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

Percentage Accurate: 98.3% → 98.4%

Time: 7.9s

Alternatives: 13

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. lower-/.f64 N/A

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

   6. frac-2neg N/A

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

   7. lower-/.f64 N/A

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

   8. neg-sub0 N/A

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

   9. lift--.f64 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. associate--r+ N/A

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

   13. neg-sub0 N/A

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

   14. remove-double-neg N/A

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

   15. lower--.f64 N/A

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

   16. neg-sub0 N/A

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

   17. lift--.f64 N/A

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

   18. sub-neg N/A

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

   19. +-commutative N/A

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

   20. associate--r+ N/A

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

   21. neg-sub0 N/A

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

   22. remove-double-neg N/A

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

   23. lower--.f64 98.4

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

4. Applied rewrites 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 82.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{z \cdot y}{a} + x\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-z}{t}, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+28}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))))
   (if (<= t_1 -5e+60)
     (+ (/ (* z y) a) x)
     (if (<= t_1 -5e+18)
       (fma y (/ (- z) t) x)
       (if (<= t_1 1e-5)
         (fma (/ z a) y x)
         (if (<= t_1 1e+28) (+ y x) (* (/ y (- a t)) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double tmp;
	if (t_1 <= -5e+60) {
		tmp = ((z * y) / a) + x;
	} else if (t_1 <= -5e+18) {
		tmp = fma(y, (-z / t), x);
	} else if (t_1 <= 1e-5) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 1e+28) {
		tmp = y + x;
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	tmp = 0.0
	if (t_1 <= -5e+60)
		tmp = Float64(Float64(Float64(z * y) / a) + x);
	elseif (t_1 <= -5e+18)
		tmp = fma(y, Float64(Float64(-z) / t), x);
	elseif (t_1 <= 1e-5)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 1e+28)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+60], N[(N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, -5e+18], N[(y * N[((-z) / t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-5], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+28], N[(y + x), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.99999999999999975e60

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 81.2

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

   5. Applied rewrites 81.2%

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

   if -4.99999999999999975e60 < (/.f64 (-.f64 z t) (-.f64 a t)) < -5e18

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

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

      17. lift--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 73.2

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

   7. Applied rewrites 73.2%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, \frac{-1 \cdot z}{t}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 73.2%

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

   if -5e18 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.00000000000000008e-5

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 82.6

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

   5. Applied rewrites 82.6%

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

   if 1.00000000000000008e-5 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999958e27

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 93.5

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

   5. Applied rewrites 93.5%

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

   if 9.99999999999999958e27 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

   7. Applied rewrites 81.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{z \cdot y}{a} + x\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-z}{t}, x\right)\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 10^{+28}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))))
   (if (<= t_1 -5e+60)
     (* (/ z a) y)
     (if (<= t_1 2e-18) (* 1.0 x) (if (<= t_1 2e+76) (+ y x) (* (/ y a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double tmp;
	if (t_1 <= -5e+60) {
		tmp = (z / a) * y;
	} else if (t_1 <= 2e-18) {
		tmp = 1.0 * x;
	} else if (t_1 <= 2e+76) {
		tmp = y + x;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - z) / (t - a)
    if (t_1 <= (-5d+60)) then
        tmp = (z / a) * y
    else if (t_1 <= 2d-18) then
        tmp = 1.0d0 * x
    else if (t_1 <= 2d+76) then
        tmp = y + x
    else
        tmp = (y / a) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double tmp;
	if (t_1 <= -5e+60) {
		tmp = (z / a) * y;
	} else if (t_1 <= 2e-18) {
		tmp = 1.0 * x;
	} else if (t_1 <= 2e+76) {
		tmp = y + x;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) / (t - a)
	tmp = 0
	if t_1 <= -5e+60:
		tmp = (z / a) * y
	elif t_1 <= 2e-18:
		tmp = 1.0 * x
	elif t_1 <= 2e+76:
		tmp = y + x
	else:
		tmp = (y / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	tmp = 0.0
	if (t_1 <= -5e+60)
		tmp = Float64(Float64(z / a) * y);
	elseif (t_1 <= 2e-18)
		tmp = Float64(1.0 * x);
	elseif (t_1 <= 2e+76)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) / (t - a);
	tmp = 0.0;
	if (t_1 <= -5e+60)
		tmp = (z / a) * y;
	elseif (t_1 <= 2e-18)
		tmp = 1.0 * x;
	elseif (t_1 <= 2e+76)
		tmp = y + x;
	else
		tmp = (y / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+60], N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 2e-18], N[(1.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 2e+76], N[(y + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.99999999999999975e60

   1. Initial program 89.8%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 62.7

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

   5. Applied rewrites 62.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.9%

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

   if -4.99999999999999975e60 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.0000000000000001e-18

   1. Initial program 98.4%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 44.7

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

   5. Applied rewrites 44.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.6%

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

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 63.0%

       \[\leadsto 1 \cdot x \]

   if 2.0000000000000001e-18 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.0000000000000001e76

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 89.5

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

   5. Applied rewrites 89.5%

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

   if 2.0000000000000001e76 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 84.0

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

   5. Applied rewrites 84.0%

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

   7. Applied rewrites 78.3%

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

   9. Applied rewrites 84.1%

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

   10. Taylor expanded in t around 0

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

   12. Applied rewrites 67.3%

       \[\leadsto \frac{y}{a} \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 2 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ t_2 := \frac{y}{a} \cdot z\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))) (t_2 (* (/ y a) z)))
   (if (<= t_1 -5e+60)
     t_2
     (if (<= t_1 2e-18) (* 1.0 x) (if (<= t_1 2e+76) (+ y x) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double t_2 = (y / a) * z;
	double tmp;
	if (t_1 <= -5e+60) {
		tmp = t_2;
	} else if (t_1 <= 2e-18) {
		tmp = 1.0 * x;
	} else if (t_1 <= 2e+76) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - z) / (t - a)
    t_2 = (y / a) * z
    if (t_1 <= (-5d+60)) then
        tmp = t_2
    else if (t_1 <= 2d-18) then
        tmp = 1.0d0 * x
    else if (t_1 <= 2d+76) then
        tmp = y + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double t_2 = (y / a) * z;
	double tmp;
	if (t_1 <= -5e+60) {
		tmp = t_2;
	} else if (t_1 <= 2e-18) {
		tmp = 1.0 * x;
	} else if (t_1 <= 2e+76) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) / (t - a)
	t_2 = (y / a) * z
	tmp = 0
	if t_1 <= -5e+60:
		tmp = t_2
	elif t_1 <= 2e-18:
		tmp = 1.0 * x
	elif t_1 <= 2e+76:
		tmp = y + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	t_2 = Float64(Float64(y / a) * z)
	tmp = 0.0
	if (t_1 <= -5e+60)
		tmp = t_2;
	elseif (t_1 <= 2e-18)
		tmp = Float64(1.0 * x);
	elseif (t_1 <= 2e+76)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) / (t - a);
	t_2 = (y / a) * z;
	tmp = 0.0;
	if (t_1 <= -5e+60)
		tmp = t_2;
	elseif (t_1 <= 2e-18)
		tmp = 1.0 * x;
	elseif (t_1 <= 2e+76)
		tmp = y + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+60], t$95$2, If[LessEqual[t$95$1, 2e-18], N[(1.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 2e+76], N[(y + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.99999999999999975e60 or 2.0000000000000001e76 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 73.9

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

   5. Applied rewrites 73.9%

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

   7. Applied rewrites 72.6%

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

   9. Applied rewrites 73.9%

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

   10. Taylor expanded in t around 0

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

   12. Applied rewrites 59.9%

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

   if -4.99999999999999975e60 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.0000000000000001e-18

   1. Initial program 98.4%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 44.7

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

   5. Applied rewrites 44.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.6%

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

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 63.0%

       \[\leadsto 1 \cdot x \]

   if 2.0000000000000001e-18 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.0000000000000001e76

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 89.5

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

   5. Applied rewrites 89.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 2 \cdot 10^{-18}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 2 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ \mathbf{if}\;t\_1 \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))))
   (if (<= t_1 1e-5)
     (fma (- z t) (/ y a) x)
     (if (<= t_1 1e+28) (fma (/ t (- t a)) y x) (* (/ y (- a t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double tmp;
	if (t_1 <= 1e-5) {
		tmp = fma((z - t), (y / a), x);
	} else if (t_1 <= 1e+28) {
		tmp = fma((t / (t - a)), y, x);
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	tmp = 0.0
	if (t_1 <= 1e-5)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t_1 <= 1e+28)
		tmp = fma(Float64(t / Float64(t - a)), y, x);
	else
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-5], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+28], N[(N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.00000000000000008e-5

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 86.2

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

   5. Applied rewrites 86.2%

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

   if 1.00000000000000008e-5 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999958e27

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

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

      17. lift--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 95.1

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

   7. Applied rewrites 95.1%

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

   9. Applied rewrites 95.1%

      \[\leadsto \mathsf{fma}\left(t, \frac{1}{\color{blue}{\frac{t - a}{y}}}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 96.1%

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

   if 9.99999999999999958e27 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

   7. Applied rewrites 81.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ \mathbf{if}\;t\_1 \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))))
   (if (<= t_1 1e-5)
     (fma (- z t) (/ y a) x)
     (if (<= t_1 1e+28) (fma t (/ y (- t a)) x) (* (/ y (- a t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double tmp;
	if (t_1 <= 1e-5) {
		tmp = fma((z - t), (y / a), x);
	} else if (t_1 <= 1e+28) {
		tmp = fma(t, (y / (t - a)), x);
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	tmp = 0.0
	if (t_1 <= 1e-5)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t_1 <= 1e+28)
		tmp = fma(t, Float64(y / Float64(t - a)), x);
	else
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-5], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+28], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.00000000000000008e-5

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 86.2

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

   5. Applied rewrites 86.2%

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

   if 1.00000000000000008e-5 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999958e27

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

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

      17. lift--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 95.1

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

   7. Applied rewrites 95.1%

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

   if 9.99999999999999958e27 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

   7. Applied rewrites 81.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ \mathbf{if}\;t\_1 \leq 0.0001:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+28}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))))
   (if (<= t_1 0.0001)
     (fma (- z t) (/ y a) x)
     (if (<= t_1 1e+28) (+ y x) (* (/ y (- a t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double tmp;
	if (t_1 <= 0.0001) {
		tmp = fma((z - t), (y / a), x);
	} else if (t_1 <= 1e+28) {
		tmp = y + x;
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	tmp = 0.0
	if (t_1 <= 0.0001)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t_1 <= 1e+28)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0001], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+28], N[(y + x), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.00000000000000005e-4

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

   if 1.00000000000000005e-4 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999958e27

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 94.4

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

   5. Applied rewrites 94.4%

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

   if 9.99999999999999958e27 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

   7. Applied rewrites 81.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq 0.0001:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 10^{+28}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ \mathbf{if}\;t\_1 \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+28}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))))
   (if (<= t_1 1e-5)
     (fma (/ z a) y x)
     (if (<= t_1 1e+28) (+ y x) (* (/ y (- a t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double tmp;
	if (t_1 <= 1e-5) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 1e+28) {
		tmp = y + x;
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	tmp = 0.0
	if (t_1 <= 1e-5)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 1e+28)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-5], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+28], N[(y + x), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.00000000000000008e-5

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if 1.00000000000000008e-5 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999958e27

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 93.5

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

   5. Applied rewrites 93.5%

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

   if 9.99999999999999958e27 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

   7. Applied rewrites 81.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 10^{+28}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{t - a}\\ t_2 := \mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{if}\;t\_1 \leq 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- t a))) (t_2 (fma (/ z a) y x)))
   (if (<= t_1 1e-5) t_2 (if (<= t_1 2000000.0) (+ y x) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (t - a);
	double t_2 = fma((z / a), y, x);
	double tmp;
	if (t_1 <= 1e-5) {
		tmp = t_2;
	} else if (t_1 <= 2000000.0) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(t - a))
	t_2 = fma(Float64(z / a), y, x)
	tmp = 0.0
	if (t_1 <= 1e-5)
		tmp = t_2;
	elseif (t_1 <= 2000000.0)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-5], t$95$2, If[LessEqual[t$95$1, 2000000.0], N[(y + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.00000000000000008e-5 or 2e6 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if 1.00000000000000008e-5 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2e6

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 95.1

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

   5. Applied rewrites 95.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{t - z}{t - a} \leq 2000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- t z) (- t a)) 2.1e-16) (* 1.0 x) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((t - z) / (t - a)) <= 2.1e-16) {
		tmp = 1.0 * x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((t - z) / (t - a)) <= 2.1d-16) then
        tmp = 1.0d0 * x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((t - z) / (t - a)) <= 2.1e-16) {
		tmp = 1.0 * x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((t - z) / (t - a)) <= 2.1e-16:
		tmp = 1.0 * x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(t - z) / Float64(t - a)) <= 2.1e-16)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((t - z) / (t - a)) <= 2.1e-16)
		tmp = 1.0 * x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], 2.1e-16], N[(1.0 * x), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 2.1000000000000001e-16

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 42.1

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

   5. Applied rewrites 42.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 42.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 56.4%

       \[\leadsto 1 \cdot x \]

   if 2.1000000000000001e-16 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 73.2

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

   5. Applied rewrites 73.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{t - a} \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

3. Final simplification 98.2%

   \[\leadsto x - \frac{t - z}{a - t} \cdot y \]
4. Add Preprocessing

Alternative 12: 98.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 98.2

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

   6. lift-/.f64 N/A

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

   7. frac-2neg N/A

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

   8. lower-/.f64 N/A

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

   9. neg-sub0 N/A

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

   10. lift--.f64 N/A

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

   11. sub-neg N/A

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

   12. +-commutative N/A

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

   13. associate--r+ N/A

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

   14. neg-sub0 N/A

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

   15. remove-double-neg N/A

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

   16. lower--.f64 N/A

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

   17. neg-sub0 N/A

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

   18. lift--.f64 N/A

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

   19. sub-neg N/A

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

   20. +-commutative N/A

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

   21. associate--r+ N/A

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

   22. neg-sub0 N/A

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

   23. remove-double-neg N/A

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

   24. lower--.f64 98.2

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

4. Applied rewrites 98.2%

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

Alternative 13: 61.3% 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 98.2%

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

3. Taylor expanded in t around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 58.1

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

5. Applied rewrites 58.1%

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

Developer Target 1: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024298 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -8508084860551241/100000000000000000000000000000000) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t)))))))

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