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

Percentage Accurate: 85.4% → 99.6%

Time: 8.9s

Alternatives: 11

Speedup: 0.3×

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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{1}{\frac{\frac{a - z}{y}}{z - t}}\\ t_2 := \left(t - z\right) \cdot y\\ t_3 := \frac{t\_2}{a - z}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x - \frac{t\_2}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ 1.0 (/ (/ (- a z) y) (- z t)))))
        (t_2 (* (- t z) y))
        (t_3 (/ t_2 (- a z))))
   (if (<= t_3 (- INFINITY))
     t_1
     (if (<= t_3 5e+286) (- x (/ t_2 (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (1.0 / (((a - z) / y) / (z - t)));
	double t_2 = (t - z) * y;
	double t_3 = t_2 / (a - z);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_3 <= 5e+286) {
		tmp = x - (t_2 / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (1.0 / (((a - z) / y) / (z - t)));
	double t_2 = (t - z) * y;
	double t_3 = t_2 / (a - z);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_3 <= 5e+286) {
		tmp = x - (t_2 / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (1.0 / (((a - z) / y) / (z - t)))
	t_2 = (t - z) * y
	t_3 = t_2 / (a - z)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_1
	elif t_3 <= 5e+286:
		tmp = x - (t_2 / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(1.0 / Float64(Float64(Float64(a - z) / y) / Float64(z - t))))
	t_2 = Float64(Float64(t - z) * y)
	t_3 = Float64(t_2 / Float64(a - z))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_3 <= 5e+286)
		tmp = Float64(x - Float64(t_2 / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (1.0 / (((a - z) / y) / (z - t)));
	t_2 = (t - z) * y;
	t_3 = t_2 / (a - z);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_1;
	elseif (t_3 <= 5e+286)
		tmp = x - (t_2 / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(1.0 / N[(N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$1, If[LessEqual[t$95$3, 5e+286], N[(x - N[(t$95$2 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 5.0000000000000004e286 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 36.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.0000000000000004e286

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq -\infty:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a - z}{y}}{z - t}}\\ \mathbf{elif}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x - \frac{\left(t - z\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a - z}{y}}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot y\\ t_2 := \frac{t\_1}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x} \cdot x, \frac{t - z}{a - z}, x\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x - \frac{t\_1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - z} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t z) y)) (t_2 (/ t_1 (- a z))))
   (if (<= t_2 (- INFINITY))
     (fma (* (/ y x) x) (/ (- t z) (- a z)) x)
     (if (<= t_2 5e+286) (- x (/ t_1 (- z a))) (* (/ y (- a z)) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) * y;
	double t_2 = t_1 / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(((y / x) * x), ((t - z) / (a - z)), x);
	} else if (t_2 <= 5e+286) {
		tmp = x - (t_1 / (z - a));
	} else {
		tmp = (y / (a - z)) * (t - z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) * y)
	t_2 = Float64(t_1 / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(Float64(Float64(y / x) * x), Float64(Float64(t - z) / Float64(a - z)), x);
	elseif (t_2 <= 5e+286)
		tmp = Float64(x - Float64(t_1 / Float64(z - a)));
	else
		tmp = Float64(Float64(y / Float64(a - z)) * Float64(t - z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(y / x), $MachinePrecision] * x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 5e+286], N[(x - N[(t$95$1 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - z), $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 40.4%

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

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. times-frac N/A

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

      4. associate-*r* N/A

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

      5. *-rgt-identity N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 91.3

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

   5. Applied rewrites 91.3%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.0000000000000004e286

   1. Initial program 99.8%

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

   if 5.0000000000000004e286 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 34.4%

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

   3. Taylor expanded in y around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 90.8

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

   5. Applied rewrites 90.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x} \cdot x, \frac{t - z}{a - z}, x\right)\\ \mathbf{elif}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x - \frac{\left(t - z\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - z} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - z} \cdot \left(t - z\right)\\ t_2 := \left(t - z\right) \cdot y\\ t_3 := \frac{t\_2}{a - z}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x - \frac{t\_2}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- a z)) (- t z)))
        (t_2 (* (- t z) y))
        (t_3 (/ t_2 (- a z))))
   (if (<= t_3 (- INFINITY))
     t_1
     (if (<= t_3 5e+286) (- x (/ t_2 (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (a - z)) * (t - z);
	double t_2 = (t - z) * y;
	double t_3 = t_2 / (a - z);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_3 <= 5e+286) {
		tmp = x - (t_2 / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (a - z)) * (t - z);
	double t_2 = (t - z) * y;
	double t_3 = t_2 / (a - z);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_3 <= 5e+286) {
		tmp = x - (t_2 / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (a - z)) * (t - z)
	t_2 = (t - z) * y
	t_3 = t_2 / (a - z)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_1
	elif t_3 <= 5e+286:
		tmp = x - (t_2 / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(a - z)) * Float64(t - z))
	t_2 = Float64(Float64(t - z) * y)
	t_3 = Float64(t_2 / Float64(a - z))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_3 <= 5e+286)
		tmp = Float64(x - Float64(t_2 / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (a - z)) * (t - z);
	t_2 = (t - z) * y;
	t_3 = t_2 / (a - z);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_1;
	elseif (t_3 <= 5e+286)
		tmp = x - (t_2 / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$1, If[LessEqual[t$95$3, 5e+286], N[(x - N[(t$95$2 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 5.0000000000000004e286 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 36.8%

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

   3. Taylor expanded in y around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 89.3

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

   5. Applied rewrites 89.3%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.0000000000000004e286

   1. Initial program 99.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq -\infty:\\ \;\;\;\;\frac{y}{a - z} \cdot \left(t - z\right)\\ \mathbf{elif}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x - \frac{\left(t - z\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - z} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -0.00062:\\ \;\;\;\;\frac{y}{z} \cdot \left(z - t\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+61)
   (+ x y)
   (if (<= z -0.00062)
     (* (/ y z) (- z t))
     (if (<= z 2.2e-12) (+ (* (/ y a) t) x) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+61) {
		tmp = x + y;
	} else if (z <= -0.00062) {
		tmp = (y / z) * (z - t);
	} else if (z <= 2.2e-12) {
		tmp = ((y / a) * t) + 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 (z <= (-8.5d+61)) then
        tmp = x + y
    else if (z <= (-0.00062d0)) then
        tmp = (y / z) * (z - t)
    else if (z <= 2.2d-12) then
        tmp = ((y / a) * t) + 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 (z <= -8.5e+61) {
		tmp = x + y;
	} else if (z <= -0.00062) {
		tmp = (y / z) * (z - t);
	} else if (z <= 2.2e-12) {
		tmp = ((y / a) * t) + x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+61:
		tmp = x + y
	elif z <= -0.00062:
		tmp = (y / z) * (z - t)
	elif z <= 2.2e-12:
		tmp = ((y / a) * t) + x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+61)
		tmp = Float64(x + y);
	elseif (z <= -0.00062)
		tmp = Float64(Float64(y / z) * Float64(z - t));
	elseif (z <= 2.2e-12)
		tmp = Float64(Float64(Float64(y / a) * t) + x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+61)
		tmp = x + y;
	elseif (z <= -0.00062)
		tmp = (y / z) * (z - t);
	elseif (z <= 2.2e-12)
		tmp = ((y / a) * t) + x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+61], N[(x + y), $MachinePrecision], If[LessEqual[z, -0.00062], N[(N[(y / z), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-12], N[(N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000035e61 or 2.19999999999999992e-12 < z

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 81.4

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

   5. Applied rewrites 81.4%

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

   if -8.50000000000000035e61 < z < -6.2e-4

   1. Initial program 83.2%

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

   3. Taylor expanded in y around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 87.4

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

   5. Applied rewrites 87.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 76.1%

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

   if -6.2e-4 < z < 2.19999999999999992e-12

   1. Initial program 93.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 95.3

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

   4. Applied rewrites 95.3%

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

   5. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 75.4

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

   7. Applied rewrites 75.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -0.00062:\\ \;\;\;\;\frac{y}{z} \cdot \left(z - t\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -0.00062:\\ \;\;\;\;\frac{y}{z} \cdot \left(z - t\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+61)
   (+ x y)
   (if (<= z -0.00062)
     (* (/ y z) (- z t))
     (if (<= z 2.2e-12) (fma (/ y a) t x) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+61) {
		tmp = x + y;
	} else if (z <= -0.00062) {
		tmp = (y / z) * (z - t);
	} else if (z <= 2.2e-12) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+61)
		tmp = Float64(x + y);
	elseif (z <= -0.00062)
		tmp = Float64(Float64(y / z) * Float64(z - t));
	elseif (z <= 2.2e-12)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+61], N[(x + y), $MachinePrecision], If[LessEqual[z, -0.00062], N[(N[(y / z), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-12], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000035e61 or 2.19999999999999992e-12 < z

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 81.4

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

   5. Applied rewrites 81.4%

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

   if -8.50000000000000035e61 < z < -6.2e-4

   1. Initial program 83.2%

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

   3. Taylor expanded in y around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 87.4

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

   5. Applied rewrites 87.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 76.1%

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

   if -6.2e-4 < z < 2.19999999999999992e-12

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 75.4

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

   5. Applied rewrites 75.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -0.00062:\\ \;\;\;\;\frac{y}{z} \cdot \left(z - t\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{t - z}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z t) z) y x)))
   (if (<= z -3e-119) t_1 (if (<= z 2.7e-138) (+ (* (/ (- t z) a) y) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - t) / z), y, x);
	double tmp;
	if (z <= -3e-119) {
		tmp = t_1;
	} else if (z <= 2.7e-138) {
		tmp = (((t - z) / a) * y) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - t) / z), y, x)
	tmp = 0.0
	if (z <= -3e-119)
		tmp = t_1;
	elseif (z <= 2.7e-138)
		tmp = Float64(Float64(Float64(Float64(t - z) / a) * y) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -3e-119], t$95$1, If[LessEqual[z, 2.7e-138], N[(N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000002e-119 or 2.70000000000000029e-138 < z

   1. Initial program 83.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 84.1

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

   5. Applied rewrites 84.1%

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

   if -3.0000000000000002e-119 < z < 2.70000000000000029e-138

   1. Initial program 92.3%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 89.9

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

   5. Applied rewrites 89.9%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-119}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{t - z}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{y}{a} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z t) z) y x)))
   (if (<= z -8.6e-122) t_1 (if (<= z 2.7e-138) (+ (* (/ y a) t) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - t) / z), y, x);
	double tmp;
	if (z <= -8.6e-122) {
		tmp = t_1;
	} else if (z <= 2.7e-138) {
		tmp = ((y / a) * t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - t) / z), y, x)
	tmp = 0.0
	if (z <= -8.6e-122)
		tmp = t_1;
	elseif (z <= 2.7e-138)
		tmp = Float64(Float64(Float64(y / a) * t) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -8.6e-122], t$95$1, If[LessEqual[z, 2.7e-138], N[(N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000037e-122 or 2.70000000000000029e-138 < z

   1. Initial program 83.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 84.1

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

   5. Applied rewrites 84.1%

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

   if -8.60000000000000037e-122 < z < 2.70000000000000029e-138

   1. Initial program 92.3%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.3

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

   4. Applied rewrites 94.3%

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

   5. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 86.8

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

   7. Applied rewrites 86.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-122}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{y}{a} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{a} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- z a)) y x)))
   (if (<= z -1.02e-118) t_1 (if (<= z 2.1e-120) (+ (* (/ y a) t) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / (z - a)), y, x);
	double tmp;
	if (z <= -1.02e-118) {
		tmp = t_1;
	} else if (z <= 2.1e-120) {
		tmp = ((y / a) * t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / Float64(z - a)), y, x)
	tmp = 0.0
	if (z <= -1.02e-118)
		tmp = t_1;
	elseif (z <= 2.1e-120)
		tmp = Float64(Float64(Float64(y / a) * t) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -1.02e-118], t$95$1, If[LessEqual[z, 2.1e-120], N[(N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e-118 or 2.1e-120 < z

   1. Initial program 83.8%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.3

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

   5. Applied rewrites 77.3%

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

   if -1.02e-118 < z < 2.1e-120

   1. Initial program 91.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.6

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

   4. Applied rewrites 94.6%

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

   5. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 85.2

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

   7. Applied rewrites 85.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-118}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{a} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-118}:\\ \;\;\;\;\frac{y}{a} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ y (- z a)) x)))
   (if (<= z -8.6e-122) t_1 (if (<= z 2.3e-118) (+ (* (/ y a) t) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, (y / (z - a)), x);
	double tmp;
	if (z <= -8.6e-122) {
		tmp = t_1;
	} else if (z <= 2.3e-118) {
		tmp = ((y / a) * t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(y / Float64(z - a)), x)
	tmp = 0.0
	if (z <= -8.6e-122)
		tmp = t_1;
	elseif (z <= 2.3e-118)
		tmp = Float64(Float64(Float64(y / a) * t) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -8.6e-122], t$95$1, If[LessEqual[z, 2.3e-118], N[(N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000037e-122 or 2.30000000000000021e-118 < z

   1. Initial program 83.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.6

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

   5. Applied rewrites 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 76.0%

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

   if -8.60000000000000037e-122 < z < 2.30000000000000021e-118

   1. Initial program 91.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.1

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 84.4

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

   7. Applied rewrites 84.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-122}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-118}:\\ \;\;\;\;\frac{y}{a} \cdot t + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e-8) (+ x y) (if (<= z 2.2e-12) (fma (/ y a) t x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e-8) {
		tmp = x + y;
	} else if (z <= 2.2e-12) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e-8)
		tmp = Float64(x + y);
	elseif (z <= 2.2e-12)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e-8], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.2e-12], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000002e-8 or 2.19999999999999992e-12 < z

   1. Initial program 79.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -4.6000000000000002e-8 < z < 2.19999999999999992e-12

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 75.4

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

   5. Applied rewrites 75.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.6% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 86.3%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 62.5

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

5. Applied rewrites 62.5%

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

6. Final simplification 62.5%

   \[\leadsto x + y \]
7. Add Preprocessing

Developer Target 1: 98.4% accurate, 0.8× 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 2024277 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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