78)))
   (+ x (* (- z t) (/ y z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e-71) || !(z <= 1.6e-78)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.4d-71)) .or. (.not. (z <= 1.6d-78))) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e-71) || !(z <= 1.6e-78)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.4e-71) or not (z <= 1.6e-78):
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.4e-71) || !(z <= 1.6e-78))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.4e-71) || ~((z <= 1.6e-78)))
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.4e-71], N[Not[LessEqual[z, 1.6e-78]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.3999999999999998e-71 or 1.6e-78 < z

   1. Initial program 75.6%

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

      1. +-commutative 75.6%

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

      2. associate-*l/ 94.5%

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

      3. fma-def 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around 0 63.0%

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

      1. +-commutative 63.0%

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

      2. associate-/l* 82.6%

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

      3. associate-/r/ 79.2%

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

   6. Simplified 79.2%

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

   if -6.3999999999999998e-71 < z < 1.6e-78

   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/ 94.9%

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

      3. fma-def 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. associate-/l* 82.9%

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

      3. associate-/r/ 86.2%

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

   6. Simplified 86.2%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-71} \lor \neg \left(z \leq 1.6 \cdot 10^{-78}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-68} \lor \neg \left(z \leq 1.35 \cdot 10^{-78}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e-68) (not (<= z 1.35e-78)))
   (+ x (* (- z t) (/ y z)))
   (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e-68) || !(z <= 1.35e-78)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + ((y / a) * (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 <= (-2.1d-68)) .or. (.not. (z <= 1.35d-78))) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + ((y / a) * (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 <= -2.1e-68) || !(z <= 1.35e-78)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e-68) or not (z <= 1.35e-78):
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e-68) || !(z <= 1.35e-78))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e-68) || ~((z <= 1.35e-78)))
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e-68], N[Not[LessEqual[z, 1.35e-78]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.10000000000000008e-68 or 1.34999999999999997e-78 < z

   1. Initial program 75.6%

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

      1. +-commutative 75.6%

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

      2. associate-*l/ 94.5%

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

      3. fma-def 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around 0 63.0%

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

      1. +-commutative 63.0%

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

      2. associate-/l* 82.6%

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

      3. associate-/r/ 79.2%

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

   6. Simplified 79.2%

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

   if -2.10000000000000008e-68 < z < 1.34999999999999997e-78

   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/ 94.9%

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

      3. fma-def 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around inf 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

      3. associate-/l* 89.2%

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

      4. associate-/r/ 87.4%

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

   6. Simplified 87.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-68} \lor \neg \left(z \leq 1.35 \cdot 10^{-78}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 10: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{-38} \lor \neg \left(t \leq 5.5 \cdot 10^{+49}\right):\\ \;\;\;\;x - t \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- z a))))
   (if (or (<= t -8.6e-38) (not (<= t 5.5e+49)))
     (- x (* t t_1))
     (+ x (* z t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - a);
	double tmp;
	if ((t <= -8.6e-38) || !(t <= 5.5e+49)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x + (z * 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 - a)
    if ((t <= (-8.6d-38)) .or. (.not. (t <= 5.5d+49))) then
        tmp = x - (t * t_1)
    else
        tmp = x + (z * 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 - a);
	double tmp;
	if ((t <= -8.6e-38) || !(t <= 5.5e+49)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z - a)
	tmp = 0
	if (t <= -8.6e-38) or not (t <= 5.5e+49):
		tmp = x - (t * t_1)
	else:
		tmp = x + (z * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z - a))
	tmp = 0.0
	if ((t <= -8.6e-38) || !(t <= 5.5e+49))
		tmp = Float64(x - Float64(t * t_1));
	else
		tmp = Float64(x + Float64(z * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z - a);
	tmp = 0.0;
	if ((t <= -8.6e-38) || ~((t <= 5.5e+49)))
		tmp = x - (t * t_1);
	else
		tmp = x + (z * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -8.6e-38], N[Not[LessEqual[t, 5.5e+49]], $MachinePrecision]], N[(x - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6000000000000004e-38 or 5.50000000000000042e49 < t

   1. Initial program 81.6%

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

   2. Taylor expanded in z around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-lft-neg-out 78.6%

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

      3. *-commutative 78.6%

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

   4. Simplified 78.6%

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

      1. div-inv 78.6%

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

      2. add-sqr-sqrt 34.0%

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

      3. sqrt-unprod 31.8%

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

      4. sqr-neg 31.8%

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

      5. sqrt-unprod 21.6%

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

      6. add-sqr-sqrt 35.6%

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

      7. distribute-rgt-neg-in 35.6%

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

      8. cancel-sign-sub-inv 35.6%

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

      9. div-inv 35.6%

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

      10. associate-/l* 37.2%

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

      11. associate-/r/ 37.2%

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

      12. add-sqr-sqrt 23.2%

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

      13. sqrt-unprod 33.7%

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

      14. sqr-neg 33.7%

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

      15. sqrt-unprod 36.5%

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

      16. add-sqr-sqrt 85.9%

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

   6. Applied egg-rr 85.9%

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

   if -8.6000000000000004e-38 < t < 5.50000000000000042e49

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-*l/ 93.7%

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

      3. fma-def 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around 0 78.9%

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

      1. +-commutative 78.9%

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

      2. associate-*l/ 90.9%

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

      3. *-commutative 90.9%

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

   6. Simplified 90.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-38} \lor \neg \left(t \leq 5.5 \cdot 10^{+49}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 11: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+98} \lor \neg \left(y \leq 6.2 \cdot 10^{+181}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7e+98) (not (<= y 6.2e+181))) (* y (- 1.0 (/ t z))) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7e+98) || !(y <= 6.2e+181)) {
		tmp = y * (1.0 - (t / z));
	} 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 ((y <= (-7d+98)) .or. (.not. (y <= 6.2d+181))) then
        tmp = y * (1.0d0 - (t / z))
    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 ((y <= -7e+98) || !(y <= 6.2e+181)) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7e+98) or not (y <= 6.2e+181):
		tmp = y * (1.0 - (t / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7e+98) || !(y <= 6.2e+181))
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -7e+98) || ~((y <= 6.2e+181)))
		tmp = y * (1.0 - (t / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7e+98], N[Not[LessEqual[y, 6.2e+181]], $MachinePrecision]], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e98 or 6.19999999999999978e181 < y

   1. Initial program 53.9%

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

      1. +-commutative 53.9%

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

      2. associate-*l/ 98.5%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in a around 0 36.3%

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

      1. +-commutative 36.3%

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

      2. associate-/l* 73.5%

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

      3. associate-/r/ 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in y around inf 66.5%

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

   if -7e98 < y < 6.19999999999999978e181

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-*l/ 93.3%

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

      3. fma-def 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 65.2%

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

      1. +-commutative 65.2%

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

   6. Simplified 65.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+98} \lor \neg \left(y \leq 6.2 \cdot 10^{+181}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 12: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-58} \lor \neg \left(z \leq 1.65 \cdot 10^{+76}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e-58) (not (<= z 1.65e+76))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e-58) || !(z <= 1.65e+76)) {
		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 <= (-4.8d-58)) .or. (.not. (z <= 1.65d+76))) 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 <= -4.8e-58) || !(z <= 1.65e+76)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e-58) or not (z <= 1.65e+76):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e-58) || !(z <= 1.65e+76))
		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 <= -4.8e-58) || ~((z <= 1.65e+76)))
		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, -4.8e-58], N[Not[LessEqual[z, 1.65e+76]], $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 < -4.8000000000000001e-58 or 1.65e76 < z

   1. Initial program 71.8%

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

      1. +-commutative 71.8%

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

      2. associate-*l/ 93.5%

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

      3. fma-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around inf 73.8%

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

      1. +-commutative 73.8%

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

   6. Simplified 73.8%

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

   if -4.8000000000000001e-58 < z < 1.65e76

   1. Initial program 95.9%

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

   2. Taylor expanded in z around 0 77.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-58} \lor \neg \left(z \leq 1.65 \cdot 10^{+76}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 13: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+29} \lor \neg \left(z \leq 1.3 \cdot 10^{+77}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e+29) (not (<= z 1.3e+77))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+29) || !(z <= 1.3e+77)) {
		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 <= (-4.4d+29)) .or. (.not. (z <= 1.3d+77))) 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 <= -4.4e+29) || !(z <= 1.3e+77)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e+29) or not (z <= 1.3e+77):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e+29) || !(z <= 1.3e+77))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e+29) || ~((z <= 1.3e+77)))
		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, -4.4e+29], N[Not[LessEqual[z, 1.3e+77]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000003e29 or 1.3000000000000001e77 < z

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 77.6%

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

      1. +-commutative 77.6%

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

   6. Simplified 77.6%

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

   if -4.4000000000000003e29 < z < 1.3000000000000001e77

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-*l/ 96.7%

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

      3. fma-def 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-/l* 74.9%

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

      3. associate-/r/ 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+29} \lor \neg \left(z \leq 1.3 \cdot 10^{+77}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 14: 62.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-104} \lor \neg \left(z \leq 1.9 \cdot 10^{+24}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e-104) (not (<= z 1.9e+24))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e-104) || !(z <= 1.9e+24)) {
		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 <= (-7d-104)) .or. (.not. (z <= 1.9d+24))) 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 <= -7e-104) || !(z <= 1.9e+24)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e-104) or not (z <= 1.9e+24):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e-104) || !(z <= 1.9e+24))
		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 <= -7e-104) || ~((z <= 1.9e+24)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7e-104], N[Not[LessEqual[z, 1.9e+24]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000057e-104 or 1.90000000000000008e24 < z

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-*l/ 93.6%

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

      3. fma-def 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around inf 71.8%

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

      1. +-commutative 71.8%

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

   6. Simplified 71.8%

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

   if -7.00000000000000057e-104 < z < 1.90000000000000008e24

   1. Initial program 95.3%

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

      1. +-commutative 95.3%

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

      2. associate-*l/ 96.3%

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

      3. fma-def 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in y around 0 54.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-104} \lor \neg \left(z \leq 1.9 \cdot 10^{+24}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 50.1% 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 82.7%

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

   1. +-commutative 82.7%

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

   2. associate-*l/ 94.7%

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

   3. fma-def 94.7%

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

3. Simplified 94.7%

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

4. Taylor expanded in y around 0 47.6%

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

5. Final simplification 47.6%

   \[\leadsto x \]

Developer target: 98.2% 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 2023333 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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