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

Percentage Accurate: 85.4% → 98.4%

Time: 10.4s

Alternatives: 12

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 N/A

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

   7. --lowering--.f64 99.5

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

4. Applied egg-rr 99.5%

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

Alternative 2: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ t_2 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+228}:\\ \;\;\;\;x + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y (- a t)) (- z t) x)) (t_2 (/ (* y (- z t)) (- a t))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 1e+228) (+ x t_2) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / (a - t)), (z - t), x);
	double t_2 = (y * (z - t)) / (a - t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+228) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / Float64(a - t)), Float64(z - t), x)
	t_2 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+228)
		tmp = Float64(x + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1e+228], N[(x + t$95$2), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0 or 9.9999999999999992e227 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 41.6%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. --lowering--.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 9.9999999999999992e227

   1. Initial program 99.4%

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

Alternative 3: 54.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+192}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (<= t_1 -2000000000.0) y (if (<= t_1 2e+192) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if (t_1 <= -2000000000.0) {
		tmp = y;
	} else if (t_1 <= 2e+192) {
		tmp = x;
	} else {
		tmp = 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 * (z - t)) / (a - t)
    if (t_1 <= (-2000000000.0d0)) then
        tmp = y
    else if (t_1 <= 2d+192) then
        tmp = x
    else
        tmp = 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 * (z - t)) / (a - t);
	double tmp;
	if (t_1 <= -2000000000.0) {
		tmp = y;
	} else if (t_1 <= 2e+192) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if t_1 <= -2000000000.0:
		tmp = y
	elif t_1 <= 2e+192:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -2000000000.0)
		tmp = y;
	elseif (t_1 <= 2e+192)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if (t_1 <= -2000000000.0)
		tmp = y;
	elseif (t_1 <= 2e+192)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2000000000.0], y, If[LessEqual[t$95$1, 2e+192], x, y]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -2e9 or 2.00000000000000008e192 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 67.0%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. --lowering--.f64 60.0

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

   5. Simplified 60.0%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 28.5%

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

   if -2e9 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 2.00000000000000008e192

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 72.5%

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

Alternative 4: 57.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+231}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{t}, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3e+231)
   (/ (* y z) a)
   (if (<= y 2.1e+38)
     (+ x y)
     (if (<= y 2.7e+186) (* z (/ y a)) (fma a (/ y t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3e+231) {
		tmp = (y * z) / a;
	} else if (y <= 2.1e+38) {
		tmp = x + y;
	} else if (y <= 2.7e+186) {
		tmp = z * (y / a);
	} else {
		tmp = fma(a, (y / t), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3e+231)
		tmp = Float64(Float64(y * z) / a);
	elseif (y <= 2.1e+38)
		tmp = Float64(x + y);
	elseif (y <= 2.7e+186)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = fma(a, Float64(y / t), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3e+231], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.1e+38], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.7e+186], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(a * N[(y / t), $MachinePrecision] + y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.0000000000000002e231

   1. Initial program 78.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 71.2

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

   5. Simplified 71.2%

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

   6. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 71.3

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

   8. Simplified 71.3%

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

   if -3.0000000000000002e231 < y < 2.1e38

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 69.7

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

   5. Simplified 69.7%

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

   if 2.1e38 < y < 2.6999999999999999e186

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. --lowering--.f64 55.5

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

   5. Simplified 55.5%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 77.5

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

   7. Applied egg-rr 77.5%

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

   8. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 58.4

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

   10. Simplified 58.4%

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

   11. Taylor expanded in z around inf

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

   13. Simplified 54.9%

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

   if 2.6999999999999999e186 < y

   1. Initial program 49.9%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. --lowering--.f64 39.5

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

   5. Simplified 39.5%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. *-lowering-*.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. /-lowering-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. --lowering--.f64 52.5

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

   8. Simplified 52.5%

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

   9. Taylor expanded in t around inf

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

       1. +-commutative N/A

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

       2. associate-/l* N/A

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

       3. accelerator-lowering-fma.f64 N/A

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

       4. /-lowering-/.f64 54.5

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

   11. Simplified 54.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(a, \frac{y}{t}, y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+231}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{t}, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+231}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.5e+231)
   (/ (* y z) a)
   (if (<= y 2e+38) (+ x y) (if (<= y 2.7e+187) (* z (/ y a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.5e+231) {
		tmp = (y * z) / a;
	} else if (y <= 2e+38) {
		tmp = x + y;
	} else if (y <= 2.7e+187) {
		tmp = z * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.5d+231)) then
        tmp = (y * z) / a
    else if (y <= 2d+38) then
        tmp = x + y
    else if (y <= 2.7d+187) then
        tmp = z * (y / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.5e+231) {
		tmp = (y * z) / a;
	} else if (y <= 2e+38) {
		tmp = x + y;
	} else if (y <= 2.7e+187) {
		tmp = z * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.5e+231:
		tmp = (y * z) / a
	elif y <= 2e+38:
		tmp = x + y
	elif y <= 2.7e+187:
		tmp = z * (y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.5e+231)
		tmp = Float64(Float64(y * z) / a);
	elseif (y <= 2e+38)
		tmp = Float64(x + y);
	elseif (y <= 2.7e+187)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.5e+231)
		tmp = (y * z) / a;
	elseif (y <= 2e+38)
		tmp = x + y;
	elseif (y <= 2.7e+187)
		tmp = z * (y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.5e+231], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2e+38], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.7e+187], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e231

   1. Initial program 78.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 71.2

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

   5. Simplified 71.2%

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

   6. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 71.3

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

   8. Simplified 71.3%

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

   if -1.5000000000000001e231 < y < 1.99999999999999995e38 or 2.70000000000000008e187 < y

   1. Initial program 89.3%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 67.0

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

   5. Simplified 67.0%

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

   if 1.99999999999999995e38 < y < 2.70000000000000008e187

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. --lowering--.f64 55.5

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

   5. Simplified 55.5%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 77.5

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

   7. Applied egg-rr 77.5%

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

   8. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 58.4

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

   10. Simplified 58.4%

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

   11. Taylor expanded in z around inf

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

   13. Simplified 54.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+231}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y a))))
   (if (<= y -2.2e+230)
     t_1
     (if (<= y 1.2e+38) (+ x y) (if (<= y 4.2e+187) t_1 (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double tmp;
	if (y <= -2.2e+230) {
		tmp = t_1;
	} else if (y <= 1.2e+38) {
		tmp = x + y;
	} else if (y <= 4.2e+187) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / a)
    if (y <= (-2.2d+230)) then
        tmp = t_1
    else if (y <= 1.2d+38) then
        tmp = x + y
    else if (y <= 4.2d+187) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double tmp;
	if (y <= -2.2e+230) {
		tmp = t_1;
	} else if (y <= 1.2e+38) {
		tmp = x + y;
	} else if (y <= 4.2e+187) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / a)
	tmp = 0
	if y <= -2.2e+230:
		tmp = t_1
	elif y <= 1.2e+38:
		tmp = x + y
	elif y <= 4.2e+187:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / a))
	tmp = 0.0
	if (y <= -2.2e+230)
		tmp = t_1;
	elseif (y <= 1.2e+38)
		tmp = Float64(x + y);
	elseif (y <= 4.2e+187)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / a);
	tmp = 0.0;
	if (y <= -2.2e+230)
		tmp = t_1;
	elseif (y <= 1.2e+38)
		tmp = x + y;
	elseif (y <= 4.2e+187)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+230], t$95$1, If[LessEqual[y, 1.2e+38], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.2e+187], t$95$1, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000001e230 or 1.20000000000000009e38 < y < 4.2e187

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. --lowering--.f64 62.6

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

   5. Simplified 62.6%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 82.2

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

   7. Applied egg-rr 82.2%

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

   8. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 64.5

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

   10. Simplified 64.5%

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

   11. Taylor expanded in z around inf

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

   13. Simplified 59.8%

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

   if -2.2000000000000001e230 < y < 1.20000000000000009e38 or 4.2e187 < y

   1. Initial program 89.3%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 67.0

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

   5. Simplified 67.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- z t) a) x)))
   (if (<= a -8.2e-41) t_1 (if (<= a 1.8e-29) (fma y (- 1.0 (/ z t)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((z - t) / a), x);
	double tmp;
	if (a <= -8.2e-41) {
		tmp = t_1;
	} else if (a <= 1.8e-29) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(z - t) / a), x)
	tmp = 0.0
	if (a <= -8.2e-41)
		tmp = t_1;
	elseif (a <= 1.8e-29)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -8.2e-41], t$95$1, If[LessEqual[a, 1.8e-29], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.20000000000000028e-41 or 1.79999999999999987e-29 < a

   1. Initial program 87.6%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 84.0

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

   5. Simplified 84.0%

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

   if -8.20000000000000028e-41 < a < 1.79999999999999987e-29

   1. Initial program 87.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{0 - \frac{z - t}{t}}, x\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{fma}\left(y, 0 - \color{blue}{\left(\frac{z}{t} - \frac{t}{t}\right)}, x\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(y, 0 - \left(\frac{z}{t} - \color{blue}{1}\right), x\right) \]

      9. associate-+l- N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(0 - \frac{z}{t}\right) + 1}, x\right) \]

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. /-lowering-/.f64 87.7

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

   5. Simplified 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.0004:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ z t)) x)))
   (if (<= t -2.2e+21) t_1 (if (<= t 0.0004) (fma y (/ z a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (z / t)), x);
	double tmp;
	if (t <= -2.2e+21) {
		tmp = t_1;
	} else if (t <= 0.0004) {
		tmp = fma(y, (z / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(z / t)), x)
	tmp = 0.0
	if (t <= -2.2e+21)
		tmp = t_1;
	elseif (t <= 0.0004)
		tmp = fma(y, Float64(z / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.2e+21], t$95$1, If[LessEqual[t, 0.0004], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e21 or 4.00000000000000019e-4 < t

   1. Initial program 80.1%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{0 - \frac{z - t}{t}}, x\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{fma}\left(y, 0 - \color{blue}{\left(\frac{z}{t} - \frac{t}{t}\right)}, x\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(y, 0 - \left(\frac{z}{t} - \color{blue}{1}\right), x\right) \]

      9. associate-+l- N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(0 - \frac{z}{t}\right) + 1}, x\right) \]

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. /-lowering-/.f64 85.3

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

   5. Simplified 85.3%

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

   if -2.2e21 < t < 4.00000000000000019e-4

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 83.3

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

   5. Simplified 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z}{a}, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 77.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+47) (+ x y) (if (<= t 1.86e+34) (fma y (/ z a) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+47) {
		tmp = x + y;
	} else if (t <= 1.86e+34) {
		tmp = fma(y, (z / a), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+47)
		tmp = Float64(x + y);
	elseif (t <= 1.86e+34)
		tmp = fma(y, Float64(z / a), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+47], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.86e+34], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5999999999999997e47 or 1.86e34 < t

   1. Initial program 78.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 77.2

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

   5. Simplified 77.2%

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

   if -4.5999999999999997e47 < t < 1.86e34

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 79.9

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

   5. Simplified 79.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z}{a}, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+182}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e+182) (fma y (- 1.0 (/ z t)) x) (fma (/ y (- a t)) (- z t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+182) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = fma((y / (a - t)), (z - t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e+182)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = fma(Float64(y / Float64(a - t)), Float64(z - t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e+182], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e182

   1. Initial program 69.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{0 - \frac{z - t}{t}}, x\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{fma}\left(y, 0 - \color{blue}{\left(\frac{z}{t} - \frac{t}{t}\right)}, x\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(y, 0 - \left(\frac{z}{t} - \color{blue}{1}\right), x\right) \]

      9. associate-+l- N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(0 - \frac{z}{t}\right) + 1}, x\right) \]

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. /-lowering-/.f64 96.7

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

   5. Simplified 96.7%

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

   if -1.3e182 < t

   1. Initial program 89.6%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. --lowering--.f64 96.0

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

   4. Applied egg-rr 96.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 62.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -4.7e+151) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e+151) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.7d+151)) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e+151) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.7e+151:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.7e+151)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.7e+151)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.7e+151], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.69999999999999989e151

   1. Initial program 86.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 76.5%

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

   if -4.69999999999999989e151 < a

   1. Initial program 87.7%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 58.8

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

   5. Simplified 58.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.3% accurate, 26.0× 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 87.4%

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

3. Taylor expanded in x around inf

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

5. Simplified 50.2%

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

Developer Target 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024205 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- a t) (- z t)))))

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