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

Percentage Accurate: 85.1% → 96.0%

Time: 11.0s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

   1. *-commutative 85.7%

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

   2. associate-/l* 98.2%

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

3. Simplified 98.2%

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

4. Final simplification 98.2%

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

Alternative 2: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+298}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- a t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+298)))
     (+ x (- y (* z (/ y t))))
     (- x (/ (* y (- t z)) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+298)) {
		tmp = x + (y - (z * (y / t)));
	} else {
		tmp = x - ((y * (t - z)) / (a - t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+298)) {
		tmp = x + (y - (z * (y / t)));
	} else {
		tmp = x - ((y * (t - z)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (a - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+298):
		tmp = x + (y - (z * (y / t)))
	else:
		tmp = x - ((y * (t - z)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+298))
		tmp = Float64(x + Float64(y - Float64(z * Float64(y / t))));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+298)))
		tmp = x + (y - (z * (y / t)));
	else
		tmp = x - ((y * (t - z)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+298]], $MachinePrecision]], N[(x + N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0 or 9.9999999999999996e297 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 29.0%

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

   2. Taylor expanded in a around 0 24.7%

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

      1. mul-1-neg 24.7%

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

      2. unsub-neg 24.7%

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

      3. associate-/l* 75.7%

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

   4. Simplified 75.7%

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

   5. Taylor expanded in t around 0 62.1%

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

      1. +-commutative 62.1%

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

      2. neg-mul-1 62.1%

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

      3. unsub-neg 62.1%

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

      4. associate-*l/ 75.7%

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

      5. *-commutative 75.7%

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

   7. Simplified 75.7%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 9.9999999999999996e297

   1. Initial program 99.8%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty \lor \neg \left(\frac{\left(z - t\right) \cdot y}{a - t} \leq 10^{+298}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a - t}\\ \end{array} \]

Alternative 3: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-241}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+33}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+94)
   (+ x y)
   (if (<= t -1.65e-90)
     (+ x (* y (/ z (- a t))))
     (if (<= t -4e-241)
       (+ x (/ (- z t) (/ a y)))
       (if (<= t 1.12e+33) (+ x (* z (/ y (- a t)))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+94) {
		tmp = x + y;
	} else if (t <= -1.65e-90) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= -4e-241) {
		tmp = x + ((z - t) / (a / y));
	} else if (t <= 1.12e+33) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + 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 (t <= (-1.8d+94)) then
        tmp = x + y
    else if (t <= (-1.65d-90)) then
        tmp = x + (y * (z / (a - t)))
    else if (t <= (-4d-241)) then
        tmp = x + ((z - t) / (a / y))
    else if (t <= 1.12d+33) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + 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 (t <= -1.8e+94) {
		tmp = x + y;
	} else if (t <= -1.65e-90) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= -4e-241) {
		tmp = x + ((z - t) / (a / y));
	} else if (t <= 1.12e+33) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+94:
		tmp = x + y
	elif t <= -1.65e-90:
		tmp = x + (y * (z / (a - t)))
	elif t <= -4e-241:
		tmp = x + ((z - t) / (a / y))
	elif t <= 1.12e+33:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+94)
		tmp = Float64(x + y);
	elseif (t <= -1.65e-90)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	elseif (t <= -4e-241)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	elseif (t <= 1.12e+33)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e+94)
		tmp = x + y;
	elseif (t <= -1.65e-90)
		tmp = x + (y * (z / (a - t)));
	elseif (t <= -4e-241)
		tmp = x + ((z - t) / (a / y));
	elseif (t <= 1.12e+33)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+94], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.65e-90], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-241], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+33], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.79999999999999996e94 or 1.12e33 < t

   1. Initial program 66.4%

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

   2. Taylor expanded in t around inf 84.3%

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

      1. +-commutative 84.3%

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

   4. Simplified 84.3%

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

   if -1.79999999999999996e94 < t < -1.65e-90

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 96.6%

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

      3. fma-def 96.6%

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

   3. Simplified 96.6%

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

      1. fma-udef 96.6%

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

      2. associate-*l/ 99.8%

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

      3. associate-/l* 99.8%

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

      4. div-inv 99.9%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 77.8%

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

   if -1.65e-90 < t < -3.9999999999999999e-241

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 96.0%

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

   if -3.9999999999999999e-241 < t < 1.12e33

   1. Initial program 93.5%

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

   2. Taylor expanded in z around inf 90.8%

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

      1. associate-*l/ 38.5%

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

      2. *-commutative 38.5%

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

   4. Simplified 96.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-241}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+33}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+20} \lor \neg \left(z \leq 185\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+20) (not (<= z 185.0)))
   (+ x (* z (/ y (- a t))))
   (- x (* y (/ t (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+20) || !(z <= 185.0)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	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 <= (-2.6d+20)) .or. (.not. (z <= 185.0d0))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y * (t / (a - t)))
    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 <= -2.6e+20) || !(z <= 185.0)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+20) or not (z <= 185.0):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y * (t / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+20) || !(z <= 185.0))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+20) || ~((z <= 185.0)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y * (t / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+20], N[Not[LessEqual[z, 185.0]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e20 or 185 < z

   1. Initial program 82.4%

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

   2. Taylor expanded in z around inf 83.4%

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

      1. associate-*l/ 46.9%

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

      2. *-commutative 46.9%

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

   4. Simplified 91.9%

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

   if -2.6e20 < z < 185

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. associate-*l/ 91.2%

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

      3. unsub-neg 91.2%

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

      4. *-commutative 91.2%

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

   4. Simplified 91.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+20} \lor \neg \left(z \leq 185\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]

Alternative 5: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+31}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+94)
   (+ x y)
   (if (<= t 4.2e+31) (+ x (* z (/ y (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+94) {
		tmp = x + y;
	} else if (t <= 4.2e+31) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + 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 (t <= (-1.5d+94)) then
        tmp = x + y
    else if (t <= 4.2d+31) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + 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 (t <= -1.5e+94) {
		tmp = x + y;
	} else if (t <= 4.2e+31) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+94:
		tmp = x + y
	elif t <= 4.2e+31:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+94)
		tmp = Float64(x + y);
	elseif (t <= 4.2e+31)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+94)
		tmp = x + y;
	elseif (t <= 4.2e+31)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+94], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.2e+31], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e94 or 4.19999999999999958e31 < t

   1. Initial program 66.4%

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

   2. Taylor expanded in t around inf 84.3%

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

      1. +-commutative 84.3%

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

   4. Simplified 84.3%

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

   if -1.5e94 < t < 4.19999999999999958e31

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 86.2%

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

      1. associate-*l/ 33.7%

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

      2. *-commutative 33.7%

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

   4. Simplified 88.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+31}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.8e-84)
   (+ x y)
   (if (<= t 3.4e-190)
     x
     (if (<= t 4e-122) (/ y (/ a z)) (if (<= t 2.6e+23) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e-84) {
		tmp = x + y;
	} else if (t <= 3.4e-190) {
		tmp = x;
	} else if (t <= 4e-122) {
		tmp = y / (a / z);
	} else if (t <= 2.6e+23) {
		tmp = x;
	} else {
		tmp = x + 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 (t <= (-7.8d-84)) then
        tmp = x + y
    else if (t <= 3.4d-190) then
        tmp = x
    else if (t <= 4d-122) then
        tmp = y / (a / z)
    else if (t <= 2.6d+23) then
        tmp = x
    else
        tmp = x + 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 (t <= -7.8e-84) {
		tmp = x + y;
	} else if (t <= 3.4e-190) {
		tmp = x;
	} else if (t <= 4e-122) {
		tmp = y / (a / z);
	} else if (t <= 2.6e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.8e-84:
		tmp = x + y
	elif t <= 3.4e-190:
		tmp = x
	elif t <= 4e-122:
		tmp = y / (a / z)
	elif t <= 2.6e+23:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.8e-84)
		tmp = Float64(x + y);
	elseif (t <= 3.4e-190)
		tmp = x;
	elseif (t <= 4e-122)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 2.6e+23)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.8e-84)
		tmp = x + y;
	elseif (t <= 3.4e-190)
		tmp = x;
	elseif (t <= 4e-122)
		tmp = y / (a / z);
	elseif (t <= 2.6e+23)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.8e-84], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.4e-190], x, If[LessEqual[t, 4e-122], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+23], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.80000000000000045e-84 or 2.59999999999999992e23 < t

   1. Initial program 78.2%

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

   2. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -7.80000000000000045e-84 < t < 3.39999999999999981e-190 or 4.00000000000000024e-122 < t < 2.59999999999999992e23

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 63.9%

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

   if 3.39999999999999981e-190 < t < 4.00000000000000024e-122

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0 68.9%

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

   3. Taylor expanded in t around 0 47.4%

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

      1. associate-/l* 67.4%

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

   5. Simplified 67.4%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+129} \lor \neg \left(z \leq 2.1 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+129) (not (<= z 2.1e+123))) (* z (/ y (- a t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+129) || !(z <= 2.1e+123)) {
		tmp = z * (y / (a - t));
	} else {
		tmp = x + 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 <= (-9.5d+129)) .or. (.not. (z <= 2.1d+123))) then
        tmp = z * (y / (a - t))
    else
        tmp = x + 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 <= -9.5e+129) || !(z <= 2.1e+123)) {
		tmp = z * (y / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+129) or not (z <= 2.1e+123):
		tmp = z * (y / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+129) || !(z <= 2.1e+123))
		tmp = Float64(z * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+129) || ~((z <= 2.1e+123)))
		tmp = z * (y / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+129], N[Not[LessEqual[z, 2.1e+123]], $MachinePrecision]], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000004e129 or 2.09999999999999994e123 < z

   1. Initial program 80.8%

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

   2. Taylor expanded in x around 0 55.8%

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

   3. Taylor expanded in z around inf 52.9%

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

      1. associate-*l/ 62.7%

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

      2. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -9.5000000000000004e129 < z < 2.09999999999999994e123

   1. Initial program 87.4%

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

   2. Taylor expanded in t around inf 72.0%

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

      1. +-commutative 72.0%

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

   4. Simplified 72.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+129} \lor \neg \left(z \leq 2.1 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+26} \lor \neg \left(t \leq 1.1 \cdot 10^{+31}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+26) (not (<= t 1.1e+31))) (+ x y) (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+26) || !(t <= 1.1e+31)) {
		tmp = x + y;
	} else {
		tmp = x + ((z * 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 ((t <= (-8.2d+26)) .or. (.not. (t <= 1.1d+31))) then
        tmp = x + y
    else
        tmp = x + ((z * 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 ((t <= -8.2e+26) || !(t <= 1.1e+31)) {
		tmp = x + y;
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+26) or not (t <= 1.1e+31):
		tmp = x + y
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+26) || !(t <= 1.1e+31))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+26) || ~((t <= 1.1e+31)))
		tmp = x + y;
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+26], N[Not[LessEqual[t, 1.1e+31]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.19999999999999967e26 or 1.10000000000000005e31 < t

   1. Initial program 73.1%

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

   2. Taylor expanded in t around inf 79.5%

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

      1. +-commutative 79.5%

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

   4. Simplified 79.5%

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

   if -8.19999999999999967e26 < t < 1.10000000000000005e31

   1. Initial program 95.9%

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

   2. Taylor expanded in t around 0 80.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+26} \lor \neg \left(t \leq 1.1 \cdot 10^{+31}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]

Alternative 9: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+25}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+25) (+ x y) (if (<= t 9.5e+31) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+25) {
		tmp = x + y;
	} else if (t <= 9.5e+31) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + 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 (t <= (-4.2d+25)) then
        tmp = x + y
    else if (t <= 9.5d+31) then
        tmp = x + (y * (z / a))
    else
        tmp = x + 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 (t <= -4.2e+25) {
		tmp = x + y;
	} else if (t <= 9.5e+31) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+25:
		tmp = x + y
	elif t <= 9.5e+31:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+25)
		tmp = Float64(x + y);
	elseif (t <= 9.5e+31)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+25)
		tmp = x + y;
	elseif (t <= 9.5e+31)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+25], N[(x + y), $MachinePrecision], If[LessEqual[t, 9.5e+31], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1999999999999998e25 or 9.5000000000000008e31 < t

   1. Initial program 73.1%

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

   2. Taylor expanded in t around inf 79.5%

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

      1. +-commutative 79.5%

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

   4. Simplified 79.5%

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

   if -4.1999999999999998e25 < t < 9.5000000000000008e31

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-*l/ 98.2%

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

      3. fma-def 98.2%

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

   3. Simplified 98.2%

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

      1. fma-udef 98.2%

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

      2. associate-*l/ 95.9%

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

      3. associate-/l* 95.8%

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

      4. div-inv 95.2%

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

      5. clear-num 95.2%

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

   5. Applied egg-rr 95.2%

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

   6. Taylor expanded in t around 0 80.3%

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

      1. associate-*r/ 81.4%

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

   8. Simplified 81.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+25}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+27) (+ x y) (if (<= t 1.9e+30) (+ x (/ y (/ a z))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+27) {
		tmp = x + y;
	} else if (t <= 1.9e+30) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + 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 (t <= (-1.1d+27)) then
        tmp = x + y
    else if (t <= 1.9d+30) then
        tmp = x + (y / (a / z))
    else
        tmp = x + 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 (t <= -1.1e+27) {
		tmp = x + y;
	} else if (t <= 1.9e+30) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+27:
		tmp = x + y
	elif t <= 1.9e+30:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+27)
		tmp = Float64(x + y);
	elseif (t <= 1.9e+30)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+27)
		tmp = x + y;
	elseif (t <= 1.9e+30)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+27], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.9e+30], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0999999999999999e27 or 1.9000000000000001e30 < t

   1. Initial program 73.1%

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

   2. Taylor expanded in t around inf 79.5%

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

      1. +-commutative 79.5%

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

   4. Simplified 79.5%

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

   if -1.0999999999999999e27 < t < 1.9000000000000001e30

   1. Initial program 95.9%

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

   2. Taylor expanded in t around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. associate-/l* 81.9%

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

   4. Simplified 81.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 63.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.8e-84) (+ x y) (if (<= t 1.9e+23) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e-84) {
		tmp = x + y;
	} else if (t <= 1.9e+23) {
		tmp = x;
	} else {
		tmp = x + 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 (t <= (-7.8d-84)) then
        tmp = x + y
    else if (t <= 1.9d+23) then
        tmp = x
    else
        tmp = x + 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 (t <= -7.8e-84) {
		tmp = x + y;
	} else if (t <= 1.9e+23) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.8e-84:
		tmp = x + y
	elif t <= 1.9e+23:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.8e-84)
		tmp = Float64(x + y);
	elseif (t <= 1.9e+23)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.8e-84)
		tmp = x + y;
	elseif (t <= 1.9e+23)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.8e-84], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.9e+23], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.80000000000000045e-84 or 1.89999999999999987e23 < t

   1. Initial program 78.2%

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

   2. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -7.80000000000000045e-84 < t < 1.89999999999999987e23

   1. Initial program 94.9%

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

   2. Taylor expanded in x around inf 60.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 52.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-287}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.5e-251) x (if (<= x 1.2e-287) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.5e-251) {
		tmp = x;
	} else if (x <= 1.2e-287) {
		tmp = y;
	} 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 (x <= (-6.5d-251)) then
        tmp = x
    else if (x <= 1.2d-287) then
        tmp = y
    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 (x <= -6.5e-251) {
		tmp = x;
	} else if (x <= 1.2e-287) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.5e-251:
		tmp = x
	elif x <= 1.2e-287:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.5e-251)
		tmp = x;
	elseif (x <= 1.2e-287)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.5e-251)
		tmp = x;
	elseif (x <= 1.2e-287)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.5e-251], x, If[LessEqual[x, 1.2e-287], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000002e-251 or 1.2e-287 < x

   1. Initial program 87.1%

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

   2. Taylor expanded in x around inf 62.8%

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

   if -6.5000000000000002e-251 < x < 1.2e-287

   1. Initial program 73.3%

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

   2. Taylor expanded in a around 0 53.8%

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

      1. mul-1-neg 53.8%

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

      2. unsub-neg 53.8%

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

      3. associate-/l* 69.4%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in y around inf 69.4%

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

   6. Taylor expanded in z around 0 54.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-287}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 50.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

2. Taylor expanded in x around inf 57.8%

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

3. Final simplification 57.8%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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