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

Percentage Accurate: 76.6% → 88.8%

Time: 6.8s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+87} \lor \neg \left(t \leq 1.25 \cdot 10^{+78}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e+87) (not (<= t 1.25e+78)))
   (fma (/ y t) (- z a) x)
   (- (+ x y) (/ (* (- z t) y) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e+87) || !(t <= 1.25e+78)) {
		tmp = fma((y / t), (z - a), x);
	} else {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e+87) || !(t <= 1.25e+78))
		tmp = fma(Float64(y / t), Float64(z - a), x);
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e+87], N[Not[LessEqual[t, 1.25e+78]], $MachinePrecision]], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9999999999999999e87 or 1.24999999999999996e78 < t

   1. Initial program 52.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. associate-*r/ N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. div-sub N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

      15. associate-/l* N/A

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

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

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 87.4%

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

   if -2.9999999999999999e87 < t < 1.24999999999999996e78

   1. Initial program 92.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+87} \lor \neg \left(t \leq 1.25 \cdot 10^{+78}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+88} \lor \neg \left(t \leq 1.46 \cdot 10^{+78}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.12e+88) (not (<= t 1.46e+78)))
   (fma (/ y t) (- z a) x)
   (- (+ x y) (/ (* z y) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.12e+88) || !(t <= 1.46e+78)) {
		tmp = fma((y / t), (z - a), x);
	} else {
		tmp = (x + y) - ((z * y) / (a - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.12e+88) || !(t <= 1.46e+78))
		tmp = fma(Float64(y / t), Float64(z - a), x);
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / Float64(a - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.12e+88], N[Not[LessEqual[t, 1.46e+78]], $MachinePrecision]], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12000000000000006e88 or 1.46000000000000005e78 < t

   1. Initial program 52.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. associate-*r/ N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. div-sub N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

      15. associate-/l* N/A

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

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

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 87.4%

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

   if -1.12000000000000006e88 < t < 1.46000000000000005e78

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 92.3

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

   5. Applied rewrites 92.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+88} \lor \neg \left(t \leq 1.46 \cdot 10^{+78}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-89}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e-89)
   (fma (/ z t) y x)
   (if (<= t 8.5e-20) (- (+ x y) (/ (* z y) a)) (fma (/ y t) (- z a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e-89) {
		tmp = fma((z / t), y, x);
	} else if (t <= 8.5e-20) {
		tmp = (x + y) - ((z * y) / a);
	} else {
		tmp = fma((y / t), (z - a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e-89)
		tmp = fma(Float64(z / t), y, x);
	elseif (t <= 8.5e-20)
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / a));
	else
		tmp = fma(Float64(y / t), Float64(z - a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e-89], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 8.5e-20], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000003e-89

   1. Initial program 71.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt1-in N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 82.3%

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

   if -1.80000000000000003e-89 < t < 8.5000000000000005e-20

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 89.5

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

   5. Applied rewrites 89.5%

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

   if 8.5000000000000005e-20 < t

   1. Initial program 53.5%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. associate-*r/ N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. div-sub N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

      15. associate-/l* N/A

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

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

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 82.5%

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

Alternative 4: 79.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-89} \lor \neg \left(t \leq 7.4 \cdot 10^{-19}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e-89) (not (<= t 7.4e-19)))
   (fma (/ z t) y x)
   (fma y (- 1.0 (/ z a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-89) || !(t <= 7.4e-19)) {
		tmp = fma((z / t), y, x);
	} else {
		tmp = fma(y, (1.0 - (z / a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e-89) || !(t <= 7.4e-19))
		tmp = fma(Float64(z / t), y, x);
	else
		tmp = fma(y, Float64(1.0 - Float64(z / a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e-89], N[Not[LessEqual[t, 7.4e-19]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.80000000000000003e-89 or 7.40000000000000011e-19 < t

   1. Initial program 62.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt1-in N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 70.1

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

   5. Applied rewrites 70.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 81.1%

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

   if -1.80000000000000003e-89 < t < 7.40000000000000011e-19

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 88.3

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

   5. Applied rewrites 88.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-89} \lor \neg \left(t \leq 7.4 \cdot 10^{-19}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-89}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e-89)
   (fma (/ z t) y x)
   (if (<= t 1.35e+71) (fma y (- 1.0 (/ z a)) x) (fma (/ y t) (- z a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e-89) {
		tmp = fma((z / t), y, x);
	} else if (t <= 1.35e+71) {
		tmp = fma(y, (1.0 - (z / a)), x);
	} else {
		tmp = fma((y / t), (z - a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e-89)
		tmp = fma(Float64(z / t), y, x);
	elseif (t <= 1.35e+71)
		tmp = fma(y, Float64(1.0 - Float64(z / a)), x);
	else
		tmp = fma(Float64(y / t), Float64(z - a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e-89], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 1.35e+71], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000003e-89

   1. Initial program 71.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt1-in N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 82.3%

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

   if -1.80000000000000003e-89 < t < 1.34999999999999998e71

   1. Initial program 93.8%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

   if 1.34999999999999998e71 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. associate-*r/ N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. div-sub N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

      15. associate-/l* N/A

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

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

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

Alternative 6: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+68} \lor \neg \left(a \leq 48000000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.15e+68) (not (<= a 48000000.0)))
   (fma y 1.0 x)
   (fma (/ z t) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e+68) || !(a <= 48000000.0)) {
		tmp = fma(y, 1.0, x);
	} else {
		tmp = fma((z / t), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.15e+68) || !(a <= 48000000.0))
		tmp = fma(y, 1.0, x);
	else
		tmp = fma(Float64(z / t), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.15e+68], N[Not[LessEqual[a, 48000000.0]], $MachinePrecision]], N[(y * 1.0 + x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15e68 or 4.8e7 < a

   1. Initial program 80.5%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.7%

      \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]

   if -1.15e68 < a < 4.8e7

   1. Initial program 71.9%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt1-in N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 65.0

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

   5. Applied rewrites 65.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 75.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+68} \lor \neg \left(a \leq 48000000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+68} \lor \neg \left(a \leq 48000000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1e+68) (not (<= a 48000000.0)))
   (fma y 1.0 x)
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1e+68) || !(a <= 48000000.0)) {
		tmp = fma(y, 1.0, x);
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1e+68) || !(a <= 48000000.0))
		tmp = fma(y, 1.0, x);
	else
		tmp = fma(Float64(y / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1e+68], N[Not[LessEqual[a, 48000000.0]], $MachinePrecision]], N[(y * 1.0 + x), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.99999999999999953e67 or 4.8e7 < a

   1. Initial program 80.5%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.7%

      \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]

   if -9.99999999999999953e67 < a < 4.8e7

   1. Initial program 71.9%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt1-in N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 65.0

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

   5. Applied rewrites 65.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+68} \lor \neg \left(a \leq 48000000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{+179}:\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1 + 1, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 3e+179) (fma y 1.0 x) (fma (+ -1.0 1.0) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3e+179) {
		tmp = fma(y, 1.0, x);
	} else {
		tmp = fma((-1.0 + 1.0), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 3e+179)
		tmp = fma(y, 1.0, x);
	else
		tmp = fma(Float64(-1.0 + 1.0), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 3e+179], N[(y * 1.0 + x), $MachinePrecision], N[(N[(-1.0 + 1.0), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.9999999999999998e179

   1. Initial program 80.5%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 69.1

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

   5. Applied rewrites 69.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 65.8%

      \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]

   if 2.9999999999999998e179 < t

   1. Initial program 42.3%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt1-in N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(-1 + 1, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 84.4%

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

Alternative 9: 60.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 1, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma y 1.0 x))

C

double code(double x, double y, double z, double t, double a) {
	return fma(y, 1.0, x);
}

Julia

function code(x, y, z, t, a)
	return fma(y, 1.0, x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(y * 1.0 + x), $MachinePrecision]

Derivation

1. Initial program 75.7%

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

3. Taylor expanded in t around 0

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

   1. associate--l+ N/A

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

   2. +-commutative N/A

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

   3. *-rgt-identity N/A

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

   4. associate-/l* N/A

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

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

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

   6. lower-fma.f64 N/A

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

   7. lower--.f64 N/A

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

   8. lower-/.f64 65.0

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

5. Applied rewrites 65.0%

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

6. Taylor expanded in z around 0

   \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
7. Step-by-step derivation

8. Applied rewrites 64.2%

   \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
9. Add Preprocessing

Alternative 10: 18.8% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot y \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 1.0 y))

C

double code(double x, double y, double z, double t, double a) {
	return 1.0 * 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 = 1.0d0 * y
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 1.0 * y;
}

Python

def code(x, y, z, t, a):
	return 1.0 * y

Julia

function code(x, y, z, t, a)
	return Float64(1.0 * y)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 1.0 * y;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(1.0 * y), $MachinePrecision]

Derivation

1. Initial program 75.7%

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

3. Taylor expanded in t around 0

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

   1. associate--l+ N/A

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

   2. +-commutative N/A

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

   3. *-rgt-identity N/A

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

   4. associate-/l* N/A

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

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

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

   6. lower-fma.f64 N/A

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

   7. lower--.f64 N/A

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

   8. lower-/.f64 65.0

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

5. Applied rewrites 65.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 30.7%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 19.8%

    \[\leadsto 1 \cdot y \]
12. Add Preprocessing

Developer Target 1: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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