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

Percentage Accurate: 98.2% → 98.8%

Time: 11.7s

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: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(y, t\_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 2e+119) (fma y t_1 x) (+ x (/ z (/ (- a t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 2e+119) {
		tmp = fma(y, t_1, x);
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 2e+119)
		tmp = fma(y, t_1, x);
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+119], N[(y * t$95$1 + x), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.99999999999999989e119

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. fma-define 97.8%

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

   3. Simplified 97.8%

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

   if 1.99999999999999989e119 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 77.3%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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* 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in z around inf 99.9%

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

Alternative 2: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;x - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e-40)
   (+ y x)
   (if (<= t 3.8e-97)
     (+ x (/ (* z y) a))
     (if (<= t 2.5e+68) (- x (/ (* z y) t)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e-40) {
		tmp = y + x;
	} else if (t <= 3.8e-97) {
		tmp = x + ((z * y) / a);
	} else if (t <= 2.5e+68) {
		tmp = x - ((z * y) / 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 <= (-1.1d-40)) then
        tmp = y + x
    else if (t <= 3.8d-97) then
        tmp = x + ((z * y) / a)
    else if (t <= 2.5d+68) then
        tmp = x - ((z * y) / 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 <= -1.1e-40) {
		tmp = y + x;
	} else if (t <= 3.8e-97) {
		tmp = x + ((z * y) / a);
	} else if (t <= 2.5e+68) {
		tmp = x - ((z * y) / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e-40:
		tmp = y + x
	elif t <= 3.8e-97:
		tmp = x + ((z * y) / a)
	elif t <= 2.5e+68:
		tmp = x - ((z * y) / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e-40)
		tmp = Float64(y + x);
	elseif (t <= 3.8e-97)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif (t <= 2.5e+68)
		tmp = Float64(x - Float64(Float64(z * y) / 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 <= -1.1e-40)
		tmp = y + x;
	elseif (t <= 3.8e-97)
		tmp = x + ((z * y) / a);
	elseif (t <= 2.5e+68)
		tmp = x - ((z * y) / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e-40], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.8e-97], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+68], N[(x - N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.10000000000000004e-40 or 2.5000000000000002e68 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 80.6%

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

      1. +-commutative 80.6%

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

   5. Simplified 80.6%

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

   if -1.10000000000000004e-40 < t < 3.8000000000000001e-97

   1. Initial program 92.2%

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

   3. Taylor expanded in t around 0 79.2%

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

   if 3.8000000000000001e-97 < t < 2.5000000000000002e68

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf 64.5%

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

      1. associate-+r+ 64.5%

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

      2. associate--l+ 64.5%

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

      3. distribute-lft-out-- 64.5%

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

      4. div-sub 64.5%

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

      5. associate-+r+ 64.5%

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

      6. +-commutative 64.5%

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

      7. mul-1-neg 64.5%

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

      8. unsub-neg 64.5%

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

      9. *-commutative 64.5%

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

      10. distribute-lft-out-- 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in z around inf 70.9%

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

      1. associate-*r/ 70.9%

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

      2. neg-mul-1 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

   8. Simplified 70.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;x - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e-41)
   (+ y x)
   (if (<= t 2.6e-60)
     (+ x (/ (* z y) a))
     (if (<= t 4.4e+67) (- x (* y (/ z t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e-41) {
		tmp = y + x;
	} else if (t <= 2.6e-60) {
		tmp = x + ((z * y) / a);
	} else if (t <= 4.4e+67) {
		tmp = x - (y * (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 (t <= (-8d-41)) then
        tmp = y + x
    else if (t <= 2.6d-60) then
        tmp = x + ((z * y) / a)
    else if (t <= 4.4d+67) then
        tmp = x - (y * (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 (t <= -8e-41) {
		tmp = y + x;
	} else if (t <= 2.6e-60) {
		tmp = x + ((z * y) / a);
	} else if (t <= 4.4e+67) {
		tmp = x - (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e-41:
		tmp = y + x
	elif t <= 2.6e-60:
		tmp = x + ((z * y) / a)
	elif t <= 4.4e+67:
		tmp = x - (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e-41)
		tmp = Float64(y + x);
	elseif (t <= 2.6e-60)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif (t <= 4.4e+67)
		tmp = Float64(x - Float64(y * 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 (t <= -8e-41)
		tmp = y + x;
	elseif (t <= 2.6e-60)
		tmp = x + ((z * y) / a);
	elseif (t <= 4.4e+67)
		tmp = x - (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8e-41], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.6e-60], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+67], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000005e-41 or 4.4e67 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 80.6%

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

      1. +-commutative 80.6%

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

   5. Simplified 80.6%

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

   if -8.00000000000000005e-41 < t < 2.5999999999999998e-60

   1. Initial program 90.3%

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

   3. Taylor expanded in t around 0 77.1%

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

   if 2.5999999999999998e-60 < t < 4.4e67

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 68.9%

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

      1. associate-+r+ 68.9%

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

      2. associate--l+ 68.9%

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

      3. distribute-lft-out-- 68.9%

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

      4. div-sub 68.9%

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

      5. associate-+r+ 68.9%

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

      6. +-commutative 68.9%

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

      7. mul-1-neg 68.9%

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

      8. unsub-neg 68.9%

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

      9. *-commutative 68.9%

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

      10. distribute-lft-out-- 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. associate-/l* 77.3%

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

      3. distribute-rgt-neg-in 77.3%

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

   8. Simplified 77.3%

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

   9. Taylor expanded in y around 0 77.5%

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

       1. mul-1-neg 77.5%

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

       2. associate-*r/ 77.3%

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

       3. sub-neg 77.3%

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

   11. Simplified 77.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+119}:\\ \;\;\;\;x + t\_1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 2e+119) (+ x (* t_1 y)) (+ x (/ z (/ (- a t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 2e+119) {
		tmp = x + (t_1 * y);
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= 2d+119) then
        tmp = x + (t_1 * y)
    else
        tmp = x + (z / ((a - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 2e+119) {
		tmp = x + (t_1 * y);
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= 2e+119:
		tmp = x + (t_1 * y)
	else:
		tmp = x + (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 2e+119)
		tmp = Float64(x + Float64(t_1 * y));
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= 2e+119)
		tmp = x + (t_1 * y);
	else
		tmp = x + (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+119], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.99999999999999989e119

   1. Initial program 97.8%

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

   if 1.99999999999999989e119 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 77.3%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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* 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in z around inf 99.9%

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

4. Final simplification 98.0%

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

Alternative 5: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-60} \lor \neg \left(t \leq 1.8 \cdot 10^{+67}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.22e-60) (not (<= t 1.8e+67)))
   (+ x (* y (/ (- t z) t)))
   (+ x (/ (* z y) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.22e-60) || !(t <= 1.8e+67)) {
		tmp = x + (y * ((t - z) / t));
	} 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 <= (-1.22d-60)) .or. (.not. (t <= 1.8d+67))) then
        tmp = x + (y * ((t - z) / t))
    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 <= -1.22e-60) || !(t <= 1.8e+67)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + ((z * y) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.22e-60) or not (t <= 1.8e+67):
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + ((z * y) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.22e-60) || !(t <= 1.8e+67))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.22e-60) || ~((t <= 1.8e+67)))
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + ((z * y) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.22e-60], N[Not[LessEqual[t, 1.8e+67]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.22e-60 or 1.7999999999999999e67 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/l* 91.9%

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

      3. distribute-rgt-neg-in 91.9%

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

      4. distribute-frac-neg 91.9%

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

      5. neg-sub0 91.9%

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

      6. sub-neg 91.9%

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

      7. +-commutative 91.9%

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

      8. associate--r+ 91.9%

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

      9. neg-sub0 91.9%

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

      10. remove-double-neg 91.9%

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

   5. Simplified 91.9%

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

   if -1.22e-60 < t < 1.7999999999999999e67

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf 90.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-60} \lor \neg \left(t \leq 1.8 \cdot 10^{+67}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-58} \lor \neg \left(t \leq 4.8 \cdot 10^{+47}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.8e-58) (not (<= t 4.8e+47)))
   (+ x (* y (/ (- t z) t)))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e-58) || !(t <= 4.8e+47)) {
		tmp = x + (y * ((t - z) / t));
	} 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 <= (-5.8d-58)) .or. (.not. (t <= 4.8d+47))) then
        tmp = x + (y * ((t - z) / t))
    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 <= -5.8e-58) || !(t <= 4.8e+47)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.8e-58) or not (t <= 4.8e+47):
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.8e-58) || !(t <= 4.8e+47))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	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 <= -5.8e-58) || ~((t <= 4.8e+47)))
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.8e-58], N[Not[LessEqual[t, 4.8e+47]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $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 < -5.7999999999999998e-58 or 4.80000000000000037e47 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-/l* 92.1%

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

      3. distribute-rgt-neg-in 92.1%

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

      4. distribute-frac-neg 92.1%

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

      5. neg-sub0 92.1%

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

      6. sub-neg 92.1%

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

      7. +-commutative 92.1%

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

      8. associate--r+ 92.1%

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

      9. neg-sub0 92.1%

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

      10. remove-double-neg 92.1%

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

   5. Simplified 92.1%

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

   if -5.7999999999999998e-58 < t < 4.80000000000000037e47

   1. Initial program 91.4%

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

      1. associate-*r/ 97.0%

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

   3. Simplified 97.0%

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

      1. *-commutative 97.0%

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

      2. associate-/l* 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in z around inf 89.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-58} \lor \neg \left(t \leq 4.8 \cdot 10^{+47}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-62} \lor \neg \left(t \leq 1.22 \cdot 10^{-39}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e-62) (not (<= t 1.22e-39)))
   (+ x (* y (/ (- t z) t)))
   (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e-62) || !(t <= 1.22e-39)) {
		tmp = x + (y * ((t - z) / t));
	} 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 <= (-3d-62)) .or. (.not. (t <= 1.22d-39))) then
        tmp = x + (y * ((t - z) / t))
    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 <= -3e-62) || !(t <= 1.22e-39)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3e-62) or not (t <= 1.22e-39):
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e-62) || !(t <= 1.22e-39))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3e-62) || ~((t <= 1.22e-39)))
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e-62], N[Not[LessEqual[t, 1.22e-39]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0000000000000001e-62 or 1.2200000000000001e-39 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 72.7%

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

      1. mul-1-neg 72.7%

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

      2. associate-/l* 89.4%

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

      3. distribute-rgt-neg-in 89.4%

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

      4. distribute-frac-neg 89.4%

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

      5. neg-sub0 89.4%

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

      6. sub-neg 89.4%

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

      7. +-commutative 89.4%

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

      8. associate--r+ 89.4%

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

      9. neg-sub0 89.4%

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

      10. remove-double-neg 89.4%

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

   5. Simplified 89.4%

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

   if -3.0000000000000001e-62 < t < 1.2200000000000001e-39

   1. Initial program 90.1%

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

   3. Taylor expanded in t around 0 77.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-62} \lor \neg \left(t \leq 1.22 \cdot 10^{-39}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e-60)
   (+ x (* y (/ (- t z) t)))
   (if (<= t 2e+67) (+ x (/ (* z y) (- a t))) (+ x (- y (* y (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e-60) {
		tmp = x + (y * ((t - z) / t));
	} else if (t <= 2e+67) {
		tmp = x + ((z * y) / (a - t));
	} else {
		tmp = x + (y - (y * (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 <= (-1.22d-60)) then
        tmp = x + (y * ((t - z) / t))
    else if (t <= 2d+67) then
        tmp = x + ((z * y) / (a - t))
    else
        tmp = x + (y - (y * (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 <= -1.22e-60) {
		tmp = x + (y * ((t - z) / t));
	} else if (t <= 2e+67) {
		tmp = x + ((z * y) / (a - t));
	} else {
		tmp = x + (y - (y * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.22e-60:
		tmp = x + (y * ((t - z) / t))
	elif t <= 2e+67:
		tmp = x + ((z * y) / (a - t))
	else:
		tmp = x + (y - (y * (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e-60)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	elseif (t <= 2e+67)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y - Float64(y * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.22e-60)
		tmp = x + (y * ((t - z) / t));
	elseif (t <= 2e+67)
		tmp = x + ((z * y) / (a - t));
	else
		tmp = x + (y - (y * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e-60], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+67], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 90.6%

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

      3. distribute-rgt-neg-in 90.6%

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

      4. distribute-frac-neg 90.6%

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

      5. neg-sub0 90.6%

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

      6. sub-neg 90.6%

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

      7. +-commutative 90.6%

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

      8. associate--r+ 90.6%

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

      9. neg-sub0 90.6%

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

      10. remove-double-neg 90.6%

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

   5. Simplified 90.6%

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

   if -1.22e-60 < t < 1.99999999999999997e67

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf 90.6%

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

   if 1.99999999999999997e67 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 71.7%

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

      1. associate-+r+ 71.7%

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

      2. associate--l+ 71.7%

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

      3. distribute-lft-out-- 71.7%

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

      4. div-sub 71.7%

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

      5. associate-+r+ 71.7%

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

      6. +-commutative 71.7%

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

      7. mul-1-neg 71.7%

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

      8. unsub-neg 71.7%

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

      9. *-commutative 71.7%

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

      10. distribute-lft-out-- 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 94.8%

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

   8. Simplified 94.8%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-40} \lor \neg \left(t \leq 1.35 \cdot 10^{+33}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e-40) (not (<= t 1.35e+33))) (+ y x) (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e-40) || !(t <= 1.35e+33)) {
		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 <= (-1.05d-40)) .or. (.not. (t <= 1.35d+33))) 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 <= -1.05e-40) || !(t <= 1.35e+33)) {
		tmp = y + x;
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e-40) or not (t <= 1.35e+33):
		tmp = y + x
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e-40) || !(t <= 1.35e+33))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e-40) || ~((t <= 1.35e+33)))
		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, -1.05e-40], N[Not[LessEqual[t, 1.35e+33]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05000000000000009e-40 or 1.34999999999999996e33 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 79.9%

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

      1. +-commutative 79.9%

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

   5. Simplified 79.9%

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

   if -1.05000000000000009e-40 < t < 1.34999999999999996e33

   1. Initial program 91.6%

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

   3. Taylor expanded in t around 0 73.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-40} \lor \neg \left(t \leq 1.35 \cdot 10^{+33}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+155}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e+138) x (if (<= a 5.8e+155) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+138) {
		tmp = x;
	} else if (a <= 5.8e+155) {
		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 <= (-2.6d+138)) then
        tmp = x
    else if (a <= 5.8d+155) 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 <= -2.6e+138) {
		tmp = x;
	} else if (a <= 5.8e+155) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e+138:
		tmp = x
	elif a <= 5.8e+155:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e+138)
		tmp = x;
	elseif (a <= 5.8e+155)
		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 <= -2.6e+138)
		tmp = x;
	elseif (a <= 5.8e+155)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e+138], x, If[LessEqual[a, 5.8e+155], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6000000000000001e138 or 5.7999999999999998e155 < a

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 73.3%

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

   if -2.6000000000000001e138 < a < 5.7999999999999998e155

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. +-commutative 56.6%

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

   5. Simplified 56.6%

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

Alternative 11: 50.1% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

3. Taylor expanded in x around inf 44.6%

   \[\leadsto \color{blue}{x} \]
4. 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 2024110 
(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)))))