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

Percentage Accurate: 84.8% → 98.4%

Time: 6.5s

Alternatives: 9

Speedup: 1.1×

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: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 83.4%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 98.0

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

4. Applied rewrites 98.0%

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

Alternative 2: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-14} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+119}\right):\\ \;\;\;\;\frac{z - t}{z - a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -1e-14) (not (<= t_1 5e+119)))
     (* (/ (- z t) (- z a)) y)
     (fma (/ z (- z a)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -1e-14) || !(t_1 <= 5e+119)) {
		tmp = ((z - t) / (z - a)) * y;
	} else {
		tmp = fma((z / (z - a)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -1e-14) || !(t_1 <= 5e+119))
		tmp = Float64(Float64(Float64(z - t) / Float64(z - a)) * y);
	else
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-14], N[Not[LessEqual[t$95$1, 5e+119]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -9.99999999999999999e-15 or 4.9999999999999999e119 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 62.2%

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

   3. Taylor expanded in x around 0

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

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

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

      2. fp-cancel-sub-sign N/A

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

      3. distribute-lft-neg-in N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-out N/A

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

      13. fp-cancel-sign-sub-inv N/A

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 80.4

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

   5. Applied rewrites 80.4%

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

   7. Applied rewrites 82.2%

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

   if -9.99999999999999999e-15 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999999e119

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 85.8

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

   5. Applied rewrites 85.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -1 \cdot 10^{-14} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+119}\right):\\ \;\;\;\;\frac{z - t}{z - a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-77} \lor \neg \left(z \leq 1.85 \cdot 10^{-8}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e-77) (not (<= z 1.85e-8)))
   (fma (/ (- z t) z) y x)
   (- x (/ (* (- z t) y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e-77) || !(z <= 1.85e-8)) {
		tmp = fma(((z - t) / z), y, x);
	} else {
		tmp = x - (((z - t) * y) / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e-77) || !(z <= 1.85e-8))
		tmp = fma(Float64(Float64(z - t) / z), y, x);
	else
		tmp = Float64(x - Float64(Float64(Float64(z - t) * y) / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.2e-77], N[Not[LessEqual[z, 1.85e-8]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision], N[(x - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999925e-77 or 1.85e-8 < z

   1. Initial program 75.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 86.2

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

   5. Applied rewrites 86.2%

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

   if -8.19999999999999925e-77 < z < 1.85e-8

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 84.3

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

   5. Applied rewrites 84.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-77} \lor \neg \left(z \leq 1.85 \cdot 10^{-8}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -750000000000 \lor \neg \left(z \leq 4.2 \cdot 10^{-79}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -750000000000.0) (not (<= z 4.2e-79)))
   (fma (/ (- z t) z) y x)
   (fma (/ t a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -750000000000.0) || !(z <= 4.2e-79)) {
		tmp = fma(((z - t) / z), y, x);
	} else {
		tmp = fma((t / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -750000000000.0) || !(z <= 4.2e-79))
		tmp = fma(Float64(Float64(z - t) / z), y, x);
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -750000000000.0], N[Not[LessEqual[z, 4.2e-79]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e11 or 4.1999999999999999e-79 < z

   1. Initial program 75.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 87.7

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

   5. Applied rewrites 87.7%

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

   if -7.5e11 < z < 4.1999999999999999e-79

   1. Initial program 93.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.4

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 79.3

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

   7. Applied rewrites 79.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -750000000000 \lor \neg \left(z \leq 4.2 \cdot 10^{-79}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+40} \lor \neg \left(z \leq 7 \cdot 10^{-105}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e+40) (not (<= z 7e-105)))
   (fma (/ z (- z a)) y x)
   (fma (/ t a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+40) || !(z <= 7e-105)) {
		tmp = fma((z / (z - a)), y, x);
	} else {
		tmp = fma((t / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e+40) || !(z <= 7e-105))
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e+40], N[Not[LessEqual[z, 7e-105]], $MachinePrecision]], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000009e40 or 7e-105 < z

   1. Initial program 76.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 86.8

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

   5. Applied rewrites 86.8%

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

   if -2.70000000000000009e40 < z < 7e-105

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.4

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 78.6

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

   7. Applied rewrites 78.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+40} \lor \neg \left(z \leq 7 \cdot 10^{-105}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+41)
   (+ y x)
   (if (<= z 2.25e-104) (fma (/ t a) y x) (fma z (/ y (- z a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+41) {
		tmp = y + x;
	} else if (z <= 2.25e-104) {
		tmp = fma((t / a), y, x);
	} else {
		tmp = fma(z, (y / (z - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+41)
		tmp = Float64(y + x);
	elseif (z <= 2.25e-104)
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = fma(z, Float64(y / Float64(z - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+41], N[(y + x), $MachinePrecision], If[LessEqual[z, 2.25e-104], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e41

   1. Initial program 67.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 90.3

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

   5. Applied rewrites 90.3%

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

   if -1.3e41 < z < 2.2499999999999999e-104

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.4

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 78.6

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

   7. Applied rewrites 78.6%

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

   if 2.2499999999999999e-104 < z

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 43.5

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

   5. Applied rewrites 43.5%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 80.4

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

   8. Applied rewrites 80.4%

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

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. lower-fma.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. lower--.f64 77.2

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

   11. Applied rewrites 77.2%

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

Alternative 7: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41} \lor \neg \left(z \leq 2 \cdot 10^{+37}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+41) (not (<= z 2e+37))) (+ y x) (fma (/ t a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+41) || !(z <= 2e+37)) {
		tmp = y + x;
	} else {
		tmp = fma((t / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+41) || !(z <= 2e+37))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+41], N[Not[LessEqual[z, 2e+37]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e41 or 1.99999999999999991e37 < z

   1. Initial program 72.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 82.1

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

   5. Applied rewrites 82.1%

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

   if -1.3e41 < z < 1.99999999999999991e37

   1. Initial program 93.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 76.7

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

   7. Applied rewrites 76.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41} \lor \neg \left(z \leq 2 \cdot 10^{+37}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41} \lor \neg \left(z \leq 1.55 \cdot 10^{+38}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+41) (not (<= z 1.55e+38))) (+ y x) (fma (/ y a) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+41) || !(z <= 1.55e+38)) {
		tmp = y + x;
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+41) || !(z <= 1.55e+38))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+41], N[Not[LessEqual[z, 1.55e+38]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e41 or 1.55000000000000009e38 < z

   1. Initial program 72.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 82.1

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

   5. Applied rewrites 82.1%

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

   if -1.3e41 < z < 1.55000000000000009e38

   1. Initial program 93.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 75.5

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

   5. Applied rewrites 75.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41} \lor \neg \left(z \leq 1.55 \cdot 10^{+38}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.5% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.4%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
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 61.0

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

5. Applied rewrites 61.0%

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

Developer Target 1: 98.5% 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 2024338 
(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))))