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

Percentage Accurate: 98.3% → 98.7%

Time: 9.3s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 10^{+297}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t_1 1e+297) (+ x t_1) (+ x (* z (/ y (- 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+297) {
		tmp = x + t_1;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t_1 <= 1d+297) then
        tmp = x + t_1
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 1e+297) {
		tmp = x + t_1;
	} else {
		tmp = x + (z * (y / (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+297:
		tmp = x + t_1
	else:
		tmp = x + (z * (y / (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+297)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t_1 <= 1e+297)
		tmp = x + t_1;
	else
		tmp = x + (z * (y / (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+297], N[(x + t$95$1), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 1e297

   1. Initial program 98.7%

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

   if 1e297 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 71.9%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. *-lft-identity 99.9%

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

      3. times-frac 100.0%

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

      4. /-rgt-identity 100.0%

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

   7. Simplified 100.0%

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

Alternative 2: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-14} \lor \neg \left(z \leq 1.95 \cdot 10^{-70}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e-14) (not (<= z 1.95e-70)))
   (+ x (* z (/ y (- a t))))
   (+ x (* y (/ t (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e-14) || !(z <= 1.95e-70)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.5d-14)) .or. (.not. (z <= 1.95d-70))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y * (t / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e-14) || !(z <= 1.95e-70)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e-14) or not (z <= 1.95e-70):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e-14) || !(z <= 1.95e-70))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e-14) || ~((z <= 1.95e-70)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e-14], N[Not[LessEqual[z, 1.95e-70]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e-14 or 1.9500000000000001e-70 < z

   1. Initial program 95.5%

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

      1. associate-*r/ 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in z around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. *-lft-identity 84.2%

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

      3. times-frac 91.8%

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

      4. /-rgt-identity 91.8%

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

   7. Simplified 91.8%

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

   if -4.4999999999999998e-14 < z < 1.9500000000000001e-70

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 94.9%

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

      1. neg-mul-1 94.9%

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

      2. distribute-neg-frac2 94.9%

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

      3. neg-sub0 94.9%

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

      4. sub-neg 94.9%

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

      5. +-commutative 94.9%

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

      6. associate--r+ 94.9%

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

      7. neg-sub0 94.9%

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

      8. remove-double-neg 94.9%

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

   5. Simplified 94.9%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-14} \lor \neg \left(z \leq 1.95 \cdot 10^{-70}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-13} \lor \neg \left(z \leq 2.45 \cdot 10^{-70}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.25e-13) (not (<= z 2.45e-70)))
   (+ x (* y (/ z (- a t))))
   (+ x (* y (/ t (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.25e-13) || !(z <= 2.45e-70)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.25d-13)) .or. (.not. (z <= 2.45d-70))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (y * (t / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.25e-13) || !(z <= 2.45e-70)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.25e-13) or not (z <= 2.45e-70):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.25e-13) || !(z <= 2.45e-70))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.25e-13) || ~((z <= 2.45e-70)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.25e-13], N[Not[LessEqual[z, 2.45e-70]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25e-13 or 2.45e-70 < z

   1. Initial program 95.5%

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

      1. associate-*r/ 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in z around inf 84.2%

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

      1. associate-/l* 88.0%

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

   7. Simplified 88.0%

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

   if -2.25e-13 < z < 2.45e-70

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 94.9%

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

      1. neg-mul-1 94.9%

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

      2. distribute-neg-frac2 94.9%

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

      3. neg-sub0 94.9%

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

      4. sub-neg 94.9%

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

      5. +-commutative 94.9%

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

      6. associate--r+ 94.9%

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

      7. neg-sub0 94.9%

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

      8. remove-double-neg 94.9%

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

   5. Simplified 94.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-13} \lor \neg \left(z \leq 2.45 \cdot 10^{-70}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-120} \lor \neg \left(t \leq 1.45 \cdot 10^{+17}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e-120) (not (<= t 1.45e+17)))
   (+ x (* y (/ t (- t a))))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e-120) || !(t <= 1.45e+17)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.6d-120)) .or. (.not. (t <= 1.45d+17))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e-120) || !(t <= 1.45e+17)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e-120) or not (t <= 1.45e+17):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e-120) || !(t <= 1.45e+17))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e-120) || ~((t <= 1.45e+17)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e-120], N[Not[LessEqual[t, 1.45e+17]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999973e-120 or 1.45e17 < t

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 85.0%

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

      1. neg-mul-1 85.0%

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

      2. distribute-neg-frac2 85.0%

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

      3. neg-sub0 85.0%

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

      4. sub-neg 85.0%

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

      5. +-commutative 85.0%

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

      6. associate--r+ 85.0%

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

      7. neg-sub0 85.0%

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

      8. remove-double-neg 85.0%

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

   5. Simplified 85.0%

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

   if -4.59999999999999973e-120 < t < 1.45e17

   1. Initial program 95.2%

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

      1. associate-*r/ 95.9%

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

      2. clear-num 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in t around 0 79.8%

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

      1. associate-/r* 83.3%

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

   7. Simplified 83.3%

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

      1. associate-/r/ 83.3%

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

      2. clear-num 83.3%

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

   9. Applied egg-rr 83.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-120} \lor \neg \left(t \leq 1.45 \cdot 10^{+17}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-85} \lor \neg \left(t \leq 6.4 \cdot 10^{-105}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e-85) (not (<= t 6.4e-105)))
   (+ x (* t (/ y (- t a))))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e-85) || !(t <= 6.4e-105)) {
		tmp = x + (t * (y / (t - a)));
	} 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 <= (-2.4d-85)) .or. (.not. (t <= 6.4d-105))) then
        tmp = x + (t * (y / (t - a)))
    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 <= -2.4e-85) || !(t <= 6.4e-105)) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e-85) or not (t <= 6.4e-105):
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e-85) || !(t <= 6.4e-105))
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	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 <= -2.4e-85) || ~((t <= 6.4e-105)))
		tmp = x + (t * (y / (t - a)));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e-85], N[Not[LessEqual[t, 6.4e-105]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4000000000000001e-85 or 6.39999999999999962e-105 < t

   1. Initial program 98.1%

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

      1. associate-*r/ 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in z around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 80.0%

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

      3. distribute-rgt-neg-in 80.0%

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

      4. distribute-neg-frac2 80.0%

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

      5. neg-sub0 80.0%

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

      6. sub-neg 80.0%

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

      7. +-commutative 80.0%

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

      8. associate--r+ 80.0%

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

      9. neg-sub0 80.0%

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

      10. remove-double-neg 80.0%

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

   7. Simplified 80.0%

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

   if -2.4000000000000001e-85 < t < 6.39999999999999962e-105

   1. Initial program 95.1%

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

      1. associate-*r/ 96.0%

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

      2. clear-num 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in t around 0 84.0%

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

      1. associate-/r* 87.3%

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

   7. Simplified 87.3%

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

      1. associate-/r/ 87.3%

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

      2. clear-num 87.4%

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

   9. Applied egg-rr 87.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-85} \lor \neg \left(t \leq 6.4 \cdot 10^{-105}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+65} \lor \neg \left(t \leq 7.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e+65) (not (<= t 7.5e+18))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+65) || !(t <= 7.5e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.6d+65)) .or. (.not. (t <= 7.5d+18))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+65) || !(t <= 7.5e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e+65) or not (t <= 7.5e+18):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e+65) || !(t <= 7.5e+18))
		tmp = Float64(x + y);
	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 <= -2.6e+65) || ~((t <= 7.5e+18)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.6e+65], N[Not[LessEqual[t, 7.5e+18]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.60000000000000003e65 or 7.5e18 < t

   1. Initial program 99.9%

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

      1. associate-*r/ 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around inf 75.1%

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

   if -2.60000000000000003e65 < t < 7.5e18

   1. Initial program 95.0%

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

      1. associate-*r/ 96.1%

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

      2. clear-num 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in t around 0 78.4%

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

      1. associate-/r* 81.7%

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

   7. Simplified 81.7%

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

      1. associate-/r/ 81.7%

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

      2. clear-num 81.7%

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

   9. Applied egg-rr 81.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+65} \lor \neg \left(t \leq 7.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+64} \lor \neg \left(t \leq 5.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e+64) (not (<= t 5.5e+18))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+64) || !(t <= 5.5e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.5d+64)) .or. (.not. (t <= 5.5d+18))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+64) || !(t <= 5.5e+18)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.5e+64) or not (t <= 5.5e+18):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e+64) || !(t <= 5.5e+18))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.5e+64) || ~((t <= 5.5e+18)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.5e+64], N[Not[LessEqual[t, 5.5e+18]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5000000000000001e64 or 5.5e18 < t

   1. Initial program 99.9%

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

      1. associate-*r/ 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around inf 75.1%

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

   if -1.5000000000000001e64 < t < 5.5e18

   1. Initial program 95.0%

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

      1. associate-*r/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around 0 78.3%

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

      1. associate-/l* 79.9%

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

   7. Simplified 79.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+64} \lor \neg \left(t \leq 5.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. clear-num 96.6%

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

   2. un-div-inv 97.3%

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

4. Applied egg-rr 97.3%

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

Alternative 9: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.5 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 6.5e+57) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 6.5e+57) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 6.5d+57) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 6.5e+57) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 6.5e+57:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 6.5e+57)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 6.5e+57)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 6.5e+57], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 6.4999999999999997e57

   1. Initial program 96.2%

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

      1. associate-*r/ 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in t around inf 60.5%

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

   if 6.4999999999999997e57 < a

   1. Initial program 99.7%

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

      1. associate-*r/ 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around 0 32.2%

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

      1. mul-1-neg 32.2%

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

      2. associate-/l* 34.0%

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

      3. distribute-rgt-neg-in 34.0%

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

      4. distribute-frac-neg 34.0%

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

      5. neg-sub0 34.0%

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

      6. sub-neg 34.0%

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

      7. +-commutative 34.0%

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

      8. associate--r+ 34.0%

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

      9. neg-sub0 34.0%

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

      10. remove-double-neg 34.0%

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

   7. Simplified 34.0%

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

   8. Taylor expanded in t around 0 35.1%

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

      1. associate-*r/ 35.1%

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

      2. associate-*r* 35.1%

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

      3. neg-mul-1 35.1%

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

   10. Simplified 35.1%

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

   11. Taylor expanded in x around inf 71.5%

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

Alternative 10: 51.1% 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 96.9%

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

   1. associate-*r/ 85.2%

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

3. Simplified 85.2%

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

5. Taylor expanded in a around 0 54.9%

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

   1. mul-1-neg 54.9%

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

   2. associate-/l* 61.1%

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

   3. distribute-rgt-neg-in 61.1%

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

   4. distribute-frac-neg 61.1%

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

   5. neg-sub0 61.1%

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

   6. sub-neg 61.1%

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

   7. +-commutative 61.1%

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

   8. associate--r+ 61.1%

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

   9. neg-sub0 61.1%

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

   10. remove-double-neg 61.1%

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

7. Simplified 61.1%

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

8. Taylor expanded in t around 0 51.4%

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

   1. associate-*r/ 51.4%

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

   2. associate-*r* 51.4%

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

   3. neg-mul-1 51.4%

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

10. Simplified 51.4%

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

11. Taylor expanded in x around inf 53.2%

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

Developer target: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(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)))))