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

Percentage Accurate: 98.2% → 95.9%

Time: 11.3s

Alternatives: 13

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: 98.2% 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: 95.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z - t, \frac{1}{a - t} \cdot y, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma (- z t) (* (/ 1.0 (- a t)) y) x))

C

double code(double x, double y, double z, double t, double a) {
	return fma((z - t), ((1.0 / (a - t)) * y), x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(z - t), Float64(Float64(1.0 / Float64(a - t)) * y), x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(z - t), $MachinePrecision] * N[(N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 97.3%

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

   1. +-commutative 97.3%

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

   2. *-commutative 97.3%

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

   3. div-inv 97.3%

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

   4. associate-*l* 97.7%

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

   5. fma-def 97.7%

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

3. Applied egg-rr 97.7%

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

4. Final simplification 97.7%

   \[\leadsto \mathsf{fma}\left(z - t, \frac{1}{a - t} \cdot y, x\right) \]

Alternative 2: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-39}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-51} \lor \neg \left(t \leq 2.4 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.65e+94)
   (+ y x)
   (if (<= t -5.6e-39)
     (- x (* z (/ y t)))
     (if (or (<= t -4.6e-51) (not (<= t 2.4e+31)))
       (+ y x)
       (+ x (/ z (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+94) {
		tmp = y + x;
	} else if (t <= -5.6e-39) {
		tmp = x - (z * (y / t));
	} else if ((t <= -4.6e-51) || !(t <= 2.4e+31)) {
		tmp = y + x;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.65d+94)) then
        tmp = y + x
    else if (t <= (-5.6d-39)) then
        tmp = x - (z * (y / t))
    else if ((t <= (-4.6d-51)) .or. (.not. (t <= 2.4d+31))) then
        tmp = y + x
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+94) {
		tmp = y + x;
	} else if (t <= -5.6e-39) {
		tmp = x - (z * (y / t));
	} else if ((t <= -4.6e-51) || !(t <= 2.4e+31)) {
		tmp = y + x;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.65e+94:
		tmp = y + x
	elif t <= -5.6e-39:
		tmp = x - (z * (y / t))
	elif (t <= -4.6e-51) or not (t <= 2.4e+31):
		tmp = y + x
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.65e+94)
		tmp = Float64(y + x);
	elseif (t <= -5.6e-39)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif ((t <= -4.6e-51) || !(t <= 2.4e+31))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.65e+94)
		tmp = y + x;
	elseif (t <= -5.6e-39)
		tmp = x - (z * (y / t));
	elseif ((t <= -4.6e-51) || ~((t <= 2.4e+31)))
		tmp = y + x;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.65e+94], N[(y + x), $MachinePrecision], If[LessEqual[t, -5.6e-39], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.6e-51], N[Not[LessEqual[t, 2.4e+31]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.65e94 or -5.6000000000000003e-39 < t < -4.60000000000000004e-51 or 2.39999999999999982e31 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 85.3%

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

      1. +-commutative 85.3%

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

   4. Simplified 85.3%

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

   if -1.65e94 < t < -5.6000000000000003e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 75.3%

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

   3. Taylor expanded in a around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

      3. associate-*l/ 70.0%

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

      4. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   if -4.60000000000000004e-51 < t < 2.39999999999999982e31

   1. Initial program 94.5%

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

   2. Taylor expanded in z around inf 89.5%

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

      1. clear-num 89.5%

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

      2. div-inv 90.2%

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

      3. div-inv 90.1%

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

      4. associate-/r* 92.7%

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

   4. Applied egg-rr 92.7%

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

   5. Taylor expanded in a around inf 80.7%

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

      1. +-commutative 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-/l* 84.7%

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

   7. Simplified 84.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-39}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-51} \lor \neg \left(t \leq 2.4 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 3: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+26}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-48}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e+26)
   (+ y x)
   (if (<= t -6.8e-31)
     (+ x (* y (/ z a)))
     (if (<= t -1.52e-48)
       (+ y x)
       (if (<= t 2.9e+29) (+ x (/ z (/ a y))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+26) {
		tmp = y + x;
	} else if (t <= -6.8e-31) {
		tmp = x + (y * (z / a));
	} else if (t <= -1.52e-48) {
		tmp = y + x;
	} else if (t <= 2.9e+29) {
		tmp = x + (z / (a / y));
	} 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 <= (-1.2d+26)) then
        tmp = y + x
    else if (t <= (-6.8d-31)) then
        tmp = x + (y * (z / a))
    else if (t <= (-1.52d-48)) then
        tmp = y + x
    else if (t <= 2.9d+29) then
        tmp = x + (z / (a / y))
    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 <= -1.2e+26) {
		tmp = y + x;
	} else if (t <= -6.8e-31) {
		tmp = x + (y * (z / a));
	} else if (t <= -1.52e-48) {
		tmp = y + x;
	} else if (t <= 2.9e+29) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e+26:
		tmp = y + x
	elif t <= -6.8e-31:
		tmp = x + (y * (z / a))
	elif t <= -1.52e-48:
		tmp = y + x
	elif t <= 2.9e+29:
		tmp = x + (z / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e+26)
		tmp = Float64(y + x);
	elseif (t <= -6.8e-31)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -1.52e-48)
		tmp = Float64(y + x);
	elseif (t <= 2.9e+29)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e+26)
		tmp = y + x;
	elseif (t <= -6.8e-31)
		tmp = x + (y * (z / a));
	elseif (t <= -1.52e-48)
		tmp = y + x;
	elseif (t <= 2.9e+29)
		tmp = x + (z / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e+26], N[(y + x), $MachinePrecision], If[LessEqual[t, -6.8e-31], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.52e-48], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.9e+29], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.20000000000000002e26 or -6.8000000000000002e-31 < t < -1.5199999999999999e-48 or 2.8999999999999999e29 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 79.2%

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

      1. +-commutative 79.2%

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

   4. Simplified 79.2%

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

   if -1.20000000000000002e26 < t < -6.8000000000000002e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 96.2%

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

   if -1.5199999999999999e-48 < t < 2.8999999999999999e29

   1. Initial program 94.5%

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

   2. Taylor expanded in z around inf 89.5%

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

      1. clear-num 89.5%

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

      2. div-inv 90.2%

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

      3. div-inv 90.1%

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

      4. associate-/r* 92.7%

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

   4. Applied egg-rr 92.7%

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

   5. Taylor expanded in a around inf 80.7%

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

      1. +-commutative 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-/l* 84.7%

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

   7. Simplified 84.7%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+26}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-48}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-104} \lor \neg \left(t \leq 9 \cdot 10^{+28}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e-104) (not (<= t 9e+28)))
   (+ x (* y (/ t (- t a))))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e-104) || !(t <= 9e+28)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.5d-104)) .or. (.not. (t <= 9d+28))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e-104) || !(t <= 9e+28)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e-104) or not (t <= 9e+28):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e-104) || !(t <= 9e+28))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.5e-104) || ~((t <= 9e+28)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e-104], N[Not[LessEqual[t, 9e+28]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999997e-104 or 8.9999999999999994e28 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 85.3%

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

      1. neg-mul-1 85.3%

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

      2. distribute-neg-frac 85.3%

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

   4. Simplified 85.3%

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

      1. frac-2neg 85.3%

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

      2. div-inv 85.2%

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

      3. remove-double-neg 85.2%

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

      4. sub-neg 85.2%

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

      5. distribute-neg-in 85.2%

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

      6. remove-double-neg 85.2%

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

   6. Applied egg-rr 85.2%

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

      1. associate-*r/ 85.3%

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

      2. *-rgt-identity 85.3%

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

      3. +-commutative 85.3%

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

      4. unsub-neg 85.3%

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

   8. Simplified 85.3%

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

   if -4.4999999999999997e-104 < t < 8.9999999999999994e28

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf 91.2%

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

      1. clear-num 91.2%

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

      2. div-inv 91.9%

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

      3. div-inv 91.8%

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

      4. associate-/r* 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in a around inf 81.6%

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

      1. +-commutative 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-/l* 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-104} \lor \neg \left(t \leq 9 \cdot 10^{+28}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+126} \lor \neg \left(z \leq 5800000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+126) (not (<= z 5800000.0)))
   (+ 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 <= -1.35e+126) || !(z <= 5800000.0)) {
		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 <= (-1.35d+126)) .or. (.not. (z <= 5800000.0d0))) 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 <= -1.35e+126) || !(z <= 5800000.0)) {
		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 <= -1.35e+126) or not (z <= 5800000.0):
		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 <= -1.35e+126) || !(z <= 5800000.0))
		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 <= -1.35e+126) || ~((z <= 5800000.0)))
		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, -1.35e+126], N[Not[LessEqual[z, 5800000.0]], $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 < -1.35000000000000001e126 or 5.8e6 < z

   1. Initial program 93.3%

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

   2. Taylor expanded in z around inf 86.6%

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

   if -1.35000000000000001e126 < z < 5.8e6

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 91.0%

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

      1. neg-mul-1 91.0%

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

      2. distribute-neg-frac 91.0%

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

   4. Simplified 91.0%

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

      1. frac-2neg 91.0%

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

      2. div-inv 90.9%

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

      3. remove-double-neg 90.9%

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

      4. sub-neg 90.9%

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

      5. distribute-neg-in 90.9%

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

      6. remove-double-neg 90.9%

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

   6. Applied egg-rr 90.9%

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

      1. associate-*r/ 91.0%

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

      2. *-rgt-identity 91.0%

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

      3. +-commutative 91.0%

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

      4. unsub-neg 91.0%

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

   8. Simplified 91.0%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+126} \lor \neg \left(z \leq 5800000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]

Alternative 6: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+20} \lor \neg \left(z \leq 185\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+20) (not (<= z 185.0)))
   (+ 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 <= -2.6e+20) || !(z <= 185.0)) {
		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 <= (-2.6d+20)) .or. (.not. (z <= 185.0d0))) 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 <= -2.6e+20) || !(z <= 185.0)) {
		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 <= -2.6e+20) or not (z <= 185.0):
		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 <= -2.6e+20) || !(z <= 185.0))
		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 <= -2.6e+20) || ~((z <= 185.0)))
		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, -2.6e+20], N[Not[LessEqual[z, 185.0]], $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 < -2.6e20 or 185 < z

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 83.4%

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

      1. associate-/l* 87.8%

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

      2. associate-/r/ 91.9%

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

   4. Simplified 91.9%

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

   if -2.6e20 < z < 185

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 91.2%

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

      1. neg-mul-1 91.2%

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

      2. distribute-neg-frac 91.2%

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

   4. Simplified 91.2%

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

      1. frac-2neg 91.2%

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

      2. div-inv 91.2%

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

      3. remove-double-neg 91.2%

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

      4. sub-neg 91.2%

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

      5. distribute-neg-in 91.2%

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

      6. remove-double-neg 91.2%

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

   6. Applied egg-rr 91.2%

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

      1. associate-*r/ 91.2%

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

      2. *-rgt-identity 91.2%

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

      3. +-commutative 91.2%

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

      4. unsub-neg 91.2%

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

   8. Simplified 91.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+20} \lor \neg \left(z \leq 185\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]

Alternative 7: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-83}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e-83)
   (+ y x)
   (if (<= t 3.2e-190)
     x
     (if (<= t 4e-122) (* y (/ z a)) (if (<= t 2.5e+22) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e-83) {
		tmp = y + x;
	} else if (t <= 3.2e-190) {
		tmp = x;
	} else if (t <= 4e-122) {
		tmp = y * (z / a);
	} else if (t <= 2.5e+22) {
		tmp = x;
	} 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 <= (-1d-83)) then
        tmp = y + x
    else if (t <= 3.2d-190) then
        tmp = x
    else if (t <= 4d-122) then
        tmp = y * (z / a)
    else if (t <= 2.5d+22) then
        tmp = x
    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 <= -1e-83) {
		tmp = y + x;
	} else if (t <= 3.2e-190) {
		tmp = x;
	} else if (t <= 4e-122) {
		tmp = y * (z / a);
	} else if (t <= 2.5e+22) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e-83:
		tmp = y + x
	elif t <= 3.2e-190:
		tmp = x
	elif t <= 4e-122:
		tmp = y * (z / a)
	elif t <= 2.5e+22:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e-83)
		tmp = Float64(y + x);
	elseif (t <= 3.2e-190)
		tmp = x;
	elseif (t <= 4e-122)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 2.5e+22)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1e-83)
		tmp = y + x;
	elseif (t <= 3.2e-190)
		tmp = x;
	elseif (t <= 4e-122)
		tmp = y * (z / a);
	elseif (t <= 2.5e+22)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e-83], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.2e-190], x, If[LessEqual[t, 4e-122], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+22], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1e-83 or 2.4999999999999998e22 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -1e-83 < t < 3.2000000000000001e-190 or 4.00000000000000024e-122 < t < 2.4999999999999998e22

   1. Initial program 94.6%

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

   2. Taylor expanded in x around inf 63.9%

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

   if 3.2000000000000001e-190 < t < 4.00000000000000024e-122

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. *-commutative 89.2%

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

      3. div-inv 89.1%

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

      4. associate-*l* 89.7%

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

      5. fma-def 89.7%

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

   3. Applied egg-rr 89.7%

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

   4. Taylor expanded in z around inf 68.7%

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

      1. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in a around inf 67.4%

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

   8. Taylor expanded in y around 0 47.4%

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

      1. associate-*r/ 67.6%

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

   10. Simplified 67.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-83}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+130} \lor \neg \left(z \leq 6.2 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+130) (not (<= z 6.2e+123))) (* z (/ y (- a t))) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+130) || !(z <= 6.2e+123)) {
		tmp = z * (y / (a - t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d+130)) .or. (.not. (z <= 6.2d+123))) then
        tmp = z * (y / (a - t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+130) || !(z <= 6.2e+123)) {
		tmp = z * (y / (a - t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+130) or not (z <= 6.2e+123):
		tmp = z * (y / (a - t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+130) || !(z <= 6.2e+123))
		tmp = Float64(z * Float64(y / Float64(a - t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+130) || ~((z <= 6.2e+123)))
		tmp = z * (y / (a - t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+130], N[Not[LessEqual[z, 6.2e+123]], $MachinePrecision]], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000005e130 or 6.20000000000000013e123 < z

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. *-commutative 92.6%

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

      3. div-inv 92.5%

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

      4. associate-*l* 98.7%

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

      5. fma-def 98.7%

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

   3. Applied egg-rr 98.7%

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

   4. Taylor expanded in z around inf 52.9%

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

      1. associate-/l* 56.7%

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

   6. Simplified 56.7%

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

      1. associate-/r/ 62.7%

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

   8. Applied egg-rr 62.7%

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

   if -8.0000000000000005e130 < z < 6.20000000000000013e123

   1. Initial program 98.9%

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

   2. Taylor expanded in t around inf 72.0%

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

      1. +-commutative 72.0%

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

   4. Simplified 72.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+130} \lor \neg \left(z \leq 6.2 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+26} \lor \neg \left(t \leq 2 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+26) (not (<= t 2e+31))) (+ y x) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+26) || !(t <= 2e+31)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.5d+26)) .or. (.not. (t <= 2d+31))) then
        tmp = y + x
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+26) || !(t <= 2e+31)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+26) or not (t <= 2e+31):
		tmp = y + x
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+26) || !(t <= 2e+31))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e+26) || ~((t <= 2e+31)))
		tmp = y + x;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e+26], N[Not[LessEqual[t, 2e+31]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5e26 or 1.9999999999999999e31 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 79.5%

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

      1. +-commutative 79.5%

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

   4. Simplified 79.5%

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

   if -8.5e26 < t < 1.9999999999999999e31

   1. Initial program 95.2%

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

   2. Taylor expanded in t around 0 81.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+26} \lor \neg \left(t \leq 2 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 10: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+23} \lor \neg \left(t \leq 1.2 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+23) (not (<= t 1.2e+31))) (+ y x) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+23) || !(t <= 1.2e+31)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.2d+23)) .or. (.not. (t <= 1.2d+31))) then
        tmp = y + x
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+23) || !(t <= 1.2e+31)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+23) or not (t <= 1.2e+31):
		tmp = y + x
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+23) || !(t <= 1.2e+31))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+23) || ~((t <= 1.2e+31)))
		tmp = y + x;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+23], N[Not[LessEqual[t, 1.2e+31]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.19999999999999992e23 or 1.19999999999999991e31 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 79.5%

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

      1. +-commutative 79.5%

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

   4. Simplified 79.5%

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

   if -8.19999999999999992e23 < t < 1.19999999999999991e31

   1. Initial program 95.2%

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

   2. Taylor expanded in t around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. associate-/l* 81.9%

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

   4. Simplified 81.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+23} \lor \neg \left(t \leq 1.2 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 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]

Derivation

1. Initial program 97.3%

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

2. Final simplification 97.3%

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

Alternative 12: 63.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e-84) (+ y x) (if (<= t 5.8e+22) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e-84) {
		tmp = y + x;
	} else if (t <= 5.8e+22) {
		tmp = x;
	} 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 <= (-8.5d-84)) then
        tmp = y + x
    else if (t <= 5.8d+22) then
        tmp = x
    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 <= -8.5e-84) {
		tmp = y + x;
	} else if (t <= 5.8e+22) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e-84:
		tmp = y + x
	elif t <= 5.8e+22:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e-84)
		tmp = Float64(y + x);
	elseif (t <= 5.8e+22)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.5e-84)
		tmp = y + x;
	elseif (t <= 5.8e+22)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e-84], N[(y + x), $MachinePrecision], If[LessEqual[t, 5.8e+22], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.4999999999999994e-84 or 5.8e22 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if -8.4999999999999994e-84 < t < 5.8e22

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf 60.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13: 50.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in x around inf 57.8%

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

3. Final simplification 57.8%

   \[\leadsto x \]

Developer target: 99.4% accurate, 0.6× 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 2023279 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (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)))))