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

Percentage Accurate: 98.1% → 98.1%

Time: 8.0s

Alternatives: 13

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 97.0

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

4. Applied rewrites 97.0%

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

Alternative 2: 78.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ t_2 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{-a}, y, x\right)\\ \mathbf{elif}\;t\_2 \leq 20000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_2 \leq 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t a) y x)) (t_2 (/ (- z t) (- z a))))
   (if (<= t_2 -1e+125)
     (* (/ (- y) z) t)
     (if (<= t_2 -5e-50)
       t_1
       (if (<= t_2 5e-16)
         (fma (/ z (- a)) y x)
         (if (<= t_2 20000000.0)
           (+ y x)
           (if (<= t_2 1e+143) t_1 (* (- z t) (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / a), y, x);
	double t_2 = (z - t) / (z - a);
	double tmp;
	if (t_2 <= -1e+125) {
		tmp = (-y / z) * t;
	} else if (t_2 <= -5e-50) {
		tmp = t_1;
	} else if (t_2 <= 5e-16) {
		tmp = fma((z / -a), y, x);
	} else if (t_2 <= 20000000.0) {
		tmp = y + x;
	} else if (t_2 <= 1e+143) {
		tmp = t_1;
	} else {
		tmp = (z - t) * (y / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / a), y, x)
	t_2 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_2 <= -1e+125)
		tmp = Float64(Float64(Float64(-y) / z) * t);
	elseif (t_2 <= -5e-50)
		tmp = t_1;
	elseif (t_2 <= 5e-16)
		tmp = fma(Float64(z / Float64(-a)), y, x);
	elseif (t_2 <= 20000000.0)
		tmp = Float64(y + x);
	elseif (t_2 <= 1e+143)
		tmp = t_1;
	else
		tmp = Float64(Float64(z - t) * Float64(y / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+125], N[(N[((-y) / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$2, -5e-50], t$95$1, If[LessEqual[t$95$2, 5e-16], N[(N[(z / (-a)), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$2, 20000000.0], N[(y + x), $MachinePrecision], If[LessEqual[t$95$2, 1e+143], t$95$1, N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.9999999999999992e124

   1. Initial program 84.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

      4. div-sub N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

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

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

      8. associate-/l* N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 67.8%

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

   if -9.9999999999999992e124 < (/.f64 (-.f64 z t) (-.f64 z a)) < -4.99999999999999968e-50 or 2e7 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e143

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 79.1

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

   7. Applied rewrites 79.1%

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

   if -4.99999999999999968e-50 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000004e-16

   1. Initial program 97.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 97.6

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 90.3

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

   7. Applied rewrites 90.3%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 90.2%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 99.1

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

   5. Applied rewrites 99.1%

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

   if 1e143 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 80.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{-50}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{-a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 20000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ t_2 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 20000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t a) y x)) (t_2 (/ (- z t) (- z a))))
   (if (<= t_2 -1e+125)
     (* (/ (- y) z) t)
     (if (<= t_2 -5e-50)
       t_1
       (if (<= t_2 20000000.0)
         (fma (/ z (- z a)) y x)
         (if (<= t_2 1e+143) t_1 (* (- z t) (/ y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / a), y, x);
	double t_2 = (z - t) / (z - a);
	double tmp;
	if (t_2 <= -1e+125) {
		tmp = (-y / z) * t;
	} else if (t_2 <= -5e-50) {
		tmp = t_1;
	} else if (t_2 <= 20000000.0) {
		tmp = fma((z / (z - a)), y, x);
	} else if (t_2 <= 1e+143) {
		tmp = t_1;
	} else {
		tmp = (z - t) * (y / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / a), y, x)
	t_2 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_2 <= -1e+125)
		tmp = Float64(Float64(Float64(-y) / z) * t);
	elseif (t_2 <= -5e-50)
		tmp = t_1;
	elseif (t_2 <= 20000000.0)
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	elseif (t_2 <= 1e+143)
		tmp = t_1;
	else
		tmp = Float64(Float64(z - t) * Float64(y / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+125], N[(N[((-y) / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$2, -5e-50], t$95$1, If[LessEqual[t$95$2, 20000000.0], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$2, 1e+143], t$95$1, N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.9999999999999992e124

   1. Initial program 84.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

      4. div-sub N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

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

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

      8. associate-/l* N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 67.8%

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

   if -9.9999999999999992e124 < (/.f64 (-.f64 z t) (-.f64 z a)) < -4.99999999999999968e-50 or 2e7 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e143

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 79.1

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

   7. Applied rewrites 79.1%

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

   if -4.99999999999999968e-50 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e7

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 95.0

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

   5. Applied rewrites 95.0%

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

   if 1e143 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 80.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.8%

      \[\leadsto \left(z - t\right) \cdot \frac{y}{\color{blue}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{-50}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 20000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;t\_1 \leq 20000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -1e+125)
     (* (/ (- y) z) t)
     (if (<= t_1 2e-53)
       (fma (/ y a) t x)
       (if (<= t_1 20000000.0)
         (+ y x)
         (if (<= t_1 1e+143) (fma (/ t a) y x) (* (- z t) (/ y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -1e+125) {
		tmp = (-y / z) * t;
	} else if (t_1 <= 2e-53) {
		tmp = fma((y / a), t, x);
	} else if (t_1 <= 20000000.0) {
		tmp = y + x;
	} else if (t_1 <= 1e+143) {
		tmp = fma((t / a), y, x);
	} else {
		tmp = (z - t) * (y / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -1e+125)
		tmp = Float64(Float64(Float64(-y) / z) * t);
	elseif (t_1 <= 2e-53)
		tmp = fma(Float64(y / a), t, x);
	elseif (t_1 <= 20000000.0)
		tmp = Float64(y + x);
	elseif (t_1 <= 1e+143)
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = Float64(Float64(z - t) * Float64(y / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+125], N[(N[((-y) / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e-53], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$1, 20000000.0], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+143], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.9999999999999992e124

   1. Initial program 84.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

      4. div-sub N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

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

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

      8. associate-/l* N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 67.8%

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

   if -9.9999999999999992e124 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2.00000000000000006e-53

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 80.8

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

   5. Applied rewrites 80.8%

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

   if 2.00000000000000006e-53 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 98.3

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

   5. Applied rewrites 98.3%

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

   if 2e7 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e143

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 70.0

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

   7. Applied rewrites 70.0%

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

   if 1e143 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 80.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 20000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \frac{-y}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;t\_1 \leq 20000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (* (/ (- y) z) t)))
   (if (<= t_1 -1e+125)
     t_2
     (if (<= t_1 2e-53)
       (fma (/ y a) t x)
       (if (<= t_1 20000000.0)
         (+ y x)
         (if (<= t_1 1e+143) (fma (/ t a) y x) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = (-y / z) * t;
	double tmp;
	if (t_1 <= -1e+125) {
		tmp = t_2;
	} else if (t_1 <= 2e-53) {
		tmp = fma((y / a), t, x);
	} else if (t_1 <= 20000000.0) {
		tmp = y + x;
	} else if (t_1 <= 1e+143) {
		tmp = fma((t / a), y, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(Float64(Float64(-y) / z) * t)
	tmp = 0.0
	if (t_1 <= -1e+125)
		tmp = t_2;
	elseif (t_1 <= 2e-53)
		tmp = fma(Float64(y / a), t, x);
	elseif (t_1 <= 20000000.0)
		tmp = Float64(y + x);
	elseif (t_1 <= 1e+143)
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-y) / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+125], t$95$2, If[LessEqual[t$95$1, 2e-53], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$1, 20000000.0], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+143], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.9999999999999992e124 or 1e143 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

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

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

      4. div-sub N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

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

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

      8. associate-/l* N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 72.3%

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

   if -9.9999999999999992e124 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2.00000000000000006e-53

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 80.8

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

   5. Applied rewrites 80.8%

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

   if 2.00000000000000006e-53 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 98.3

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

   5. Applied rewrites 98.3%

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

   if 2e7 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e143

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 70.0

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

   7. Applied rewrites 70.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 20000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-50}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (fma (/ (- z t) z) y x)))
   (if (<= t_1 -1e+125)
     t_2
     (if (<= t_1 -5e-50)
       (fma (/ t a) y x)
       (if (<= t_1 1e-5) (fma (/ z (- z a)) y x) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = fma(((z - t) / z), y, x);
	double tmp;
	if (t_1 <= -1e+125) {
		tmp = t_2;
	} else if (t_1 <= -5e-50) {
		tmp = fma((t / a), y, x);
	} else if (t_1 <= 1e-5) {
		tmp = fma((z / (z - a)), y, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = fma(Float64(Float64(z - t) / z), y, x)
	tmp = 0.0
	if (t_1 <= -1e+125)
		tmp = t_2;
	elseif (t_1 <= -5e-50)
		tmp = fma(Float64(t / a), y, x);
	elseif (t_1 <= 1e-5)
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+125], t$95$2, If[LessEqual[t$95$1, -5e-50], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-5], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.9999999999999992e124 or 1.00000000000000008e-5 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 96.1%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

      6. *-lft-identity N/A

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

      7. metadata-eval N/A

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

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

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

      9. lower-fma.f64 N/A

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

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

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

      11. *-inverses N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. div-sub N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if -9.9999999999999992e124 < (/.f64 (-.f64 z t) (-.f64 z a)) < -4.99999999999999968e-50

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 87.8

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

   7. Applied rewrites 87.8%

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

   if -4.99999999999999968e-50 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1.00000000000000008e-5

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 90.4

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

   5. Applied rewrites 90.4%

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

Alternative 7: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+162} \lor \neg \left(t\_1 \leq 10^{+127}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- z a)))))
   (if (or (<= t_1 -1e+162) (not (<= t_1 1e+127)))
     (* (- z t) (/ y (- z a)))
     (fma (/ z (- z a)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if ((t_1 <= -1e+162) || !(t_1 <= 1e+127)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = fma((z / (z - a)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if ((t_1 <= -1e+162) || !(t_1 <= 1e+127))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	else
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+162], N[Not[LessEqual[t$95$1, 1e+127]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < -9.9999999999999994e161 or 9.99999999999999955e126 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

   1. Initial program 90.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 90.5

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

   5. Applied rewrites 90.5%

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

   if -9.9999999999999994e161 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < 9.99999999999999955e126

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 88.6

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

   5. Applied rewrites 88.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{z - a} \leq -1 \cdot 10^{+162} \lor \neg \left(y \cdot \frac{z - t}{z - a} \leq 10^{+127}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+300} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+248}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- z a)))))
   (if (or (<= t_1 -2e+300) (not (<= t_1 2e+248))) (* t (/ y a)) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if ((t_1 <= -2e+300) || !(t_1 <= 2e+248)) {
		tmp = t * (y / a);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (z - a))
    if ((t_1 <= (-2d+300)) .or. (.not. (t_1 <= 2d+248))) then
        tmp = t * (y / a)
    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 t_1 = y * ((z - t) / (z - a));
	double tmp;
	if ((t_1 <= -2e+300) || !(t_1 <= 2e+248)) {
		tmp = t * (y / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (z - a))
	tmp = 0
	if (t_1 <= -2e+300) or not (t_1 <= 2e+248):
		tmp = t * (y / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if ((t_1 <= -2e+300) || !(t_1 <= 2e+248))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if ((t_1 <= -2e+300) || ~((t_1 <= 2e+248)))
		tmp = t * (y / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+300], N[Not[LessEqual[t$95$1, 2e+248]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < -2.0000000000000001e300 or 2.00000000000000009e248 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 94.4

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

   5. Applied rewrites 94.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 68.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 59.2%

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

   13. Applied rewrites 66.7%

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

   if -2.0000000000000001e300 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < 2.00000000000000009e248

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 70.9

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

   5. Applied rewrites 70.9%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{z - a} \leq -2 \cdot 10^{+300} \lor \neg \left(y \cdot \frac{z - t}{z - a} \leq 2 \cdot 10^{+248}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-50} \lor \neg \left(t\_1 \leq 1.00005\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (or (<= t_1 -5e-50) (not (<= t_1 1.00005)))
     (fma (/ (- t) (- z a)) y x)
     (fma (/ z (- z a)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if ((t_1 <= -5e-50) || !(t_1 <= 1.00005)) {
		tmp = fma((-t / (z - a)), y, x);
	} else {
		tmp = fma((z / (z - a)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -5e-50) || !(t_1 <= 1.00005))
		tmp = fma(Float64(Float64(-t) / Float64(z - a)), y, x);
	else
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-50], N[Not[LessEqual[t$95$1, 1.00005]], $MachinePrecision]], N[(N[((-t) / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -4.99999999999999968e-50 or 1.00005000000000011 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 93.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 93.0

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

   7. Applied rewrites 93.0%

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

   if -4.99999999999999968e-50 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1.00005000000000011

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 94.9

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

   5. Applied rewrites 94.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -5 \cdot 10^{-50} \lor \neg \left(\frac{z - t}{z - a} \leq 1.00005\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-16} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (or (<= t_1 -4e-16) (not (<= t_1 5e+16)))
     (* (- t) (/ y (- z a)))
     (fma (/ z (- z a)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if ((t_1 <= -4e-16) || !(t_1 <= 5e+16)) {
		tmp = -t * (y / (z - a));
	} else {
		tmp = fma((z / (z - a)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -4e-16) || !(t_1 <= 5e+16))
		tmp = Float64(Float64(-t) * Float64(y / Float64(z - a)));
	else
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-16], N[Not[LessEqual[t$95$1, 5e+16]], $MachinePrecision]], N[((-t) * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -3.9999999999999999e-16 or 5e16 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 74.8

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 74.6%

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

   if -3.9999999999999999e-16 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5e16

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 93.7

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

   5. Applied rewrites 93.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -4 \cdot 10^{-16} \lor \neg \left(\frac{z - t}{z - a} \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-53} \lor \neg \left(t\_1 \leq 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (or (<= t_1 2e-53) (not (<= t_1 1e+27))) (fma (/ y a) t x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if ((t_1 <= 2e-53) || !(t_1 <= 1e+27)) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= 2e-53) || !(t_1 <= 1e+27))
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, 2e-53], N[Not[LessEqual[t$95$1, 1e+27]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 2.00000000000000006e-53 or 1e27 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 71.9

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

   5. Applied rewrites 71.9%

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

   if 2.00000000000000006e-53 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e27

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 94.2

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

   5. Applied rewrites 94.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq 2 \cdot 10^{-53} \lor \neg \left(\frac{z - t}{z - a} \leq 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;t\_1 \leq 20000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 2e-53)
     (fma (/ y a) t x)
     (if (<= t_1 20000000.0) (+ y x) (fma (/ t a) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= 2e-53) {
		tmp = fma((y / a), t, x);
	} else if (t_1 <= 20000000.0) {
		tmp = y + x;
	} else {
		tmp = fma((t / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= 2e-53)
		tmp = fma(Float64(y / a), t, x);
	elseif (t_1 <= 20000000.0)
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-53], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$1, 20000000.0], N[(y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 2.00000000000000006e-53

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if 2.00000000000000006e-53 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 98.3

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

   5. Applied rewrites 98.3%

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

   if 2e7 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 92.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 92.4

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

   4. Applied rewrites 92.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 58.9

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

   7. Applied rewrites 58.9%

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

Alternative 13: 60.7% 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 97.0%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 62.2

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

5. Applied rewrites 62.2%

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

Developer Target 1: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024329 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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