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

Percentage Accurate: 98.2% → 98.9%

Time: 8.2s

Alternatives: 11

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: 98.2% 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: 98.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 61.2%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

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

   1. Initial program 98.7%

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

4. Final simplification 98.8%

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

Alternative 2: 98.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 61.2%

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

   3. Taylor expanded in z around inf 99.7%

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

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

   1. Initial program 98.7%

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

4. Final simplification 98.8%

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

Alternative 3: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+49} \lor \neg \left(t \leq 1.65 \cdot 10^{+84}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+49) (not (<= t 1.65e+84)))
   (+ y x)
   (+ x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+49) || !(t <= 1.65e+84)) {
		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 <= (-2.3d+49)) .or. (.not. (t <= 1.65d+84))) 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 <= -2.3e+49) || !(t <= 1.65e+84)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+49) or not (t <= 1.65e+84):
		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 <= -2.3e+49) || !(t <= 1.65e+84))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e+49) || ~((t <= 1.65e+84)))
		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, -2.3e+49], N[Not[LessEqual[t, 1.65e+84]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.30000000000000002e49 or 1.65000000000000008e84 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 84.8%

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

      1. +-commutative 84.8%

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

   5. Simplified 84.8%

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

   if -2.30000000000000002e49 < t < 1.65000000000000008e84

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf 88.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+49} \lor \neg \left(t \leq 1.65 \cdot 10^{+84}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+56} \lor \neg \left(t \leq 3.7 \cdot 10^{+84}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+56) (not (<= t 3.7e+84)))
   (+ y x)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+56) || !(t <= 3.7e+84)) {
		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 <= (-4.8d+56)) .or. (.not. (t <= 3.7d+84))) 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 <= -4.8e+56) || !(t <= 3.7e+84)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e+56) or not (t <= 3.7e+84):
		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 <= -4.8e+56) || !(t <= 3.7e+84))
		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 <= -4.8e+56) || ~((t <= 3.7e+84)))
		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, -4.8e+56], N[Not[LessEqual[t, 3.7e+84]], $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 < -4.80000000000000027e56 or 3.7e84 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 84.7%

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

      1. +-commutative 84.7%

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

   5. Simplified 84.7%

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

   if -4.80000000000000027e56 < t < 3.7e84

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf 88.0%

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

      1. associate-/l* 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+56} \lor \neg \left(t \leq 3.7 \cdot 10^{+84}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e-24)
   (+ x (* y (/ t (- t a))))
   (if (<= t 3e+25) (+ x (/ (* y z) (- a t))) (+ x (* y (- 1.0 (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e-24) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 3e+25) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (1.0 - (z / 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 <= (-4.4d-24)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 3d+25) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (y * (1.0d0 - (z / 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 <= -4.4e-24) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 3e+25) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (1.0 - (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e-24:
		tmp = x + (y * (t / (t - a)))
	elif t <= 3e+25:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (y * (1.0 - (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e-24)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 3e+25)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e-24)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 3e+25)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (y * (1.0 - (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e-24], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+25], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.40000000000000003e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.8%

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

      1. mul-1-neg 83.8%

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

      2. unsub-neg 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-/l* 95.1%

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

   5. Simplified 95.1%

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

   if -4.40000000000000003e-24 < t < 3.00000000000000006e25

   1. Initial program 94.3%

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

   3. Taylor expanded in z around inf 89.9%

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

   if 3.00000000000000006e25 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. unsub-neg 72.6%

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

      3. associate-/l* 89.1%

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

      4. div-sub 89.1%

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

      5. sub-neg 89.1%

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

      6. *-inverses 89.1%

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

      7. metadata-eval 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+50}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+50)
   (+ y x)
   (if (<= t 4.5e+31) (+ x (/ (* y z) (- a t))) (+ x (* y (- 1.0 (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+50) {
		tmp = y + x;
	} else if (t <= 4.5e+31) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (1.0 - (z / 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 <= (-9d+50)) then
        tmp = y + x
    else if (t <= 4.5d+31) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (y * (1.0d0 - (z / 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 <= -9e+50) {
		tmp = y + x;
	} else if (t <= 4.5e+31) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (1.0 - (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+50:
		tmp = y + x
	elif t <= 4.5e+31:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (y * (1.0 - (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+50)
		tmp = Float64(y + x);
	elseif (t <= 4.5e+31)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+50)
		tmp = y + x;
	elseif (t <= 4.5e+31)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (y * (1.0 - (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+50], N[(y + x), $MachinePrecision], If[LessEqual[t, 4.5e+31], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.00000000000000027e50

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 93.1%

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

      1. +-commutative 93.1%

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

   5. Simplified 93.1%

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

   if -9.00000000000000027e50 < t < 4.4999999999999996e31

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 89.9%

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

   if 4.4999999999999996e31 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. unsub-neg 72.6%

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

      3. associate-/l* 89.1%

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

      4. div-sub 89.1%

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

      5. sub-neg 89.1%

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

      6. *-inverses 89.1%

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

      7. metadata-eval 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+50}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-57} \lor \neg \left(t \leq 4.5 \cdot 10^{+42}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.05e-57) (not (<= t 4.5e+42))) (+ y x) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.05e-57) || !(t <= 4.5e+42)) {
		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 <= (-2.05d-57)) .or. (.not. (t <= 4.5d+42))) 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 <= -2.05e-57) || !(t <= 4.5e+42)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.05e-57) or not (t <= 4.5e+42):
		tmp = y + x
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.05e-57) || !(t <= 4.5e+42))
		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 <= -2.05e-57) || ~((t <= 4.5e+42)))
		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, -2.05e-57], N[Not[LessEqual[t, 4.5e+42]], $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 < -2.0500000000000001e-57 or 4.50000000000000012e42 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.6%

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

      1. +-commutative 81.6%

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

   5. Simplified 81.6%

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

   if -2.0500000000000001e-57 < t < 4.50000000000000012e42

   1. Initial program 94.1%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.0%

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

   4. Applied egg-rr 94.0%

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

   5. Taylor expanded in t around 0 79.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-57} \lor \neg \left(t \leq 4.5 \cdot 10^{+42}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-57} \lor \neg \left(t \leq 1.18 \cdot 10^{+38}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e-57) (not (<= t 1.18e+38))) (+ y x) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-57) || !(t <= 1.18e+38)) {
		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 <= (-1.8d-57)) .or. (.not. (t <= 1.18d+38))) 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 <= -1.8e-57) || !(t <= 1.18e+38)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e-57) or not (t <= 1.18e+38):
		tmp = y + x
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e-57) || !(t <= 1.18e+38))
		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 <= -1.8e-57) || ~((t <= 1.18e+38)))
		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, -1.8e-57], N[Not[LessEqual[t, 1.18e+38]], $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 < -1.8000000000000001e-57 or 1.18e38 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.6%

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

      1. +-commutative 81.6%

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

   5. Simplified 81.6%

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

   if -1.8000000000000001e-57 < t < 1.18e38

   1. Initial program 94.1%

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

   3. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 77.7%

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

   5. Applied egg-rr 77.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-57} \lor \neg \left(t \leq 1.18 \cdot 10^{+38}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3e-75) x (if (<= x 3.3e-255) (* y (- 1.0 (/ z t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3e-75) {
		tmp = x;
	} else if (x <= 3.3e-255) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3d-75)) then
        tmp = x
    else if (x <= 3.3d-255) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3e-75) {
		tmp = x;
	} else if (x <= 3.3e-255) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3e-75:
		tmp = x
	elif x <= 3.3e-255:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3e-75)
		tmp = x;
	elseif (x <= 3.3e-255)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3e-75)
		tmp = x;
	elseif (x <= 3.3e-255)
		tmp = y * (1.0 - (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3e-75], x, If[LessEqual[x, 3.3e-255], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9999999999999999e-75

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 73.2%

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

   if -2.9999999999999999e-75 < x < 3.29999999999999988e-255

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

      3. associate-/l* 59.0%

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

      4. div-sub 59.0%

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

      5. sub-neg 59.0%

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

      6. *-inverses 59.0%

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

      7. metadata-eval 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in y around inf 51.8%

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

   if 3.29999999999999988e-255 < x

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 67.5%

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

      1. +-commutative 67.5%

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

   5. Simplified 67.5%

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

Alternative 10: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-41} \lor \neg \left(t \leq 1.2 \cdot 10^{+32}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.55e-41) (not (<= t 1.2e+32))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.55e-41) || !(t <= 1.2e+32)) {
		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 <= (-1.55d-41)) .or. (.not. (t <= 1.2d+32))) 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 <= -1.55e-41) || !(t <= 1.2e+32)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.55e-41) or not (t <= 1.2e+32):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.55e-41) || !(t <= 1.2e+32))
		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 <= -1.55e-41) || ~((t <= 1.2e+32)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.55e-41], N[Not[LessEqual[t, 1.2e+32]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e-41 or 1.19999999999999996e32 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.2%

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

      1. +-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -1.55e-41 < t < 1.19999999999999996e32

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 48.9%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-41} \lor \neg \left(t \leq 1.2 \cdot 10^{+32}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% 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 97.0%

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

3. Taylor expanded in x around inf 52.5%

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

Developer target: 99.3% 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 2024087 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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