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

Percentage Accurate: 85.4% → 98.3%

Time: 9.5s

Alternatives: 12

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: 85.4% 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 87.7%

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

   1. +-commutative 87.7%

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

   2. associate-/l* 99.6%

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

   3. fma-define 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(t - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+299}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- t z)) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+299)))
     (* (- z t) (/ y (- z a)))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (t - z)) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+299)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (t - z)) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+299)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (t - z)) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+299):
		tmp = (z - t) * (y / (z - a))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(t - z)) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+299))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (t - z)) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+299)))
		tmp = (z - t) * (y / (z - a));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+299]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 1.0000000000000001e299 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 41.0%

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

      1. +-commutative 41.0%

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

      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 87.1%

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

      1. div-sub 87.2%

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

      2. associate-*r/ 41.0%

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

      3. associate-*l/ 87.2%

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

   7. Simplified 87.2%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.0000000000000001e299

   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 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(t - z\right)}{a - z} \leq -\infty \lor \neg \left(\frac{y \cdot \left(t - z\right)}{a - z} \leq 10^{+299}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(t - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{-1}{a - z} \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- t z)) (- a z))))
   (if (<= t_1 -2e+103)
     (* (- z t) (/ y (- z a)))
     (if (<= t_1 5e-8)
       (+ x (* (/ -1.0 (- a z)) (* y z)))
       (/ (- z t) (/ (- z a) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (t - z)) / (a - z);
	double tmp;
	if (t_1 <= -2e+103) {
		tmp = (z - t) * (y / (z - a));
	} else if (t_1 <= 5e-8) {
		tmp = x + ((-1.0 / (a - z)) * (y * z));
	} else {
		tmp = (z - t) / ((z - a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (t - z)) / (a - z)
    if (t_1 <= (-2d+103)) then
        tmp = (z - t) * (y / (z - a))
    else if (t_1 <= 5d-8) then
        tmp = x + (((-1.0d0) / (a - z)) * (y * z))
    else
        tmp = (z - t) / ((z - a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (t - z)) / (a - z);
	double tmp;
	if (t_1 <= -2e+103) {
		tmp = (z - t) * (y / (z - a));
	} else if (t_1 <= 5e-8) {
		tmp = x + ((-1.0 / (a - z)) * (y * z));
	} else {
		tmp = (z - t) / ((z - a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (t - z)) / (a - z)
	tmp = 0
	if t_1 <= -2e+103:
		tmp = (z - t) * (y / (z - a))
	elif t_1 <= 5e-8:
		tmp = x + ((-1.0 / (a - z)) * (y * z))
	else:
		tmp = (z - t) / ((z - a) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(t - z)) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -2e+103)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (t_1 <= 5e-8)
		tmp = Float64(x + Float64(Float64(-1.0 / Float64(a - z)) * Float64(y * z)));
	else
		tmp = Float64(Float64(z - t) / Float64(Float64(z - a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (t - z)) / (a - z);
	tmp = 0.0;
	if (t_1 <= -2e+103)
		tmp = (z - t) * (y / (z - a));
	elseif (t_1 <= 5e-8)
		tmp = x + ((-1.0 / (a - z)) * (y * z));
	else
		tmp = (z - t) / ((z - a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+103], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-8], N[(x + N[(N[(-1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -2e103

   1. Initial program 61.7%

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

      1. +-commutative 61.7%

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

      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 87.4%

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

      1. div-sub 87.5%

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

      2. associate-*r/ 57.5%

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

      3. associate-*l/ 83.6%

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

   7. Simplified 83.6%

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

   if -2e103 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999998e-8

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. associate-/l/ 99.9%

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

      2. associate-/r/ 99.9%

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

      3. *-commutative 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in z around inf 94.9%

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

   if 4.9999999999999998e-8 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 76.2%

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

      1. +-commutative 76.2%

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

      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 inf 82.0%

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

      1. div-sub 82.0%

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

      2. associate-*r/ 65.1%

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

      3. associate-*l/ 80.2%

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

   7. Simplified 80.2%

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

      1. *-commutative 80.2%

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

      2. clear-num 80.2%

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

      3. un-div-inv 80.3%

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

   9. Applied egg-rr 80.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(t - z\right)}{a - z} \leq -2 \cdot 10^{+103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;\frac{y \cdot \left(t - z\right)}{a - z} \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{-1}{a - z} \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(t - z\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{z - t}{z - a}}{\frac{1}{y}}\\ \mathbf{elif}\;t\_1 \leq 10^{+299}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- t z)) (- a z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ (- z t) (- z a)) (/ 1.0 y))
     (if (<= t_1 1e+299) (+ x t_1) (* (- z t) (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (t - z)) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((z - t) / (z - a)) / (1.0 / y);
	} else if (t_1 <= 1e+299) {
		tmp = x + t_1;
	} else {
		tmp = (z - t) * (y / (z - a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (t - z)) / (a - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((z - t) / (z - a)) / (1.0 / y);
	} else if (t_1 <= 1e+299) {
		tmp = x + t_1;
	} else {
		tmp = (z - t) * (y / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (t - z)) / (a - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((z - t) / (z - a)) / (1.0 / y)
	elif t_1 <= 1e+299:
		tmp = x + t_1
	else:
		tmp = (z - t) * (y / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(t - z)) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z - t) / Float64(z - a)) / Float64(1.0 / y));
	elseif (t_1 <= 1e+299)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (t - z)) / (a - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((z - t) / (z - a)) / (1.0 / y);
	elseif (t_1 <= 1e+299)
		tmp = x + t_1;
	else
		tmp = (z - t) * (y / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] / N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+299], N[(x + t$95$1), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0

   1. Initial program 40.1%

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

      1. +-commutative 40.1%

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

      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 87.0%

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

      1. div-sub 87.2%

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

      2. associate-*r/ 40.1%

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

      3. associate-*l/ 87.2%

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

   7. Simplified 87.2%

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

      1. associate-/r/ 87.2%

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

      2. clear-num 87.1%

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

      3. div-inv 87.1%

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

      4. associate-/r* 87.3%

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

      5. clear-num 87.3%

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

   9. Applied egg-rr 87.3%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.0000000000000001e299

   1. Initial program 99.9%

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

   if 1.0000000000000001e299 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 42.2%

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

      1. +-commutative 42.2%

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

      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 87.3%

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

      1. div-sub 87.3%

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

      2. associate-*r/ 42.2%

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

      3. associate-*l/ 87.3%

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

   7. Simplified 87.3%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(t - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\frac{\frac{z - t}{z - a}}{\frac{1}{y}}\\ \mathbf{elif}\;\frac{y \cdot \left(t - z\right)}{a - z} \leq 10^{+299}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+167}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+34}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-45} \lor \neg \left(z \leq 7 \cdot 10^{+35}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+167)
   (+ y x)
   (if (<= z -4e+34)
     (- x (* t (/ y z)))
     (if (or (<= z -5.2e-45) (not (<= z 7e+35)))
       (+ y x)
       (+ x (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+167) {
		tmp = y + x;
	} else if (z <= -4e+34) {
		tmp = x - (t * (y / z));
	} else if ((z <= -5.2e-45) || !(z <= 7e+35)) {
		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 <= (-6.5d+167)) then
        tmp = y + x
    else if (z <= (-4d+34)) then
        tmp = x - (t * (y / z))
    else if ((z <= (-5.2d-45)) .or. (.not. (z <= 7d+35))) 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 <= -6.5e+167) {
		tmp = y + x;
	} else if (z <= -4e+34) {
		tmp = x - (t * (y / z));
	} else if ((z <= -5.2e-45) || !(z <= 7e+35)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+167:
		tmp = y + x
	elif z <= -4e+34:
		tmp = x - (t * (y / z))
	elif (z <= -5.2e-45) or not (z <= 7e+35):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+167)
		tmp = Float64(y + x);
	elseif (z <= -4e+34)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif ((z <= -5.2e-45) || !(z <= 7e+35))
		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 <= -6.5e+167)
		tmp = y + x;
	elseif (z <= -4e+34)
		tmp = x - (t * (y / z));
	elseif ((z <= -5.2e-45) || ~((z <= 7e+35)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+167], N[(y + x), $MachinePrecision], If[LessEqual[z, -4e+34], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5.2e-45], N[Not[LessEqual[z, 7e+35]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e167 or -3.99999999999999978e34 < z < -5.19999999999999973e-45 or 7.0000000000000001e35 < z

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      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 80.7%

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

      1. +-commutative 80.7%

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

   7. Simplified 80.7%

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

   if -6.5e167 < z < -3.99999999999999978e34

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 79.6%

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

      1. associate-*r/ 79.6%

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

      2. mul-1-neg 79.6%

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

      3. distribute-lft-neg-out 79.6%

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

      4. *-commutative 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in z around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-*r/ 76.3%

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

      3. *-commutative 76.3%

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

      4. distribute-rgt-neg-in 76.3%

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

   8. Simplified 76.3%

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

   if -5.19999999999999973e-45 < z < 7.0000000000000001e35

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-/l* 84.9%

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

   5. Applied egg-rr 84.9%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+167}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+34}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-45} \lor \neg \left(z \leq 7 \cdot 10^{+35}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{-45} \lor \neg \left(z \leq 4.8 \cdot 10^{-29}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.38e-45) (not (<= z 4.8e-29)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.38e-45) || !(z <= 4.8e-29)) {
		tmp = x + (y * ((z - t) / z));
	} 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 <= (-1.38d-45)) .or. (.not. (z <= 4.8d-29))) then
        tmp = x + (y * ((z - t) / z))
    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 <= -1.38e-45) || !(z <= 4.8e-29)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.38e-45) or not (z <= 4.8e-29):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.38e-45) || !(z <= 4.8e-29))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	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 <= -1.38e-45) || ~((z <= 4.8e-29)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.38e-45], N[Not[LessEqual[z, 4.8e-29]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.38e-45 or 4.79999999999999984e-29 < z

   1. Initial program 78.9%

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

      1. +-commutative 78.9%

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

      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 a around 0 69.4%

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

      1. +-commutative 69.4%

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

      2. associate-/l* 87.4%

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

   7. Simplified 87.4%

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

   if -1.38e-45 < z < 4.79999999999999984e-29

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 86.0%

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

   5. Applied egg-rr 86.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{-45} \lor \neg \left(z \leq 4.8 \cdot 10^{-29}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-45} \lor \neg \left(z \leq 2.1 \cdot 10^{+41}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e-45) (not (<= z 2.1e+41)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e-45) || !(z <= 2.1e+41)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (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 ((z <= (-5.2d-45)) .or. (.not. (z <= 2.1d+41))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (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 ((z <= -5.2e-45) || !(z <= 2.1e+41)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e-45) or not (z <= 2.1e+41):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e-45) || !(z <= 2.1e+41))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + 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 ((z <= -5.2e-45) || ~((z <= 2.1e+41)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e-45], N[Not[LessEqual[z, 2.1e+41]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999973e-45 or 2.1e41 < z

   1. Initial program 77.0%

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

      1. +-commutative 77.0%

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

      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 a around 0 69.4%

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

      1. +-commutative 69.4%

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

      2. associate-/l* 89.0%

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

   7. Simplified 89.0%

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

   if -5.19999999999999973e-45 < z < 2.1e41

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      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 a around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. unsub-neg 89.8%

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

      3. associate-/l* 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-45} \lor \neg \left(z \leq 2.1 \cdot 10^{+41}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-45} \lor \neg \left(z \leq 8.6 \cdot 10^{+35}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e-45) (not (<= z 8.6e+35))) (+ y x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e-45) || !(z <= 8.6e+35)) {
		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 <= (-5.2d-45)) .or. (.not. (z <= 8.6d+35))) 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 <= -5.2e-45) || !(z <= 8.6e+35)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e-45) or not (z <= 8.6e+35):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e-45) || !(z <= 8.6e+35))
		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 <= -5.2e-45) || ~((z <= 8.6e+35)))
		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, -5.2e-45], N[Not[LessEqual[z, 8.6e+35]], $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 < -5.19999999999999973e-45 or 8.5999999999999995e35 < z

   1. Initial program 77.2%

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

      1. +-commutative 77.2%

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

      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 75.5%

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

      1. +-commutative 75.5%

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

   7. Simplified 75.5%

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

   if -5.19999999999999973e-45 < z < 8.5999999999999995e35

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-/l* 84.9%

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

   5. Applied egg-rr 84.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-45} \lor \neg \left(z \leq 8.6 \cdot 10^{+35}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-48} \lor \neg \left(z \leq 1.24 \cdot 10^{-110}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e-48) (not (<= z 1.24e-110))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e-48) || !(z <= 1.24e-110)) {
		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 <= (-9.2d-48)) .or. (.not. (z <= 1.24d-110))) 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 <= -9.2e-48) || !(z <= 1.24e-110)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.2e-48) or not (z <= 1.24e-110):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2e-48) || !(z <= 1.24e-110))
		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 <= -9.2e-48) || ~((z <= 1.24e-110)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2e-48], N[Not[LessEqual[z, 1.24e-110]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000003e-48 or 1.24000000000000006e-110 < z

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      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 74.6%

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

      1. +-commutative 74.6%

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

   7. Simplified 74.6%

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

   if -9.2000000000000003e-48 < z < 1.24000000000000006e-110

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      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 57.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-48} \lor \neg \left(z \leq 1.24 \cdot 10^{-110}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.3% 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 87.7%

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

   1. clear-num 87.6%

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

   2. inv-pow 87.6%

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

4. Applied egg-rr 87.6%

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

   1. unpow-1 87.6%

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

   2. *-commutative 87.6%

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

   3. associate-/r* 99.4%

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

6. Simplified 99.4%

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

7. Final simplification 99.4%

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

Alternative 11: 52.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-248}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.3e-188) x (if (<= x 2.6e-248) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e-188) {
		tmp = x;
	} else if (x <= 2.6e-248) {
		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 <= (-1.3d-188)) then
        tmp = x
    else if (x <= 2.6d-248) 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 <= -1.3e-188) {
		tmp = x;
	} else if (x <= 2.6e-248) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.3e-188:
		tmp = x
	elif x <= 2.6e-248:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.3e-188)
		tmp = x;
	elseif (x <= 2.6e-248)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.3e-188)
		tmp = x;
	elseif (x <= 2.6e-248)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.3e-188], x, If[LessEqual[x, 2.6e-248], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e-188 or 2.60000000000000007e-248 < x

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. associate-/l* 99.5%

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

      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 0 62.0%

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

   if -1.3e-188 < x < 2.60000000000000007e-248

   1. Initial program 85.7%

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

      1. +-commutative 85.7%

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

      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 y around inf 92.7%

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

      1. div-sub 92.7%

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

      2. associate-*r/ 78.4%

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

      3. associate-*l/ 80.5%

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

   7. Simplified 80.5%

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

      1. *-commutative 80.5%

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

      2. clear-num 79.6%

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

      3. un-div-inv 79.8%

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

   9. Applied egg-rr 79.8%

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

   10. Taylor expanded in z around inf 47.8%

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

   11. Taylor expanded in z around inf 41.2%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-248}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.2% 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 87.7%

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

   1. +-commutative 87.7%

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

   2. associate-/l* 99.6%

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

   3. fma-define 99.6%

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

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 0 55.1%

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

6. Final simplification 55.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.4% 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 2024066 
(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))))