Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.6% → 98.3%

Time: 12.3s

Alternatives: 19

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

   1. +-commutative 88.5%

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

   2. associate-/l* 99.1%

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

   3. fma-define 99.1%

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

3. Simplified 99.1%

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

Alternative 2: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(t - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+305}\right):\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- t z)) (- a z)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+305)))
     (/ y (/ (- z a) (- z t)))
     t_1)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (t - z)) / (a - z));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+305)) {
		tmp = y / ((z - a) / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (t - z)) / (a - z));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+305)) {
		tmp = y / ((z - a) / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (t - z)) / (a - z))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+305):
		tmp = y / ((z - a) / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(t - z)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+305))
		tmp = Float64(y / Float64(Float64(z - a) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (t - z)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+305)))
		tmp = y / ((z - a) / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+305]], $MachinePrecision]], N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))) < -inf.0 or 9.9999999999999994e304 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

   1. Initial program 47.1%

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

      1. +-commutative 47.1%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 92.8%

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

      1. div-sub 92.8%

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

      2. associate-*r/ 47.1%

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

      3. associate-*l/ 92.6%

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

   7. Simplified 92.6%

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

      1. associate-/r/ 92.8%

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

   9. Applied egg-rr 92.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))) < 9.9999999999999994e304

   1. Initial program 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(t - z\right)}{a - z} \leq -\infty \lor \neg \left(x + \frac{y \cdot \left(t - z\right)}{a - z} \leq 10^{+305}\right):\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+140}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t z) (/ y (- a z)))))
   (if (<= z -1.95e+26)
     (+ x (* y (/ z (- z a))))
     (if (<= z 5.8e-9)
       (+ x (/ y (/ a t)))
       (if (<= z 3.4e+35)
         t_1
         (if (<= z 1.1e+140)
           (- x (/ (* y (- t z)) z))
           (if (<= z 2.7e+152) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) * (y / (a - z));
	double tmp;
	if (z <= -1.95e+26) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 5.8e-9) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.4e+35) {
		tmp = t_1;
	} else if (z <= 1.1e+140) {
		tmp = x - ((y * (t - z)) / z);
	} else if (z <= 2.7e+152) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t - z) * (y / (a - z))
    if (z <= (-1.95d+26)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 5.8d-9) then
        tmp = x + (y / (a / t))
    else if (z <= 3.4d+35) then
        tmp = t_1
    else if (z <= 1.1d+140) then
        tmp = x - ((y * (t - z)) / z)
    else if (z <= 2.7d+152) then
        tmp = t_1
    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 t_1 = (t - z) * (y / (a - z));
	double tmp;
	if (z <= -1.95e+26) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 5.8e-9) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.4e+35) {
		tmp = t_1;
	} else if (z <= 1.1e+140) {
		tmp = x - ((y * (t - z)) / z);
	} else if (z <= 2.7e+152) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) * (y / (a - z))
	tmp = 0
	if z <= -1.95e+26:
		tmp = x + (y * (z / (z - a)))
	elif z <= 5.8e-9:
		tmp = x + (y / (a / t))
	elif z <= 3.4e+35:
		tmp = t_1
	elif z <= 1.1e+140:
		tmp = x - ((y * (t - z)) / z)
	elif z <= 2.7e+152:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.95e+26)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 5.8e-9)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 3.4e+35)
		tmp = t_1;
	elseif (z <= 1.1e+140)
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / z));
	elseif (z <= 2.7e+152)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) * (y / (a - z));
	tmp = 0.0;
	if (z <= -1.95e+26)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 5.8e-9)
		tmp = x + (y / (a / t));
	elseif (z <= 3.4e+35)
		tmp = t_1;
	elseif (z <= 1.1e+140)
		tmp = x - ((y * (t - z)) / z);
	elseif (z <= 2.7e+152)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+26], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-9], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+35], t$95$1, If[LessEqual[z, 1.1e+140], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+152], t$95$1, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.95e26

   1. Initial program 80.9%

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

   3. Taylor expanded in t around 0 77.1%

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

      1. associate-/l* 92.7%

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

   5. Simplified 92.7%

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

   if -1.95e26 < z < 5.79999999999999982e-9

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-/l* 86.8%

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

   5. Applied egg-rr 86.8%

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

      1. clear-num 86.8%

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

      2. un-div-inv 86.9%

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

   7. Applied egg-rr 86.9%

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

   if 5.79999999999999982e-9 < z < 3.4000000000000001e35 or 1.0999999999999999e140 < z < 2.70000000000000015e152

   1. Initial program 81.3%

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

      1. +-commutative 81.3%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 93.3%

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

      1. div-sub 93.3%

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

      2. associate-*r/ 74.8%

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

      3. associate-*l/ 93.3%

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

   7. Simplified 93.3%

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

   if 3.4000000000000001e35 < z < 1.0999999999999999e140

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 86.5%

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

   if 2.70000000000000015e152 < z

   1. Initial program 67.2%

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

      1. +-commutative 67.2%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+35}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+140}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+152}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.4e+22)
   (+ x (* y (/ z (- z a))))
   (if (<= z 1.04e-8)
     (+ x (/ y (/ a t)))
     (if (<= z 5.2e+35)
       (* (- t z) (/ y (- a z)))
       (if (<= z 9.2e+79) (+ x (/ (* y t) a)) (+ x (* y (/ (- z t) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e+22) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 1.04e-8) {
		tmp = x + (y / (a / t));
	} else if (z <= 5.2e+35) {
		tmp = (t - z) * (y / (a - z));
	} else if (z <= 9.2e+79) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x + (y * ((z - t) / 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 (z <= (-6.4d+22)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 1.04d-8) then
        tmp = x + (y / (a / t))
    else if (z <= 5.2d+35) then
        tmp = (t - z) * (y / (a - z))
    else if (z <= 9.2d+79) then
        tmp = x + ((y * t) / a)
    else
        tmp = x + (y * ((z - t) / 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 (z <= -6.4e+22) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 1.04e-8) {
		tmp = x + (y / (a / t));
	} else if (z <= 5.2e+35) {
		tmp = (t - z) * (y / (a - z));
	} else if (z <= 9.2e+79) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.4e+22:
		tmp = x + (y * (z / (z - a)))
	elif z <= 1.04e-8:
		tmp = x + (y / (a / t))
	elif z <= 5.2e+35:
		tmp = (t - z) * (y / (a - z))
	elif z <= 9.2e+79:
		tmp = x + ((y * t) / a)
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.4e+22)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 1.04e-8)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 5.2e+35)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(a - z)));
	elseif (z <= 9.2e+79)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.4e+22)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 1.04e-8)
		tmp = x + (y / (a / t));
	elseif (z <= 5.2e+35)
		tmp = (t - z) * (y / (a - z));
	elseif (z <= 9.2e+79)
		tmp = x + ((y * t) / a);
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.4e+22], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.04e-8], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+35], N[(N[(t - z), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+79], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.4e22

   1. Initial program 80.9%

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

   3. Taylor expanded in t around 0 77.1%

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

      1. associate-/l* 92.7%

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

   5. Simplified 92.7%

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

   if -6.4e22 < z < 1.04e-8

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-/l* 86.8%

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

   5. Applied egg-rr 86.8%

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

      1. clear-num 86.8%

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

      2. un-div-inv 86.9%

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

   7. Applied egg-rr 86.9%

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

   if 1.04e-8 < z < 5.20000000000000013e35

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 90.9%

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

      1. div-sub 90.9%

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

      2. associate-*r/ 90.7%

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

      3. associate-*l/ 91.2%

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

   7. Simplified 91.2%

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

   if 5.20000000000000013e35 < z < 9.2000000000000002e79

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   if 9.2000000000000002e79 < z

   1. Initial program 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. associate-/l* 93.2%

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

   7. Simplified 93.2%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{z} + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5400:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+35}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5400.0)
   (+ y x)
   (if (<= z 1.14e-8)
     (+ x (/ y (/ a t)))
     (if (<= z 5.4e+35)
       (* (- t z) (/ y (- a z)))
       (if (<= z 4.5e+101) (- x (* t (/ y z))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5400.0) {
		tmp = y + x;
	} else if (z <= 1.14e-8) {
		tmp = x + (y / (a / t));
	} else if (z <= 5.4e+35) {
		tmp = (t - z) * (y / (a - z));
	} else if (z <= 4.5e+101) {
		tmp = x - (t * (y / z));
	} 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 <= (-5400.0d0)) then
        tmp = y + x
    else if (z <= 1.14d-8) then
        tmp = x + (y / (a / t))
    else if (z <= 5.4d+35) then
        tmp = (t - z) * (y / (a - z))
    else if (z <= 4.5d+101) then
        tmp = x - (t * (y / z))
    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 <= -5400.0) {
		tmp = y + x;
	} else if (z <= 1.14e-8) {
		tmp = x + (y / (a / t));
	} else if (z <= 5.4e+35) {
		tmp = (t - z) * (y / (a - z));
	} else if (z <= 4.5e+101) {
		tmp = x - (t * (y / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5400.0:
		tmp = y + x
	elif z <= 1.14e-8:
		tmp = x + (y / (a / t))
	elif z <= 5.4e+35:
		tmp = (t - z) * (y / (a - z))
	elif z <= 4.5e+101:
		tmp = x - (t * (y / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5400.0)
		tmp = Float64(y + x);
	elseif (z <= 1.14e-8)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 5.4e+35)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(a - z)));
	elseif (z <= 4.5e+101)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5400.0)
		tmp = y + x;
	elseif (z <= 1.14e-8)
		tmp = x + (y / (a / t));
	elseif (z <= 5.4e+35)
		tmp = (t - z) * (y / (a - z));
	elseif (z <= 4.5e+101)
		tmp = x - (t * (y / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5400.0], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.14e-8], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+35], N[(N[(t - z), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+101], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5400 or 4.5000000000000002e101 < z

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 88.9%

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

      1. +-commutative 88.9%

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

   7. Simplified 88.9%

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

   if -5400 < z < 1.14e-8

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-/l* 87.8%

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

   5. Applied egg-rr 87.8%

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

      1. clear-num 87.8%

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

      2. un-div-inv 87.9%

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

   7. Applied egg-rr 87.9%

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

   if 1.14e-8 < z < 5.40000000000000005e35

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 90.9%

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

      1. div-sub 90.9%

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

      2. associate-*r/ 90.7%

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

      3. associate-*l/ 91.2%

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

   7. Simplified 91.2%

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

   if 5.40000000000000005e35 < z < 4.5000000000000002e101

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 79.7%

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

   4. Taylor expanded in z around 0 92.4%

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

      1. associate-*r/ 92.4%

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

      2. associate-*r* 92.4%

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

      3. neg-mul-1 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in x around 0 92.4%

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

      1. mul-1-neg 92.4%

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

      2. associate-*r/ 92.4%

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

      3. sub-neg 92.4%

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

   9. Simplified 92.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5400:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+35}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3600:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+35}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3600.0)
   (+ x (* y (/ z (- z a))))
   (if (<= z 1.24e-8)
     (+ x (* y (/ (- t z) a)))
     (if (<= z 3.4e+35) (* (- t z) (/ y (- a z))) (+ x (* y (/ (- z t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3600.0) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 1.24e-8) {
		tmp = x + (y * ((t - z) / a));
	} else if (z <= 3.4e+35) {
		tmp = (t - z) * (y / (a - z));
	} else {
		tmp = x + (y * ((z - t) / 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 (z <= (-3600.0d0)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 1.24d-8) then
        tmp = x + (y * ((t - z) / a))
    else if (z <= 3.4d+35) then
        tmp = (t - z) * (y / (a - z))
    else
        tmp = x + (y * ((z - t) / 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 (z <= -3600.0) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 1.24e-8) {
		tmp = x + (y * ((t - z) / a));
	} else if (z <= 3.4e+35) {
		tmp = (t - z) * (y / (a - z));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3600.0:
		tmp = x + (y * (z / (z - a)))
	elif z <= 1.24e-8:
		tmp = x + (y * ((t - z) / a))
	elif z <= 3.4e+35:
		tmp = (t - z) * (y / (a - z))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3600.0)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 1.24e-8)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (z <= 3.4e+35)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3600.0)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 1.24e-8)
		tmp = x + (y * ((t - z) / a));
	elseif (z <= 3.4e+35)
		tmp = (t - z) * (y / (a - z));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3600.0], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.24e-8], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+35], N[(N[(t - z), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3600

   1. Initial program 82.2%

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

   3. Taylor expanded in t around 0 78.6%

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

      1. associate-/l* 93.2%

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

   5. Simplified 93.2%

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

   if -3600 < z < 1.24000000000000002e-8

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-/l* 98.4%

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

      3. fma-define 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in a around inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. unsub-neg 85.1%

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

      3. associate-/l* 89.9%

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

   7. Simplified 89.9%

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

   if 1.24000000000000002e-8 < z < 3.4000000000000001e35

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 90.9%

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

      1. div-sub 90.9%

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

      2. associate-*r/ 90.7%

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

      3. associate-*l/ 91.2%

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

   7. Simplified 91.2%

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

   if 3.4000000000000001e35 < z

   1. Initial program 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-/l* 92.3%

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

   7. Simplified 92.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3600:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+35}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.95 \cdot 10^{+72} \lor \neg \left(y \leq 1.56 \cdot 10^{+162}\right) \land y \leq 1.3 \cdot 10^{+259}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y 2.95e+72) (and (not (<= y 1.56e+162)) (<= y 1.3e+259)))
   (+ y x)
   (* t (/ y (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= 2.95e+72) || (!(y <= 1.56e+162) && (y <= 1.3e+259))) {
		tmp = y + x;
	} else {
		tmp = t * (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 ((y <= 2.95d+72) .or. (.not. (y <= 1.56d+162)) .and. (y <= 1.3d+259)) then
        tmp = y + x
    else
        tmp = t * (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 ((y <= 2.95e+72) || (!(y <= 1.56e+162) && (y <= 1.3e+259))) {
		tmp = y + x;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= 2.95e+72) or (not (y <= 1.56e+162) and (y <= 1.3e+259)):
		tmp = y + x
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= 2.95e+72) || (!(y <= 1.56e+162) && (y <= 1.3e+259)))
		tmp = Float64(y + x);
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= 2.95e+72) || (~((y <= 1.56e+162)) && (y <= 1.3e+259)))
		tmp = y + x;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, 2.95e+72], And[N[Not[LessEqual[y, 1.56e+162]], $MachinePrecision], LessEqual[y, 1.3e+259]]], N[(y + x), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.9500000000000001e72 or 1.5600000000000001e162 < y < 1.30000000000000001e259

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-/l* 99.1%

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

      3. fma-define 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. +-commutative 67.6%

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

   7. Simplified 67.6%

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

   if 2.9500000000000001e72 < y < 1.5600000000000001e162 or 1.30000000000000001e259 < y

   1. Initial program 79.6%

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

      1. +-commutative 79.6%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 80.5%

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

      1. div-sub 80.5%

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

      2. associate-*r/ 61.2%

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

      3. associate-*l/ 80.9%

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

   7. Simplified 80.9%

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

      1. associate-/r/ 77.7%

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

   9. Applied egg-rr 77.7%

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

   10. Taylor expanded in t around inf 53.8%

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

       1. mul-1-neg 53.8%

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

       2. associate-/l* 62.7%

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

       3. distribute-rgt-neg-in 62.7%

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

       4. distribute-neg-frac2 62.7%

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

       5. neg-sub0 62.7%

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

       6. associate-+l- 62.7%

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

       7. neg-sub0 62.7%

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

       8. +-commutative 62.7%

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

       9. unsub-neg 62.7%

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

   12. Simplified 62.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.95 \cdot 10^{+72} \lor \neg \left(y \leq 1.56 \cdot 10^{+162}\right) \land y \leq 1.3 \cdot 10^{+259}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-37}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+46)
   (+ y x)
   (if (<= z 4.8e-77) x (if (<= z 3e-37) (/ y (/ a t)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+46) {
		tmp = y + x;
	} else if (z <= 4.8e-77) {
		tmp = x;
	} else if (z <= 3e-37) {
		tmp = 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 <= (-2.15d+46)) then
        tmp = y + x
    else if (z <= 4.8d-77) then
        tmp = x
    else if (z <= 3d-37) then
        tmp = 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 <= -2.15e+46) {
		tmp = y + x;
	} else if (z <= 4.8e-77) {
		tmp = x;
	} else if (z <= 3e-37) {
		tmp = y / (a / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.15e+46:
		tmp = y + x
	elif z <= 4.8e-77:
		tmp = x
	elif z <= 3e-37:
		tmp = y / (a / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+46)
		tmp = Float64(y + x);
	elseif (z <= 4.8e-77)
		tmp = x;
	elseif (z <= 3e-37)
		tmp = 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 <= -2.15e+46)
		tmp = y + x;
	elseif (z <= 4.8e-77)
		tmp = x;
	elseif (z <= 3e-37)
		tmp = y / (a / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+46], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.8e-77], x, If[LessEqual[z, 3e-37], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15000000000000002e46 or 3e-37 < z

   1. Initial program 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.1%

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

      1. +-commutative 79.1%

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

   7. Simplified 79.1%

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

   if -2.15000000000000002e46 < z < 4.7999999999999998e-77

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-/l* 98.4%

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

      3. fma-define 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in y around 0 59.3%

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

   if 4.7999999999999998e-77 < z < 3e-37

   1. Initial program 59.4%

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

      1. +-commutative 59.4%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 86.3%

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

      1. div-sub 86.3%

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

      2. associate-*r/ 46.0%

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

      3. associate-*l/ 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in z around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. neg-mul-1 86.1%

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

   10. Simplified 86.1%

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

   11. Taylor expanded in y around 0 46.0%

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

       1. mul-1-neg 46.0%

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

       2. distribute-frac-neg2 46.0%

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

       3. associate-/l* 86.4%

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

   13. Simplified 86.4%

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

   14. Taylor expanded in z around 0 85.9%

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

       1. clear-num 99.8%

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

       2. un-div-inv 100.0%

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

   16. Applied egg-rr 86.2%

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

Alternative 9: 63.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+47)
   (+ y x)
   (if (<= z 5e-77) x (if (<= z 2.2e-37) (* y (/ t a)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+47) {
		tmp = y + x;
	} else if (z <= 5e-77) {
		tmp = x;
	} else if (z <= 2.2e-37) {
		tmp = y * (t / a);
	} 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 <= (-1.45d+47)) then
        tmp = y + x
    else if (z <= 5d-77) then
        tmp = x
    else if (z <= 2.2d-37) then
        tmp = y * (t / a)
    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 <= -1.45e+47) {
		tmp = y + x;
	} else if (z <= 5e-77) {
		tmp = x;
	} else if (z <= 2.2e-37) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+47:
		tmp = y + x
	elif z <= 5e-77:
		tmp = x
	elif z <= 2.2e-37:
		tmp = y * (t / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+47)
		tmp = Float64(y + x);
	elseif (z <= 5e-77)
		tmp = x;
	elseif (z <= 2.2e-37)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+47)
		tmp = y + x;
	elseif (z <= 5e-77)
		tmp = x;
	elseif (z <= 2.2e-37)
		tmp = y * (t / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+47], N[(y + x), $MachinePrecision], If[LessEqual[z, 5e-77], x, If[LessEqual[z, 2.2e-37], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e47 or 2.20000000000000002e-37 < z

   1. Initial program 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.1%

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

      1. +-commutative 79.1%

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

   7. Simplified 79.1%

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

   if -1.4499999999999999e47 < z < 4.99999999999999963e-77

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-/l* 98.4%

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

      3. fma-define 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in y around 0 59.3%

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

   if 4.99999999999999963e-77 < z < 2.20000000000000002e-37

   1. Initial program 59.4%

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

      1. +-commutative 59.4%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 86.3%

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

      1. div-sub 86.3%

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

      2. associate-*r/ 46.0%

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

      3. associate-*l/ 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in z around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. neg-mul-1 86.1%

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

   10. Simplified 86.1%

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

   11. Taylor expanded in y around 0 46.0%

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

       1. mul-1-neg 46.0%

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

       2. distribute-frac-neg2 46.0%

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

       3. associate-/l* 86.4%

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

   13. Simplified 86.4%

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

   14. Taylor expanded in z around 0 85.9%

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

Alternative 10: 81.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+23} \lor \neg \left(z \leq 1.65 \cdot 10^{+18}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e+23) (not (<= z 1.65e+18)))
   (+ x (* y (/ z (- z a))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+23) || !(z <= 1.65e+18)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.75d+23)) .or. (.not. (z <= 1.65d+18))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+23) || !(z <= 1.65e+18)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.75e+23) or not (z <= 1.65e+18):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e+23) || !(z <= 1.65e+18))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.75e+23) || ~((z <= 1.65e+18)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e+23], N[Not[LessEqual[z, 1.65e+18]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75000000000000002e23 or 1.65e18 < z

   1. Initial program 81.0%

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

   3. Taylor expanded in t around 0 74.1%

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

      1. associate-/l* 90.1%

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

   5. Simplified 90.1%

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

   if -2.75000000000000002e23 < z < 1.65e18

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-/l* 86.4%

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

   5. Applied egg-rr 86.4%

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

      1. clear-num 86.4%

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

      2. un-div-inv 86.5%

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

   7. Applied egg-rr 86.5%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+23} \lor \neg \left(z \leq 1.65 \cdot 10^{+18}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3800 \lor \neg \left(z \leq 1.38 \cdot 10^{+101}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3800.0) (not (<= z 1.38e+101))) (+ y x) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3800.0) || !(z <= 1.38e+101)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3800.0d0)) .or. (.not. (z <= 1.38d+101))) then
        tmp = y + x
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3800.0) || !(z <= 1.38e+101)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3800.0) or not (z <= 1.38e+101):
		tmp = y + x
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3800.0) || !(z <= 1.38e+101))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3800.0) || ~((z <= 1.38e+101)))
		tmp = y + x;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3800.0], N[Not[LessEqual[z, 1.38e+101]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3800 or 1.38e101 < z

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 88.9%

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

      1. +-commutative 88.9%

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

   7. Simplified 88.9%

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

   if -3800 < z < 1.38e101

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-/l* 84.1%

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

   5. Applied egg-rr 84.1%

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

      1. clear-num 84.1%

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

      2. un-div-inv 84.8%

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

   7. Applied egg-rr 84.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3800 \lor \neg \left(z \leq 1.38 \cdot 10^{+101}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -700 \lor \neg \left(z \leq 1.9 \cdot 10^{+101}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -700.0) (not (<= z 1.9e+101))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -700.0) || !(z <= 1.9e+101)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-700.0d0)) .or. (.not. (z <= 1.9d+101))) then
        tmp = y + x
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -700.0) || !(z <= 1.9e+101)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -700.0) or not (z <= 1.9e+101):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -700.0) || !(z <= 1.9e+101))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -700.0) || ~((z <= 1.9e+101)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -700.0], N[Not[LessEqual[z, 1.9e+101]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -700 or 1.8999999999999999e101 < z

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 88.9%

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

      1. +-commutative 88.9%

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

   7. Simplified 88.9%

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

   if -700 < z < 1.8999999999999999e101

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-/l* 84.1%

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

   5. Applied egg-rr 84.1%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -700 \lor \neg \left(z \leq 1.9 \cdot 10^{+101}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+86} \lor \neg \left(y \leq 4.7 \cdot 10^{+80}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.5e+86) (not (<= y 4.7e+80))) (* y (/ (- t z) a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.5e+86) || !(y <= 4.7e+80)) {
		tmp = y * ((t - z) / a);
	} 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 ((y <= (-9.5d+86)) .or. (.not. (y <= 4.7d+80))) then
        tmp = y * ((t - z) / a)
    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 ((y <= -9.5e+86) || !(y <= 4.7e+80)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.5e+86) or not (y <= 4.7e+80):
		tmp = y * ((t - z) / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9.5e+86) || !(y <= 4.7e+80))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -9.5e+86) || ~((y <= 4.7e+80)))
		tmp = y * ((t - z) / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9.5e+86], N[Not[LessEqual[y, 4.7e+80]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000028e86 or 4.70000000000000009e80 < y

   1. Initial program 70.8%

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

      1. +-commutative 70.8%

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

      2. associate-/l* 98.7%

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

      3. fma-define 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around inf 82.7%

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

      1. div-sub 82.7%

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

      2. associate-*r/ 58.4%

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

      3. associate-*l/ 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in z around 0 54.3%

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

      1. associate-*r/ 54.3%

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

      2. neg-mul-1 54.3%

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

   10. Simplified 54.3%

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

   11. Taylor expanded in y around 0 45.1%

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

       1. associate-*r/ 54.2%

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

       2. neg-mul-1 54.2%

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

       3. distribute-rgt-neg-in 54.2%

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

       4. neg-sub0 54.2%

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

       5. div-sub 52.9%

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

       6. associate--r- 52.9%

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

       7. neg-sub0 52.9%

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

       8. +-commutative 52.9%

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

       9. sub-neg 52.9%

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

       10. distribute-lft-out-- 52.7%

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

       11. associate-/l* 43.4%

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

       12. *-commutative 43.4%

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

       13. associate-*r/ 51.7%

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

       14. associate-/l* 50.1%

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

       15. associate-*l/ 50.5%

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

       16. *-commutative 50.5%

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

       17. distribute-rgt-out-- 54.3%

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

   13. Simplified 54.3%

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

   14. Taylor expanded in y around 0 45.1%

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

       1. associate-/l* 54.2%

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

   16. Simplified 54.2%

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

   if -9.50000000000000028e86 < y < 4.70000000000000009e80

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. associate-/l* 99.4%

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

      3. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 76.5%

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

      1. +-commutative 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+86} \lor \neg \left(y \leq 4.7 \cdot 10^{+80}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+80}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.4e+95)
   (* (/ y a) (- t z))
   (if (<= y 7.5e+80) (+ y x) (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.4e+95) {
		tmp = (y / a) * (t - z);
	} else if (y <= 7.5e+80) {
		tmp = y + x;
	} else {
		tmp = y * ((t - 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 (y <= (-4.4d+95)) then
        tmp = (y / a) * (t - z)
    else if (y <= 7.5d+80) then
        tmp = y + x
    else
        tmp = y * ((t - 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 (y <= -4.4e+95) {
		tmp = (y / a) * (t - z);
	} else if (y <= 7.5e+80) {
		tmp = y + x;
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.4e+95:
		tmp = (y / a) * (t - z)
	elif y <= 7.5e+80:
		tmp = y + x
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.4e+95)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (y <= 7.5e+80)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.4e+95)
		tmp = (y / a) * (t - z);
	elseif (y <= 7.5e+80)
		tmp = y + x;
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.4e+95], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+80], N[(y + x), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3999999999999998e95

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 97.0%

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

      3. fma-define 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around inf 82.1%

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

      1. div-sub 82.1%

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

      2. associate-*r/ 68.0%

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

      3. associate-*l/ 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in z around 0 50.4%

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

      1. associate-*r/ 50.4%

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

      2. neg-mul-1 50.4%

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

   10. Simplified 50.4%

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

   11. Taylor expanded in y around 0 44.8%

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

       1. associate-*r/ 47.5%

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

       2. neg-mul-1 47.5%

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

       3. distribute-rgt-neg-in 47.5%

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

       4. neg-sub0 47.5%

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

       5. div-sub 47.3%

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

       6. associate--r- 47.3%

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

       7. neg-sub0 47.3%

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

       8. +-commutative 47.3%

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

       9. sub-neg 47.3%

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

       10. distribute-lft-out-- 47.3%

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

       11. associate-/l* 41.7%

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

       12. *-commutative 41.7%

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

       13. associate-*r/ 47.5%

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

       14. associate-/l* 50.5%

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

       15. associate-*l/ 47.2%

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

       16. *-commutative 47.2%

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

       17. distribute-rgt-out-- 50.4%

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

   13. Simplified 50.4%

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

   if -4.3999999999999998e95 < y < 7.49999999999999994e80

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. associate-/l* 99.4%

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

      3. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 76.0%

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

      1. +-commutative 76.0%

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

   7. Simplified 76.0%

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

   if 7.49999999999999994e80 < y

   1. Initial program 64.6%

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

      1. +-commutative 64.6%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 82.8%

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

      1. div-sub 82.8%

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

      2. associate-*r/ 51.7%

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

      3. associate-*l/ 81.2%

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

   7. Simplified 81.2%

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

   8. Taylor expanded in z around 0 55.9%

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

      1. associate-*r/ 55.9%

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

      2. neg-mul-1 55.9%

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

   10. Simplified 55.9%

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

   11. Taylor expanded in y around 0 44.3%

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

       1. associate-*r/ 57.5%

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

       2. neg-mul-1 57.5%

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

       3. distribute-rgt-neg-in 57.5%

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

       4. neg-sub0 57.5%

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

       5. div-sub 55.4%

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

       6. associate--r- 55.4%

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

       7. neg-sub0 55.4%

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

       8. +-commutative 55.4%

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

       9. sub-neg 55.4%

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

       10. distribute-lft-out-- 55.1%

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

       11. associate-/l* 43.4%

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

       12. *-commutative 43.4%

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

       13. associate-*r/ 53.4%

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

       14. associate-/l* 48.9%

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

       15. associate-*l/ 51.7%

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

       16. *-commutative 51.7%

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

       17. distribute-rgt-out-- 55.9%

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

   13. Simplified 55.9%

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

   14. Taylor expanded in y around 0 44.3%

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

       1. associate-/l* 57.5%

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

   16. Simplified 57.5%

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

Alternative 15: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{+72}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.1e+72)
   (+ y x)
   (if (<= y 7.6e+161) (* t (/ y (- a z))) (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.1e+72) {
		tmp = y + x;
	} else if (y <= 7.6e+161) {
		tmp = t * (y / (a - z));
	} else {
		tmp = y * (z / (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 (y <= 1.1d+72) then
        tmp = y + x
    else if (y <= 7.6d+161) then
        tmp = t * (y / (a - z))
    else
        tmp = y * (z / (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 (y <= 1.1e+72) {
		tmp = y + x;
	} else if (y <= 7.6e+161) {
		tmp = t * (y / (a - z));
	} else {
		tmp = y * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.1e+72:
		tmp = y + x
	elif y <= 7.6e+161:
		tmp = t * (y / (a - z))
	else:
		tmp = y * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.1e+72)
		tmp = Float64(y + x);
	elseif (y <= 7.6e+161)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(y * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.1e+72)
		tmp = y + x;
	elseif (y <= 7.6e+161)
		tmp = t * (y / (a - z));
	else
		tmp = y * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.1e+72], N[(y + x), $MachinePrecision], If[LessEqual[y, 7.6e+161], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.1e72

   1. Initial program 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-/l* 99.0%

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

      3. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around inf 70.0%

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

      1. +-commutative 70.0%

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

   7. Simplified 70.0%

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

   if 1.1e72 < y < 7.6000000000000005e161

   1. Initial program 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 75.1%

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

      1. div-sub 75.1%

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

      2. associate-*r/ 60.8%

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

      3. associate-*l/ 75.0%

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

   7. Simplified 75.0%

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

      1. associate-/r/ 75.0%

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

   9. Applied egg-rr 75.0%

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

   10. Taylor expanded in t around inf 60.2%

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

       1. mul-1-neg 60.2%

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

       2. associate-/l* 69.7%

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

       3. distribute-rgt-neg-in 69.7%

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

       4. distribute-neg-frac2 69.7%

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

       5. neg-sub0 69.7%

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

       6. associate-+l- 69.7%

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

       7. neg-sub0 69.7%

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

       8. +-commutative 69.7%

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

       9. unsub-neg 69.7%

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

   12. Simplified 69.7%

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

   if 7.6000000000000005e161 < y

   1. Initial program 54.6%

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

      1. +-commutative 54.6%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

      2. associate-*r/ 46.6%

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

      3. associate-*l/ 83.1%

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

   7. Simplified 83.1%

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

      1. associate-/r/ 83.0%

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

   9. Applied egg-rr 83.0%

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

   10. Taylor expanded in t around 0 24.0%

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

       1. associate-/l* 48.1%

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

   12. Simplified 48.1%

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

Alternative 16: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+24} \lor \neg \left(z \leq 4.5 \cdot 10^{-138}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e+24) (not (<= z 4.5e-138))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+24) || !(z <= 4.5e-138)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d+24)) .or. (.not. (z <= 4.5d-138))) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+24) || !(z <= 4.5e-138)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e+24) or not (z <= 4.5e-138):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e+24) || !(z <= 4.5e-138))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e+24) || ~((z <= 4.5e-138)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e+24], N[Not[LessEqual[z, 4.5e-138]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e24 or 4.50000000000000008e-138 < z

   1. Initial program 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-/l* 99.2%

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

      3. fma-define 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 73.5%

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

      1. +-commutative 73.5%

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

   7. Simplified 73.5%

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

   if -2.7e24 < z < 4.50000000000000008e-138

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-/l* 99.0%

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

      3. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 57.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+24} \lor \neg \left(z \leq 4.5 \cdot 10^{-138}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{-1}{\frac{\frac{z - a}{t - z}}{y}} \end{array} \]

FPCore

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

C

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

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 + ((-1.0d0) / (((z - a) / (t - z)) / y))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (-1.0 / (((z - a) / (t - z)) / y));
}

Python

def code(x, y, z, t, a):
	return x + (-1.0 / (((z - a) / (t - z)) / y))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (-1.0 / (((z - a) / (t - z)) / y));
end

Wolfram

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

Derivation

1. Initial program 88.5%

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

   1. clear-num 88.5%

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

   2. inv-pow 88.5%

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

4. Applied egg-rr 88.5%

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

   1. unpow-1 88.5%

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

   2. *-commutative 88.5%

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

   3. associate-/r* 99.1%

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

6. Simplified 99.1%

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

7. Final simplification 99.1%

   \[\leadsto x + \frac{-1}{\frac{\frac{z - a}{t - z}}{y}} \]
8. Add Preprocessing

Alternative 18: 53.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-168}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.5e-136) x (if (<= x 1.02e-168) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.5e-136) {
		tmp = x;
	} else if (x <= 1.02e-168) {
		tmp = 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 (x <= (-7.5d-136)) then
        tmp = x
    else if (x <= 1.02d-168) then
        tmp = 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 (x <= -7.5e-136) {
		tmp = x;
	} else if (x <= 1.02e-168) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.5e-136:
		tmp = x
	elif x <= 1.02e-168:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.5e-136)
		tmp = x;
	elseif (x <= 1.02e-168)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.5e-136)
		tmp = x;
	elseif (x <= 1.02e-168)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.5e-136], x, If[LessEqual[x, 1.02e-168], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000003e-136 or 1.01999999999999999e-168 < x

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-/l* 99.4%

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

      3. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 65.2%

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

   if -7.5000000000000003e-136 < x < 1.01999999999999999e-168

   1. Initial program 83.7%

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

   3. Taylor expanded in a around 0 47.2%

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

   4. Taylor expanded in z around inf 57.0%

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

      1. associate-+r+ 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

      4. +-commutative 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in y around inf 52.1%

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

   8. Taylor expanded in t around 0 35.3%

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

Alternative 19: 51.3% 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 88.5%

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

   1. +-commutative 88.5%

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

   2. associate-/l* 99.1%

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

   3. fma-define 99.1%

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

3. Simplified 99.1%

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

5. Taylor expanded in y around 0 54.6%

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

Developer target: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024105 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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