AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 61.0% → 89.0%

Time: 10.6s

Alternatives: 16

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* z (+ y x))) (* b y)) (+ (+ t x) y)))
        (t_2 (fma 1.0 a (* (/ (- z b) (+ t y)) y))))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 5e+257) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / ((t + x) + y);
	double t_2 = fma(1.0, a, (((z - b) / (t + y)) * y));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 5e+257) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(z * Float64(y + x))) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = fma(1.0, a, Float64(Float64(Float64(z - b) / Float64(t + y)) * y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 5e+257)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 * a + N[(N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 5e+257], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.00000000000000028e257 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.8%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 33.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 26.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 33.9%

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

   13. Applied rewrites 74.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000028e257

   1. Initial program 99.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;z - \left(-a\right) \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{t + \left(y + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.3e+89)
   (- z (* (- a) (/ (+ t y) x)))
   (if (<= x 3e-85)
     (fma 1.0 a (* (/ (- z b) (+ t y)) y))
     (if (<= x 5.6e+170)
       (fma 1.0 a (/ (fma x z (* (- z b) y)) (+ t (+ y x))))
       (- z (* (/ (- b a) x) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.3e+89) {
		tmp = z - (-a * ((t + y) / x));
	} else if (x <= 3e-85) {
		tmp = fma(1.0, a, (((z - b) / (t + y)) * y));
	} else if (x <= 5.6e+170) {
		tmp = fma(1.0, a, (fma(x, z, ((z - b) * y)) / (t + (y + x))));
	} else {
		tmp = z - (((b - a) / x) * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.3e+89)
		tmp = Float64(z - Float64(Float64(-a) * Float64(Float64(t + y) / x)));
	elseif (x <= 3e-85)
		tmp = fma(1.0, a, Float64(Float64(Float64(z - b) / Float64(t + y)) * y));
	elseif (x <= 5.6e+170)
		tmp = fma(1.0, a, Float64(fma(x, z, Float64(Float64(z - b) * y)) / Float64(t + Float64(y + x))));
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) / x) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.3e+89], N[(z - N[((-a) * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-85], N[(1.0 * a + N[(N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+170], N[(1.0 * a + N[(N[(x * z + N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2999999999999999e89

   1. Initial program 52.7%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 59.5%

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

   6. Taylor expanded in a around -inf

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

   8. Applied rewrites 73.1%

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

   if -2.2999999999999999e89 < x < 3.00000000000000022e-85

   1. Initial program 64.3%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 71.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 66.6%

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

   13. Applied rewrites 84.8%

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

   if 3.00000000000000022e-85 < x < 5.6000000000000003e170

   1. Initial program 77.4%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 85.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 75.8%

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

   if 5.6000000000000003e170 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 87.2%

      \[\leadsto z - \frac{b - a}{x} \cdot \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;z - \left(-a\right) \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{t + \left(y + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;z - \left(-a\right) \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+79}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.3e+89)
   (- z (* (- a) (/ (+ t y) x)))
   (if (<= x 9.2e-13)
     (fma 1.0 a (* (/ (- z b) (+ t y)) y))
     (if (<= x 1.7e+79)
       (/ (fma (+ y x) z (* (+ t y) a)) (+ (+ t x) y))
       (- z (* (/ (- b a) x) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.3e+89) {
		tmp = z - (-a * ((t + y) / x));
	} else if (x <= 9.2e-13) {
		tmp = fma(1.0, a, (((z - b) / (t + y)) * y));
	} else if (x <= 1.7e+79) {
		tmp = fma((y + x), z, ((t + y) * a)) / ((t + x) + y);
	} else {
		tmp = z - (((b - a) / x) * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.3e+89)
		tmp = Float64(z - Float64(Float64(-a) * Float64(Float64(t + y) / x)));
	elseif (x <= 9.2e-13)
		tmp = fma(1.0, a, Float64(Float64(Float64(z - b) / Float64(t + y)) * y));
	elseif (x <= 1.7e+79)
		tmp = Float64(fma(Float64(y + x), z, Float64(Float64(t + y) * a)) / Float64(Float64(t + x) + y));
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) / x) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.3e+89], N[(z - N[((-a) * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e-13], N[(1.0 * a + N[(N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+79], N[(N[(N[(y + x), $MachinePrecision] * z + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2999999999999999e89

   1. Initial program 52.7%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 59.5%

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

   6. Taylor expanded in a around -inf

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

   8. Applied rewrites 73.1%

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

   if -2.2999999999999999e89 < x < 9.19999999999999917e-13

   1. Initial program 66.2%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 73.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 66.8%

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

   13. Applied rewrites 83.8%

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

   if 9.19999999999999917e-13 < x < 1.70000000000000016e79

   1. Initial program 90.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 80.2

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

   5. Applied rewrites 80.2%

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

   if 1.70000000000000016e79 < x

   1. Initial program 54.1%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 58.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 78.4%

      \[\leadsto z - \frac{b - a}{x} \cdot \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;z - \left(-a\right) \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+79}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y + x}{t + \left(y + x\right)} \cdot z\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (+ y x) (+ t (+ y x))) z)) (t_2 (- (+ a z) b)))
   (if (<= y -1.45e+88)
     t_2
     (if (<= y -3e-124)
       t_1
       (if (<= y 5.2e-48)
         (/ (fma x z (* a t)) (+ t x))
         (if (<= y 2.6e+56) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + x) / (t + (y + x))) * z;
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -1.45e+88) {
		tmp = t_2;
	} else if (y <= -3e-124) {
		tmp = t_1;
	} else if (y <= 5.2e-48) {
		tmp = fma(x, z, (a * t)) / (t + x);
	} else if (y <= 2.6e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + x) / Float64(t + Float64(y + x))) * z)
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -1.45e+88)
		tmp = t_2;
	elseif (y <= -3e-124)
		tmp = t_1;
	elseif (y <= 5.2e-48)
		tmp = Float64(fma(x, z, Float64(a * t)) / Float64(t + x));
	elseif (y <= 2.6e+56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + x), $MachinePrecision] / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.45e+88], t$95$2, If[LessEqual[y, -3e-124], t$95$1, If[LessEqual[y, 5.2e-48], N[(N[(x * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e88 or 2.60000000000000011e56 < y

   1. Initial program 38.5%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 78.9

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 78.9%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   if -1.45e88 < y < -3e-124 or 5.19999999999999975e-48 < y < 2.60000000000000011e56

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 52.4

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

   5. Applied rewrites 52.4%

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

   7. Applied rewrites 59.3%

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

   if -3e-124 < y < 5.19999999999999975e-48

   1. Initial program 81.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 63.9

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

   5. Applied rewrites 63.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+88}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-124}:\\ \;\;\;\;\frac{y + x}{t + \left(y + x\right)} \cdot z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+56}:\\ \;\;\;\;\frac{y + x}{t + \left(y + x\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;z - \left(-a\right) \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.3e+89)
   (- z (* (- a) (/ (+ t y) x)))
   (if (<= x 5.6e+170)
     (fma 1.0 a (* (/ (- z b) (+ t y)) y))
     (- z (* (/ (- b a) x) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.3e+89) {
		tmp = z - (-a * ((t + y) / x));
	} else if (x <= 5.6e+170) {
		tmp = fma(1.0, a, (((z - b) / (t + y)) * y));
	} else {
		tmp = z - (((b - a) / x) * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.3e+89)
		tmp = Float64(z - Float64(Float64(-a) * Float64(Float64(t + y) / x)));
	elseif (x <= 5.6e+170)
		tmp = fma(1.0, a, Float64(Float64(Float64(z - b) / Float64(t + y)) * y));
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) / x) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.3e+89], N[(z - N[((-a) * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+170], N[(1.0 * a + N[(N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999999e89

   1. Initial program 52.7%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 59.5%

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

   6. Taylor expanded in a around -inf

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

   8. Applied rewrites 73.1%

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

   if -2.2999999999999999e89 < x < 5.6000000000000003e170

   1. Initial program 68.3%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 72.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 63.1%

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

   13. Applied rewrites 78.7%

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

   if 5.6000000000000003e170 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 87.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;z - \left(-a\right) \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{z - b}{t + y} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;z - \left(-a\right) \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.4e+15)
   (- z (* (- a) (/ (+ t y) x)))
   (if (<= x 5.6e+170) (- (+ a z) b) (- z (* (/ (- b a) x) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+15) {
		tmp = z - (-a * ((t + y) / x));
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = z - (((b - a) / x) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.4d+15)) then
        tmp = z - (-a * ((t + y) / x))
    else if (x <= 5.6d+170) then
        tmp = (a + z) - b
    else
        tmp = z - (((b - a) / x) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+15) {
		tmp = z - (-a * ((t + y) / x));
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = z - (((b - a) / x) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.4e+15:
		tmp = z - (-a * ((t + y) / x))
	elif x <= 5.6e+170:
		tmp = (a + z) - b
	else:
		tmp = z - (((b - a) / x) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.4e+15)
		tmp = Float64(z - Float64(Float64(-a) * Float64(Float64(t + y) / x)));
	elseif (x <= 5.6e+170)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) / x) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.4e+15)
		tmp = z - (-a * ((t + y) / x));
	elseif (x <= 5.6e+170)
		tmp = (a + z) - b;
	else
		tmp = z - (((b - a) / x) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.4e+15], N[(z - N[((-a) * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+170], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4e15

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in a around -inf

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

   8. Applied rewrites 64.6%

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

   if -4.4e15 < x < 5.6000000000000003e170

   1. Initial program 69.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 57.1

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 57.1%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   if 5.6000000000000003e170 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 87.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;z - \left(-a\right) \cdot \frac{t + y}{x}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{b - a}{x} \cdot y\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (* (/ (- b a) x) y))))
   (if (<= x -2.15e+18) t_1 (if (<= x 5.6e+170) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (((b - a) / x) * y);
	double tmp;
	if (x <= -2.15e+18) {
		tmp = t_1;
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z - (((b - a) / x) * y)
    if (x <= (-2.15d+18)) then
        tmp = t_1
    else if (x <= 5.6d+170) then
        tmp = (a + z) - b
    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 b) {
	double t_1 = z - (((b - a) / x) * y);
	double tmp;
	if (x <= -2.15e+18) {
		tmp = t_1;
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (((b - a) / x) * y)
	tmp = 0
	if x <= -2.15e+18:
		tmp = t_1
	elif x <= 5.6e+170:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(Float64(Float64(b - a) / x) * y))
	tmp = 0.0
	if (x <= -2.15e+18)
		tmp = t_1;
	elseif (x <= 5.6e+170)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - (((b - a) / x) * y);
	tmp = 0.0;
	if (x <= -2.15e+18)
		tmp = t_1;
	elseif (x <= 5.6e+170)
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(N[(N[(b - a), $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+18], t$95$1, If[LessEqual[x, 5.6e+170], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e18 or 5.6000000000000003e170 < x

   1. Initial program 52.8%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.8%

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

   if -2.15e18 < x < 5.6000000000000003e170

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 56.8

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 56.8%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;z - \frac{-t}{x} \cdot a\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{-y}{x} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.4e+15)
   (- z (* (/ (- t) x) a))
   (if (<= x 5.6e+170) (- (+ a z) b) (- z (* (/ (- y) x) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+15) {
		tmp = z - ((-t / x) * a);
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = z - ((-y / x) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.4d+15)) then
        tmp = z - ((-t / x) * a)
    else if (x <= 5.6d+170) then
        tmp = (a + z) - b
    else
        tmp = z - ((-y / x) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+15) {
		tmp = z - ((-t / x) * a);
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = z - ((-y / x) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.4e+15:
		tmp = z - ((-t / x) * a)
	elif x <= 5.6e+170:
		tmp = (a + z) - b
	else:
		tmp = z - ((-y / x) * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.4e+15)
		tmp = Float64(z - Float64(Float64(Float64(-t) / x) * a));
	elseif (x <= 5.6e+170)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z - Float64(Float64(Float64(-y) / x) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.4e+15)
		tmp = z - ((-t / x) * a);
	elseif (x <= 5.6e+170)
		tmp = (a + z) - b;
	else
		tmp = z - ((-y / x) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.4e+15], N[(z - N[(N[((-t) / x), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+170], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z - N[(N[((-y) / x), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4e15

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 60.7%

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

   9. Taylor expanded in a around -inf

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

   11. Applied rewrites 64.6%

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

   12. Taylor expanded in t around inf

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

   14. Applied rewrites 59.8%

       \[\leadsto z - a \cdot \frac{-t}{x} \]

   if -4.4e15 < x < 5.6000000000000003e170

   1. Initial program 69.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 57.1

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 57.1%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   if 5.6000000000000003e170 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in a around -inf

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

   11. Applied rewrites 79.2%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 74.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;z - \frac{-t}{x} \cdot a\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{-y}{x} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;z - \frac{-t}{x} \cdot a\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.4e+15)
   (- z (* (/ (- t) x) a))
   (if (<= x 5.6e+170) (- (+ a z) b) (- z (/ (* b y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+15) {
		tmp = z - ((-t / x) * a);
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = z - ((b * y) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.4d+15)) then
        tmp = z - ((-t / x) * a)
    else if (x <= 5.6d+170) then
        tmp = (a + z) - b
    else
        tmp = z - ((b * y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+15) {
		tmp = z - ((-t / x) * a);
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = z - ((b * y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.4e+15:
		tmp = z - ((-t / x) * a)
	elif x <= 5.6e+170:
		tmp = (a + z) - b
	else:
		tmp = z - ((b * y) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.4e+15)
		tmp = Float64(z - Float64(Float64(Float64(-t) / x) * a));
	elseif (x <= 5.6e+170)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z - Float64(Float64(b * y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.4e+15)
		tmp = z - ((-t / x) * a);
	elseif (x <= 5.6e+170)
		tmp = (a + z) - b;
	else
		tmp = z - ((b * y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.4e+15], N[(z - N[(N[((-t) / x), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+170], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z - N[(N[(b * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4e15

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 60.7%

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

   9. Taylor expanded in a around -inf

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

   11. Applied rewrites 64.6%

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

   12. Taylor expanded in t around inf

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

   14. Applied rewrites 59.8%

       \[\leadsto z - a \cdot \frac{-t}{x} \]

   if -4.4e15 < x < 5.6000000000000003e170

   1. Initial program 69.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 57.1

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 57.1%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   if 5.6000000000000003e170 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 73.8%

      \[\leadsto z - \frac{b \cdot y}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;z - \frac{-t}{x} \cdot a\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{b \cdot y}{x}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (/ (* b y) x))))
   (if (<= x -2.15e+18) t_1 (if (<= x 5.6e+170) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - ((b * y) / x);
	double tmp;
	if (x <= -2.15e+18) {
		tmp = t_1;
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z - ((b * y) / x)
    if (x <= (-2.15d+18)) then
        tmp = t_1
    else if (x <= 5.6d+170) then
        tmp = (a + z) - b
    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 b) {
	double t_1 = z - ((b * y) / x);
	double tmp;
	if (x <= -2.15e+18) {
		tmp = t_1;
	} else if (x <= 5.6e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - ((b * y) / x)
	tmp = 0
	if x <= -2.15e+18:
		tmp = t_1
	elif x <= 5.6e+170:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(Float64(b * y) / x))
	tmp = 0.0
	if (x <= -2.15e+18)
		tmp = t_1;
	elseif (x <= 5.6e+170)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - ((b * y) / x);
	tmp = 0.0;
	if (x <= -2.15e+18)
		tmp = t_1;
	elseif (x <= 5.6e+170)
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(N[(b * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+18], t$95$1, If[LessEqual[x, 5.6e+170], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e18 or 5.6000000000000003e170 < x

   1. Initial program 52.8%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 60.3%

      \[\leadsto z - \frac{b \cdot y}{x} \]

   if -2.15e18 < x < 5.6000000000000003e170

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 56.8

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 56.8%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -320000000:\\ \;\;\;\;a + z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{z}{x} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -320000000.0)
   (+ a z)
   (if (<= x 5.8e+170) (- (+ a z) b) (- z (* (/ z x) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -320000000.0) {
		tmp = a + z;
	} else if (x <= 5.8e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = z - ((z / x) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (x <= (-320000000.0d0)) then
        tmp = a + z
    else if (x <= 5.8d+170) then
        tmp = (a + z) - b
    else
        tmp = z - ((z / x) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -320000000.0) {
		tmp = a + z;
	} else if (x <= 5.8e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = z - ((z / x) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -320000000.0:
		tmp = a + z
	elif x <= 5.8e+170:
		tmp = (a + z) - b
	else:
		tmp = z - ((z / x) * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -320000000.0)
		tmp = Float64(a + z);
	elseif (x <= 5.8e+170)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z - Float64(Float64(z / x) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -320000000.0)
		tmp = a + z;
	elseif (x <= 5.8e+170)
		tmp = (a + z) - b;
	else
		tmp = z - ((z / x) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -320000000.0], N[(a + z), $MachinePrecision], If[LessEqual[x, 5.8e+170], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z - N[(N[(z / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2e8

   1. Initial program 53.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 39.9

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 39.9%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   6. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.9%

      \[\leadsto z + \color{blue}{a} \]

   if -3.2e8 < x < 5.8000000000000001e170

   1. Initial program 69.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 58.2

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 58.2%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   if 5.8000000000000001e170 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 66.1%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -320000000:\\ \;\;\;\;a + z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{z}{x} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -320000000:\\ \;\;\;\;a + z\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -320000000.0)
   (+ a z)
   (if (<= x 7.8e+170) (- (+ a z) b) (* (/ z y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -320000000.0) {
		tmp = a + z;
	} else if (x <= 7.8e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = (z / y) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (x <= (-320000000.0d0)) then
        tmp = a + z
    else if (x <= 7.8d+170) then
        tmp = (a + z) - b
    else
        tmp = (z / y) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -320000000.0) {
		tmp = a + z;
	} else if (x <= 7.8e+170) {
		tmp = (a + z) - b;
	} else {
		tmp = (z / y) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -320000000.0:
		tmp = a + z
	elif x <= 7.8e+170:
		tmp = (a + z) - b
	else:
		tmp = (z / y) * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -320000000.0)
		tmp = Float64(a + z);
	elseif (x <= 7.8e+170)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(z / y) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -320000000.0)
		tmp = a + z;
	elseif (x <= 7.8e+170)
		tmp = (a + z) - b;
	else
		tmp = (z / y) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -320000000.0], N[(a + z), $MachinePrecision], If[LessEqual[x, 7.8e+170], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(z / y), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2e8

   1. Initial program 53.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 39.9

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 39.9%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   6. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.9%

      \[\leadsto z + \color{blue}{a} \]

   if -3.2e8 < x < 7.8000000000000005e170

   1. Initial program 69.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 58.2

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 58.2%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   if 7.8000000000000005e170 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 55.9

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

   5. Applied rewrites 55.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 40.2%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 65.9%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -320000000:\\ \;\;\;\;a + z\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+170}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+55}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -5.5e+108) t_1 (if (<= y 1.3e+55) (+ a z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -5.5e+108) {
		tmp = t_1;
	} else if (y <= 1.3e+55) {
		tmp = a + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-5.5d+108)) then
        tmp = t_1
    else if (y <= 1.3d+55) then
        tmp = a + z
    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 b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -5.5e+108) {
		tmp = t_1;
	} else if (y <= 1.3e+55) {
		tmp = a + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -5.5e+108:
		tmp = t_1
	elif y <= 1.3e+55:
		tmp = a + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -5.5e+108)
		tmp = t_1;
	elseif (y <= 1.3e+55)
		tmp = Float64(a + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -5.5e+108)
		tmp = t_1;
	elseif (y <= 1.3e+55)
		tmp = a + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.5e+108], t$95$1, If[LessEqual[y, 1.3e+55], N[(a + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999998e108 or 1.3e55 < y

   1. Initial program 36.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 79.0

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 79.0%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   if -5.4999999999999998e108 < y < 1.3e55

   1. Initial program 77.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 34.9

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 34.9%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   6. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.5%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+108}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+55}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{+143}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 8.2e+143) (+ a z) (- z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 8.2e+143) {
		tmp = a + z;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (y <= 8.2d+143) then
        tmp = a + z
    else
        tmp = z - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 8.2e+143) {
		tmp = a + z;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 8.2e+143:
		tmp = a + z
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 8.2e+143)
		tmp = Float64(a + z);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 8.2e+143)
		tmp = a + z;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 8.2e+143], N[(a + z), $MachinePrecision], N[(z - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.2000000000000007e143

   1. Initial program 68.6%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 45.5

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 45.5%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   6. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.8%

      \[\leadsto z + \color{blue}{a} \]

   if 8.2000000000000007e143 < y

   1. Initial program 22.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(a + z\right) - b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

      3. lower-+.f64 85.0

         \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   5. Applied rewrites 85.0%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]

   6. Taylor expanded in a around 0

      \[\leadsto z - \color{blue}{b} \]
   7. Step-by-step derivation

   8. Applied rewrites 66.0%

      \[\leadsto z - \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{+143}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.9% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ a + z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + z), $MachinePrecision]

Derivation

1. Initial program 63.1%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   3. lower-+.f64 50.2

      \[\leadsto \color{blue}{\left(z + a\right)} - b \]

5. Applied rewrites 50.2%

   \[\leadsto \color{blue}{\left(z + a\right) - b} \]

6. Taylor expanded in b around 0

   \[\leadsto a + \color{blue}{z} \]
7. Step-by-step derivation

8. Applied rewrites 49.5%

   \[\leadsto z + \color{blue}{a} \]

9. Final simplification 49.5%

   \[\leadsto a + z \]
10. Add Preprocessing

Alternative 16: 13.4% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ -b \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := (-b)

Derivation

1. Initial program 63.1%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(z + a\right)} - b \]

   3. lower-+.f64 50.2

      \[\leadsto \color{blue}{\left(z + a\right)} - b \]

5. Applied rewrites 50.2%

   \[\leadsto \color{blue}{\left(z + a\right) - b} \]

6. Taylor expanded in b around inf

   \[\leadsto -1 \cdot \color{blue}{b} \]
7. Step-by-step derivation

8. Applied rewrites 10.6%

   \[\leadsto -b \]
9. Add Preprocessing

Developer Target 1: 82.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2024249 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

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