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

Percentage Accurate: 98.3% → 98.3%

Time: 10.8s

Alternatives: 14

Speedup: 0.5×

Specification

Math

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

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

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

Alternative 1: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(y, t\_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 1.0) (fma y t_1 x) (+ x (* (- z t) (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 1.0) {
		tmp = fma(y, t_1, x);
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 1.0)
		tmp = fma(y, t_1, x);
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1.0], N[(y * t$95$1 + x), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   if 1 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 89.3%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-/l* 99.8%

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

   6. Applied egg-rr 99.8%

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

Alternative 2: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 1:\\ \;\;\;\;x + t\_1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 1.0) (+ x (* t_1 y)) (+ x (* (- z t) (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 1.0) {
		tmp = x + (t_1 * y);
	} else {
		tmp = x + ((z - t) * (y / (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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= 1.0d0) then
        tmp = x + (t_1 * y)
    else
        tmp = x + ((z - t) * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 1.0) {
		tmp = x + (t_1 * y);
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= 1.0:
		tmp = x + (t_1 * y)
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 1.0)
		tmp = Float64(x + Float64(t_1 * y));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= 1.0)
		tmp = x + (t_1 * y);
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1.0], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1

   1. Initial program 99.6%

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

   if 1 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 89.3%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-/l* 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 99.6%

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

Alternative 3: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 2:\\ \;\;\;\;x + t\_1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 2.0) (+ x (* t_1 y)) (+ x (* z (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 2.0) {
		tmp = x + (t_1 * y);
	} else {
		tmp = x + (z * (y / (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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= 2.0d0) then
        tmp = x + (t_1 * y)
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 2.0) {
		tmp = x + (t_1 * y);
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= 2.0:
		tmp = x + (t_1 * y)
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 2.0)
		tmp = Float64(x + Float64(t_1 * y));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= 2.0)
		tmp = x + (t_1 * y);
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2.0], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 2

   1. Initial program 99.6%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 88.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 88.8%

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

      2. un-div-inv 88.8%

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

   4. Applied egg-rr 88.8%

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

   5. Taylor expanded in z around inf 88.8%

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

      1. associate-/r/ 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 2:\\ \;\;\;\;x + \frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+79} \lor \neg \left(t \leq 2 \cdot 10^{+119}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.1e+79) (not (<= t 2e+119)))
   (+ y x)
   (+ x (/ z (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e+79) || !(t <= 2e+119)) {
		tmp = y + x;
	} else {
		tmp = x + (z / ((a - t) / 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 <= (-3.1d+79)) .or. (.not. (t <= 2d+119))) then
        tmp = y + x
    else
        tmp = x + (z / ((a - t) / 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 <= -3.1e+79) || !(t <= 2e+119)) {
		tmp = y + x;
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.1e+79) or not (t <= 2e+119):
		tmp = y + x
	else:
		tmp = x + (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.1e+79) || !(t <= 2e+119))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.1e+79) || ~((t <= 2e+119)))
		tmp = y + x;
	else
		tmp = x + (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.1e+79], N[Not[LessEqual[t, 2e+119]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0999999999999999e79 or 1.99999999999999989e119 < t

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   if -3.0999999999999999e79 < t < 1.99999999999999989e119

   1. Initial program 96.9%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-/l* 96.7%

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

   6. Applied egg-rr 96.7%

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

      1. clear-num 96.6%

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

      2. un-div-inv 97.1%

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

   8. Applied egg-rr 97.1%

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

   9. Taylor expanded in z around inf 88.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+79} \lor \neg \left(t \leq 2 \cdot 10^{+119}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+80} \lor \neg \left(t \leq 1.35 \cdot 10^{+118}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.6e+80) (not (<= t 1.35e+118)))
   (+ y x)
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.6e+80) || !(t <= 1.35e+118)) {
		tmp = y + x;
	} 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 ((t <= (-8.6d+80)) .or. (.not. (t <= 1.35d+118))) then
        tmp = y + x
    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 ((t <= -8.6e+80) || !(t <= 1.35e+118)) {
		tmp = y + x;
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.6e+80) or not (t <= 1.35e+118):
		tmp = y + x
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.6e+80) || !(t <= 1.35e+118))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.6e+80) || ~((t <= 1.35e+118)))
		tmp = y + x;
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.6e+80], N[Not[LessEqual[t, 1.35e+118]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.60000000000000008e80 or 1.35e118 < t

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   if -8.60000000000000008e80 < t < 1.35e118

   1. Initial program 96.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 96.7%

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

      2. un-div-inv 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in z around inf 88.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+80} \lor \neg \left(t \leq 1.35 \cdot 10^{+118}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+73} \lor \neg \left(t \leq 2.3 \cdot 10^{+118}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e+73) (not (<= t 2.3e+118)))
   (+ y x)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+73) || !(t <= 2.3e+118)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / (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 ((t <= (-1.5d+73)) .or. (.not. (t <= 2.3d+118))) then
        tmp = y + x
    else
        tmp = x + (y * (z / (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 ((t <= -1.5e+73) || !(t <= 2.3e+118)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.5e+73) or not (t <= 2.3e+118):
		tmp = y + x
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e+73) || !(t <= 2.3e+118))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.5e+73) || ~((t <= 2.3e+118)))
		tmp = y + x;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.5e+73], N[Not[LessEqual[t, 2.3e+118]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000005e73 or 2.30000000000000016e118 < t

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   if -1.50000000000000005e73 < t < 2.30000000000000016e118

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 86.6%

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

      1. associate-/l* 88.5%

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

   5. Simplified 88.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+73} \lor \neg \left(t \leq 2.3 \cdot 10^{+118}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e-13)
   (+ x (/ z (/ (- a t) y)))
   (if (<= z 4.8e-13) (+ x (* y (/ t (- t a)))) (+ x (* z (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e-13) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 4.8e-13) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (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 <= (-4.7d-13)) then
        tmp = x + (z / ((a - t) / y))
    else if (z <= 4.8d-13) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (z * (y / (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 <= -4.7e-13) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 4.8e-13) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e-13:
		tmp = x + (z / ((a - t) / y))
	elif z <= 4.8e-13:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e-13)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (z <= 4.8e-13)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.7e-13)
		tmp = x + (z / ((a - t) / y));
	elseif (z <= 4.8e-13)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e-13], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-13], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7000000000000002e-13

   1. Initial program 96.3%

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

      1. associate-*r/ 86.1%

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

   3. Simplified 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in z around inf 93.3%

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

   if -4.7000000000000002e-13 < z < 4.7999999999999997e-13

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 86.6%

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

      1. +-commutative 86.6%

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

      2. associate-*r/ 86.6%

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

      3. mul-1-neg 86.6%

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

      4. distribute-lft-neg-out 86.6%

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

      5. *-commutative 86.6%

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

      6. *-lft-identity 86.6%

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

      7. times-frac 92.7%

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

      8. /-rgt-identity 92.7%

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

      9. distribute-neg-frac 92.7%

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

      10. distribute-neg-frac2 92.7%

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

      11. neg-sub0 92.7%

          \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} + x \]

      12. sub-neg 92.7%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} + x \]

      13. +-commutative 92.7%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} + x \]

      14. associate--r+ 92.7%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} + x \]

      15. neg-sub0 92.7%

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

      16. remove-double-neg 92.7%

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

   7. Simplified 92.7%

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

   if 4.7999999999999997e-13 < z

   1. Initial program 96.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 96.0%

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

      2. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in z around inf 89.4%

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

      1. associate-/r/ 90.7%

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

   7. Applied egg-rr 90.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+31} \lor \neg \left(t \leq 5.3 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e+31) (not (<= t 5.3e-17))) (+ y x) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+31) || !(t <= 5.3e-17)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2d+31)) .or. (.not. (t <= 5.3d-17))) then
        tmp = y + x
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+31) || !(t <= 5.3e-17)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e+31) or not (t <= 5.3e-17):
		tmp = y + x
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e+31) || !(t <= 5.3e-17))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2e+31) || ~((t <= 5.3e-17)))
		tmp = y + x;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e+31], N[Not[LessEqual[t, 5.3e-17]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999999e31 or 5.2999999999999998e-17 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 76.7%

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

      1. +-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -1.9999999999999999e31 < t < 5.2999999999999998e-17

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 83.4%

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

   7. Simplified 83.4%

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

      1. clear-num 83.4%

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

      2. un-div-inv 83.4%

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

   9. Applied egg-rr 83.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+31} \lor \neg \left(t \leq 5.3 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+38} \lor \neg \left(t \leq 4.4 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.65e+38) (not (<= t 4.4e-17))) (+ y x) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.65e+38) || !(t <= 4.4e-17)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.65d+38)) .or. (.not. (t <= 4.4d-17))) then
        tmp = y + x
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.65e+38) || !(t <= 4.4e-17)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.65e+38) or not (t <= 4.4e-17):
		tmp = y + x
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.65e+38) || !(t <= 4.4e-17))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.65e+38) || ~((t <= 4.4e-17)))
		tmp = y + x;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.65e+38], N[Not[LessEqual[t, 4.4e-17]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65e38 or 4.4e-17 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 76.7%

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

      1. +-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -1.65e38 < t < 4.4e-17

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+38} \lor \neg \left(t \leq 4.4 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+31} \lor \neg \left(t \leq 7.5 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e+31) (not (<= t 7.5e-17))) (+ y x) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e+31) || !(t <= 7.5e-17)) {
		tmp = y + x;
	} 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 <= (-4.6d+31)) .or. (.not. (t <= 7.5d-17))) then
        tmp = y + x
    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 <= -4.6e+31) || !(t <= 7.5e-17)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e+31) or not (t <= 7.5e-17):
		tmp = y + x
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e+31) || !(t <= 7.5e-17))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e+31) || ~((t <= 7.5e-17)))
		tmp = y + x;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e+31], N[Not[LessEqual[t, 7.5e-17]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5999999999999999e31 or 7.49999999999999984e-17 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 76.7%

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

      1. +-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -4.5999999999999999e31 < t < 7.49999999999999984e-17

   1. Initial program 96.2%

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

      1. associate-*r/ 94.2%

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

   3. Simplified 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-/l* 96.6%

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

   6. Applied egg-rr 96.6%

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

      1. clear-num 96.6%

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

      2. un-div-inv 97.2%

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

   8. Applied egg-rr 97.2%

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

   9. Taylor expanded in t around 0 80.0%

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

       1. *-commutative 80.0%

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

       2. associate-*r/ 82.6%

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

   11. Simplified 82.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+31} \lor \neg \left(t \leq 7.5 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+131}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.9e+115)
   (* y (- 1.0 (/ z t)))
   (if (<= y 7.5e+131) (+ y x) (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e+115) {
		tmp = y * (1.0 - (z / t));
	} else if (y <= 7.5e+131) {
		tmp = y + x;
	} else {
		tmp = y * ((z - 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 (y <= (-2.9d+115)) then
        tmp = y * (1.0d0 - (z / t))
    else if (y <= 7.5d+131) then
        tmp = y + x
    else
        tmp = y * ((z - 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 (y <= -2.9e+115) {
		tmp = y * (1.0 - (z / t));
	} else if (y <= 7.5e+131) {
		tmp = y + x;
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.9e+115:
		tmp = y * (1.0 - (z / t))
	elif y <= 7.5e+131:
		tmp = y + x
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.9e+115)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (y <= 7.5e+131)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(Float64(z - t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.9e+115)
		tmp = y * (1.0 - (z / t));
	elseif (y <= 7.5e+131)
		tmp = y + x;
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.9e+115], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+131], N[(y + x), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.90000000000000005e115

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. unsub-neg 43.6%

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

      3. associate-/l* 53.3%

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

      4. div-sub 53.3%

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

      5. *-inverses 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in x around 0 53.3%

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

      1. mul-1-neg 53.3%

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

      2. sub-neg 53.3%

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

      3. metadata-eval 53.3%

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

      4. distribute-rgt-neg-in 53.3%

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

      5. +-commutative 53.3%

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

      6. distribute-neg-in 53.3%

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

      7. metadata-eval 53.3%

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

      8. sub-neg 53.3%

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

   10. Simplified 53.3%

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

   if -2.90000000000000005e115 < y < 7.4999999999999995e131

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. fma-define 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 71.1%

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

      1. +-commutative 71.1%

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

   7. Simplified 71.1%

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

   if 7.4999999999999995e131 < y

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf 55.1%

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

   4. Taylor expanded in y around inf 58.9%

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

   5. Taylor expanded in a around 0 58.9%

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

Alternative 12: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+130}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.18e+114)
   (* y (- 1.0 (/ z t)))
   (if (<= y 4.4e+130) (+ y x) (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.18e+114) {
		tmp = y * (1.0 - (z / t));
	} else if (y <= 4.4e+130) {
		tmp = y + x;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.18d+114)) then
        tmp = y * (1.0d0 - (z / t))
    else if (y <= 4.4d+130) then
        tmp = y + x
    else
        tmp = y * (z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.18e+114) {
		tmp = y * (1.0 - (z / t));
	} else if (y <= 4.4e+130) {
		tmp = y + x;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.18e+114:
		tmp = y * (1.0 - (z / t))
	elif y <= 4.4e+130:
		tmp = y + x
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.18e+114)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (y <= 4.4e+130)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.18e+114)
		tmp = y * (1.0 - (z / t));
	elseif (y <= 4.4e+130)
		tmp = y + x;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.18e+114], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+130], N[(y + x), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.18000000000000005e114

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. unsub-neg 43.6%

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

      3. associate-/l* 53.3%

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

      4. div-sub 53.3%

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

      5. *-inverses 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in x around 0 53.3%

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

      1. mul-1-neg 53.3%

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

      2. sub-neg 53.3%

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

      3. metadata-eval 53.3%

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

      4. distribute-rgt-neg-in 53.3%

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

      5. +-commutative 53.3%

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

      6. distribute-neg-in 53.3%

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

      7. metadata-eval 53.3%

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

      8. sub-neg 53.3%

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

   10. Simplified 53.3%

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

   if -1.18000000000000005e114 < y < 4.39999999999999987e130

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. fma-define 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 71.1%

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

      1. +-commutative 71.1%

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

   7. Simplified 71.1%

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

   if 4.39999999999999987e130 < y

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf 55.1%

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

   4. Taylor expanded in y around inf 58.9%

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

   5. Taylor expanded in z around inf 43.6%

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

Alternative 13: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-118} \lor \neg \left(t \leq 2.5 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e-118) (not (<= t 2.5e-17))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e-118) || !(t <= 2.5e-17)) {
		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 ((t <= (-4d-118)) .or. (.not. (t <= 2.5d-17))) 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 ((t <= -4e-118) || !(t <= 2.5e-17)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e-118) or not (t <= 2.5e-17):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e-118) || !(t <= 2.5e-17))
		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 ((t <= -4e-118) || ~((t <= 2.5e-17)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e-118], N[Not[LessEqual[t, 2.5e-17]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999994e-118 or 2.4999999999999999e-17 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 72.9%

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

      1. +-commutative 72.9%

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

   7. Simplified 72.9%

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

   if -3.99999999999999994e-118 < t < 2.4999999999999999e-17

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. fma-define 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around 0 55.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-118} \lor \neg \left(t \leq 2.5 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.0% 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 97.8%

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

   1. +-commutative 97.8%

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

   2. fma-define 97.8%

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

3. Simplified 97.8%

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

5. Taylor expanded in y around 0 54.0%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -8508084860551241/100000000000000000000000000000000) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t)))))))

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