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

Percentage Accurate: 98.1% → 98.5%

Time: 9.6s

Alternatives: 11

Speedup: 0.5×

• could not determine a ground truth

  1. x = 1.4324249733704828e+22
  2. y = 3.572043286161266e+22
  3. z = 5.582963953920292e-289
  4. t = 9.519354759624401e+114
  5. a = -7.799674529685176e+76

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: 98.1% 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: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq 10^{+295}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y (/ (- z t) (- a t))) 1e+295)
   (+ x (/ y (/ (- a t) (- z t))))
   (+ x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * ((z - t) / (a - t))) <= 1e+295) {
		tmp = x + (y / ((a - t) / (z - t)));
	} 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 ((y * ((z - t) / (a - t))) <= 1d+295) then
        tmp = x + (y / ((a - t) / (z - t)))
    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 ((y * ((z - t) / (a - t))) <= 1e+295) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y * ((z - t) / (a - t))) <= 1e+295:
		tmp = x + (y / ((a - t) / (z - t)))
	else:
		tmp = x + ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * Float64(Float64(z - t) / Float64(a - t))) <= 1e+295)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	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 ((y * ((z - t) / (a - t))) <= 1e+295)
		tmp = x + (y / ((a - t) / (z - t)));
	else
		tmp = x + ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+295], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 9.9999999999999998e294

   1. Initial program 99.5%

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

      1. clear-num 99.4%

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

      2. un-div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

   if 9.9999999999999998e294 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 66.4%

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

   3. Taylor expanded in z around inf 99.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq 10^{+295}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+179}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+119}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+86}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.8e+179)
   (+ y x)
   (if (<= t -3.5e+119)
     (- x (* y (/ z t)))
     (if (<= t -4.5e+86)
       (+ y x)
       (if (<= t -9.6e+41)
         (+ x (/ y (/ a (- z t))))
         (if (<= t 1.6e+134) (+ x (* z (/ y (- a t)))) (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+179) {
		tmp = y + x;
	} else if (t <= -3.5e+119) {
		tmp = x - (y * (z / t));
	} else if (t <= -4.5e+86) {
		tmp = y + x;
	} else if (t <= -9.6e+41) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 1.6e+134) {
		tmp = x + (z * (y / (a - 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 (t <= (-7.8d+179)) then
        tmp = y + x
    else if (t <= (-3.5d+119)) then
        tmp = x - (y * (z / t))
    else if (t <= (-4.5d+86)) then
        tmp = y + x
    else if (t <= (-9.6d+41)) then
        tmp = x + (y / (a / (z - t)))
    else if (t <= 1.6d+134) then
        tmp = x + (z * (y / (a - 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 (t <= -7.8e+179) {
		tmp = y + x;
	} else if (t <= -3.5e+119) {
		tmp = x - (y * (z / t));
	} else if (t <= -4.5e+86) {
		tmp = y + x;
	} else if (t <= -9.6e+41) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 1.6e+134) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.8e+179:
		tmp = y + x
	elif t <= -3.5e+119:
		tmp = x - (y * (z / t))
	elif t <= -4.5e+86:
		tmp = y + x
	elif t <= -9.6e+41:
		tmp = x + (y / (a / (z - t)))
	elif t <= 1.6e+134:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.8e+179)
		tmp = Float64(y + x);
	elseif (t <= -3.5e+119)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= -4.5e+86)
		tmp = Float64(y + x);
	elseif (t <= -9.6e+41)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t <= 1.6e+134)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.8e+179)
		tmp = y + x;
	elseif (t <= -3.5e+119)
		tmp = x - (y * (z / t));
	elseif (t <= -4.5e+86)
		tmp = y + x;
	elseif (t <= -9.6e+41)
		tmp = x + (y / (a / (z - t)));
	elseif (t <= 1.6e+134)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.8e+179], N[(y + x), $MachinePrecision], If[LessEqual[t, -3.5e+119], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.5e+86], N[(y + x), $MachinePrecision], If[LessEqual[t, -9.6e+41], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+134], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.79999999999999947e179 or -3.5000000000000001e119 < t < -4.49999999999999993e86 or 1.6e134 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 84.4%

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

      1. +-commutative 84.4%

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

   5. Simplified 84.4%

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

   if -7.79999999999999947e179 < t < -3.5000000000000001e119

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

      3. associate-/l* 75.9%

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

      4. div-sub 75.9%

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

      5. sub-neg 75.9%

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

      6. *-inverses 75.9%

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

      7. metadata-eval 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in z around inf 76.9%

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

      1. associate-*r/ 86.1%

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

   8. Simplified 86.1%

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

   if -4.49999999999999993e86 < t < -9.6000000000000007e41

   1. Initial program 99.9%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around inf 77.8%

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

   if -9.6000000000000007e41 < t < 1.6e134

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-/l* 90.2%

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

   5. Applied egg-rr 90.2%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+179}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+119}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+86}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+180}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+119}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{+86} \lor \neg \left(t \leq 11500000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+180)
   (+ y x)
   (if (<= t -9.5e+119)
     (- x (* y (/ z t)))
     (if (or (<= t -4.3e+86) (not (<= t 11500000000.0)))
       (+ 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+180) {
		tmp = y + x;
	} else if (t <= -9.5e+119) {
		tmp = x - (y * (z / t));
	} else if ((t <= -4.3e+86) || !(t <= 11500000000.0)) {
		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+180)) then
        tmp = y + x
    else if (t <= (-9.5d+119)) then
        tmp = x - (y * (z / t))
    else if ((t <= (-4.3d+86)) .or. (.not. (t <= 11500000000.0d0))) 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+180) {
		tmp = y + x;
	} else if (t <= -9.5e+119) {
		tmp = x - (y * (z / t));
	} else if ((t <= -4.3e+86) || !(t <= 11500000000.0)) {
		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+180:
		tmp = y + x
	elif t <= -9.5e+119:
		tmp = x - (y * (z / t))
	elif (t <= -4.3e+86) or not (t <= 11500000000.0):
		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+180)
		tmp = Float64(y + x);
	elseif (t <= -9.5e+119)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif ((t <= -4.3e+86) || !(t <= 11500000000.0))
		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+180)
		tmp = y + x;
	elseif (t <= -9.5e+119)
		tmp = x - (y * (z / t));
	elseif ((t <= -4.3e+86) || ~((t <= 11500000000.0)))
		tmp = y + x;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+180], N[(y + x), $MachinePrecision], If[LessEqual[t, -9.5e+119], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.3e+86], N[Not[LessEqual[t, 11500000000.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8000000000000001e180 or -9.4999999999999994e119 < t < -4.3000000000000002e86 or 1.15e10 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 79.0%

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

      1. +-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -1.8000000000000001e180 < t < -9.4999999999999994e119

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

      3. associate-/l* 75.9%

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

      4. div-sub 75.9%

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

      5. sub-neg 75.9%

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

      6. *-inverses 75.9%

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

      7. metadata-eval 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in z around inf 76.9%

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

      1. associate-*r/ 86.1%

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

   8. Simplified 86.1%

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

   if -4.3000000000000002e86 < t < 1.15e10

   1. Initial program 95.8%

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

   3. Taylor expanded in t around 0 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 77.0%

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

   5. Applied egg-rr 77.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+180}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+119}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{+86} \lor \neg \left(t \leq 11500000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+55}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+137}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (+ (/ z t) -1.0)))))
   (if (<= t -4.2e+135)
     t_1
     (if (<= t -2.2e+55)
       (- x (* y (/ t (- a t))))
       (if (<= t 1.75e+137) (+ x (* z (/ y (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z / t) + -1.0));
	double tmp;
	if (t <= -4.2e+135) {
		tmp = t_1;
	} else if (t <= -2.2e+55) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 1.75e+137) {
		tmp = x + (z * (y / (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) + (-1.0d0)))
    if (t <= (-4.2d+135)) then
        tmp = t_1
    else if (t <= (-2.2d+55)) then
        tmp = x - (y * (t / (a - t)))
    else if (t <= 1.75d+137) then
        tmp = x + (z * (y / (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) + -1.0));
	double tmp;
	if (t <= -4.2e+135) {
		tmp = t_1;
	} else if (t <= -2.2e+55) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 1.75e+137) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z / t) + -1.0))
	tmp = 0
	if t <= -4.2e+135:
		tmp = t_1
	elif t <= -2.2e+55:
		tmp = x - (y * (t / (a - t)))
	elif t <= 1.75e+137:
		tmp = x + (z * (y / (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) + -1.0)))
	tmp = 0.0
	if (t <= -4.2e+135)
		tmp = t_1;
	elseif (t <= -2.2e+55)
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	elseif (t <= 1.75e+137)
		tmp = Float64(x + Float64(z * Float64(y / 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) + -1.0));
	tmp = 0.0;
	if (t <= -4.2e+135)
		tmp = t_1;
	elseif (t <= -2.2e+55)
		tmp = x - (y * (t / (a - t)));
	elseif (t <= 1.75e+137)
		tmp = x + (z * (y / (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] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+135], t$95$1, If[LessEqual[t, -2.2e+55], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+137], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000019e135 or 1.7500000000000001e137 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

      3. associate-/l* 95.1%

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

      4. div-sub 95.1%

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

      5. sub-neg 95.1%

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

      6. *-inverses 95.1%

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

      7. metadata-eval 95.1%

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

   5. Simplified 95.1%

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

   if -4.20000000000000019e135 < t < -2.2000000000000001e55

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

      3. *-commutative 86.8%

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

      4. associate-/l* 95.5%

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

   5. Simplified 95.5%

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

   if -2.2000000000000001e55 < t < 1.7500000000000001e137

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-/l* 89.4%

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

   5. Applied egg-rr 89.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+135}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+55}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+137}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 10^{+295}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t_1 1e+295) (+ t_1 x) (+ x (/ (* y z) (- a t))))))

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 <= 1e+295) {
		tmp = t_1 + 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t_1 <= 1d+295) then
        tmp = t_1 + 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 t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 1e+295) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t_1 <= 1e+295:
		tmp = t_1 + x
	else:
		tmp = x + ((y * z) / (a - t))
	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 <= 1e+295)
		tmp = Float64(t_1 + 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)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t_1 <= 1e+295)
		tmp = t_1 + x;
	else
		tmp = x + ((y * z) / (a - t));
	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, 1e+295], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 9.9999999999999998e294

   1. Initial program 99.5%

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

   if 9.9999999999999998e294 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 66.4%

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

   3. Taylor expanded in z around inf 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq 10^{+295}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t_1 2e+220) (+ t_1 x) (- x (* (- z t) (/ y (- t a)))))))

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 <= 2e+220) {
		tmp = t_1 + x;
	} else {
		tmp = x - ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t_1 <= 2d+220) then
        tmp = t_1 + x
    else
        tmp = x - ((z - t) * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 2e+220) {
		tmp = t_1 + x;
	} else {
		tmp = x - ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t_1 <= 2e+220:
		tmp = t_1 + x
	else:
		tmp = x - ((z - t) * (y / (t - a)))
	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 <= 2e+220)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x - Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	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 <= 2e+220)
		tmp = t_1 + x;
	else
		tmp = x - ((z - t) * (y / (t - a)));
	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, 2e+220], N[(t$95$1 + x), $MachinePrecision], N[(x - N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 2e220

   1. Initial program 99.5%

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

   if 2e220 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 82.5%

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

      1. associate-*r/ 69.0%

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

   3. Simplified 69.0%

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

      1. *-commutative 69.0%

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

      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 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq 2 \cdot 10^{+220}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+179} \lor \neg \left(t \leq 4.6 \cdot 10^{+133}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7e+179) (not (<= t 4.6e+133)))
   (+ y x)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+179) || !(t <= 4.6e+133)) {
		tmp = y + x;
	} 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 ((t <= (-7d+179)) .or. (.not. (t <= 4.6d+133))) then
        tmp = y + x
    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 ((t <= -7e+179) || !(t <= 4.6e+133)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7e+179) or not (t <= 4.6e+133):
		tmp = y + x
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7e+179) || !(t <= 4.6e+133))
		tmp = Float64(y + x);
	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 ((t <= -7e+179) || ~((t <= 4.6e+133)))
		tmp = y + x;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7e+179], N[Not[LessEqual[t, 4.6e+133]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.0000000000000003e179 or 4.5999999999999998e133 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 85.0%

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

      1. +-commutative 85.0%

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

   5. Simplified 85.0%

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

   if -7.0000000000000003e179 < t < 4.5999999999999998e133

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-/l* 86.0%

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

   5. Applied egg-rr 86.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+179} \lor \neg \left(t \leq 4.6 \cdot 10^{+133}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+86} \lor \neg \left(t \leq 7 \cdot 10^{+135}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+86) (not (<= t 7e+135)))
   (- x (* y (+ (/ z t) -1.0)))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+86) || !(t <= 7e+135)) {
		tmp = x - (y * ((z / t) + -1.0));
	} 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 ((t <= (-4.5d+86)) .or. (.not. (t <= 7d+135))) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    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 ((t <= -4.5e+86) || !(t <= 7e+135)) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+86) or not (t <= 7e+135):
		tmp = x - (y * ((z / t) + -1.0))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+86) || !(t <= 7e+135))
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	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 ((t <= -4.5e+86) || ~((t <= 7e+135)))
		tmp = x - (y * ((z / t) + -1.0));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+86], N[Not[LessEqual[t, 7e+135]], $MachinePrecision]], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999993e86 or 7.0000000000000005e135 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. unsub-neg 64.8%

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

      3. associate-/l* 91.6%

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

      4. div-sub 91.6%

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

      5. sub-neg 91.6%

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

      6. *-inverses 91.6%

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

      7. metadata-eval 91.6%

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

   5. Simplified 91.6%

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

   if -4.49999999999999993e86 < t < 7.0000000000000005e135

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/l* 88.7%

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

   5. Applied egg-rr 88.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+86} \lor \neg \left(t \leq 7 \cdot 10^{+135}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+86} \lor \neg \left(t \leq 300000000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+86) (not (<= t 300000000000.0)))
   (+ y x)
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+86) || !(t <= 300000000000.0)) {
		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 <= (-8.5d+86)) .or. (.not. (t <= 300000000000.0d0))) 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 <= -8.5e+86) || !(t <= 300000000000.0)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+86) or not (t <= 300000000000.0):
		tmp = y + x
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+86) || !(t <= 300000000000.0))
		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 <= -8.5e+86) || ~((t <= 300000000000.0)))
		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, -8.5e+86], N[Not[LessEqual[t, 300000000000.0]], $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 < -8.5000000000000005e86 or 3e11 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 75.6%

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

      1. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   if -8.5000000000000005e86 < t < 3e11

   1. Initial program 95.8%

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

   3. Taylor expanded in t around 0 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 77.0%

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

   5. Applied egg-rr 77.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+86} \lor \neg \left(t \leq 300000000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+135}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e+183) x (if (<= a 3.2e+135) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e+183) {
		tmp = x;
	} else if (a <= 3.2e+135) {
		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 (a <= (-8d+183)) then
        tmp = x
    else if (a <= 3.2d+135) 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 (a <= -8e+183) {
		tmp = x;
	} else if (a <= 3.2e+135) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e+183:
		tmp = x
	elif a <= 3.2e+135:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e+183)
		tmp = x;
	elseif (a <= 3.2e+135)
		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 (a <= -8e+183)
		tmp = x;
	elseif (a <= 3.2e+135)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e+183], x, If[LessEqual[a, 3.2e+135], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.99999999999999957e183 or 3.19999999999999975e135 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.8%

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

   if -7.99999999999999957e183 < a < 3.19999999999999975e135

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 63.2%

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

      1. +-commutative 63.2%

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

   5. Simplified 63.2%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+135}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 97.7%

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

3. Taylor expanded in x around inf 49.4%

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

4. Final simplification 49.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 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 2024079 
(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)))))