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

Percentage Accurate: 59.7% → 93.8%

Time: 10.3s

Alternatives: 18

Speedup: 0.4×

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: 59.7% 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: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{-78} \lor \neg \left(z \leq 1.75 \cdot 10^{-51}\right):\\ \;\;\;\;z \cdot \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{t\_2}, \frac{x + y}{t\_2}\right) - b \cdot \left({\left(\left(x + y\right) + t\right)}^{-1} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t\_1} + \frac{y}{t\_1}, a, \frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (+ t (+ x y))))
   (if (or (<= z -1.52e-78) (not (<= z 1.75e-51)))
     (-
      (* z (fma (/ a z) (/ (+ t y) t_2) (/ (+ x y) t_2)))
      (* b (* (pow (+ (+ x y) t) -1.0) y)))
     (fma (+ (/ t t_1) (/ y t_1)) a (/ (fma z x (* y (- z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = t + (x + y);
	double tmp;
	if ((z <= -1.52e-78) || !(z <= 1.75e-51)) {
		tmp = (z * fma((a / z), ((t + y) / t_2), ((x + y) / t_2))) - (b * (pow(((x + y) + t), -1.0) * y));
	} else {
		tmp = fma(((t / t_1) + (y / t_1)), a, (fma(z, x, (y * (z - b))) / t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if ((z <= -1.52e-78) || !(z <= 1.75e-51))
		tmp = Float64(Float64(z * fma(Float64(a / z), Float64(Float64(t + y) / t_2), Float64(Float64(x + y) / t_2))) - Float64(b * Float64((Float64(Float64(x + y) + t) ^ -1.0) * y)));
	else
		tmp = fma(Float64(Float64(t / t_1) + Float64(y / t_1)), a, Float64(fma(z, x, Float64(y * Float64(z - b))) / t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.52e-78], N[Not[LessEqual[z, 1.75e-51]], $MachinePrecision]], N[(N[(z * N[(N[(a / z), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[Power[N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision], -1.0], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] * a + N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.52e-78 or 1.7499999999999999e-51 < z

   1. Initial program 58.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 57.9%

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

   5. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. times-frac N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower-+.f64 N/A

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

      16. lower-+.f64 N/A

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

      17. lower-+.f64 95.4

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

   7. Applied rewrites 95.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. associate-+r+ N/A

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

      6. lift-+.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. div-inv N/A

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

      10. associate-*l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. inv-pow N/A

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

      14. lower-pow.f64 98.7

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lift-+.f64 98.7

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

   9. Applied rewrites 98.7%

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

   if -1.52e-78 < z < 1.7499999999999999e-51

   1. Initial program 68.9%

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

   3. Taylor expanded in 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

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

   5. Applied rewrites 90.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-78} \lor \neg \left(z \leq 1.75 \cdot 10^{-51}\right):\\ \;\;\;\;z \cdot \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{t + \left(x + y\right)}, \frac{x + y}{t + \left(x + y\right)}\right) - b \cdot \left({\left(\left(x + y\right) + t\right)}^{-1} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\left(y + x\right) + t} + \frac{y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{\left(y + x\right) + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;t\_2 \leq 10^{+226}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t\_1} + \frac{y}{t\_1}, a, \frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{\left(x + y\right) + t}, b, a + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_2 (- INFINITY))
     (- (+ a z) (* y (/ b (+ (+ t x) y))))
     (if (<= t_2 1e+226)
       (fma (+ (/ t t_1) (/ y t_1)) a (/ (fma z x (* y (- z b))) t_1))
       (fma (/ (- y) (+ (+ x y) t)) b (+ a z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (a + z) - (y * (b / ((t + x) + y)));
	} else if (t_2 <= 1e+226) {
		tmp = fma(((t / t_1) + (y / t_1)), a, (fma(z, x, (y * (z - b))) / t_1));
	} else {
		tmp = fma((-y / ((x + y) + t)), b, (a + z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	elseif (t_2 <= 1e+226)
		tmp = fma(Float64(Float64(t / t_1) + Float64(y / t_1)), a, Float64(fma(z, x, Float64(y * Float64(z - b))) / t_1));
	else
		tmp = fma(Float64(Float64(-y) / Float64(Float64(x + y) + t)), b, Float64(a + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+226], N[(N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] * a + N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[((-y) / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * b + N[(a + z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 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

   1. Initial program 6.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 16.1%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 84.8

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

   7. Applied rewrites 84.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999961e225

   1. Initial program 99.1%

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

   3. Taylor expanded in 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

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

   5. Applied rewrites 99.2%

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

   if 9.99999999999999961e225 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 12.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 18.7%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 80.4

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

   7. Applied rewrites 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

   9. Applied rewrites 81.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+226}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\left(y + x\right) + t} + \frac{y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{\left(y + x\right) + t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{\left(x + y\right) + t}, b, a + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;t\_1 \leq 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{\left(x + y\right) + t}, b, a + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 (- INFINITY))
     (- (+ a z) (* y (/ b (+ (+ t x) y))))
     (if (<= t_1 1e+226) t_1 (fma (/ (- y) (+ (+ x y) t)) b (+ a z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (a + z) - (y * (b / ((t + x) + y)));
	} else if (t_1 <= 1e+226) {
		tmp = t_1;
	} else {
		tmp = fma((-y / ((x + y) + t)), b, (a + z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	elseif (t_1 <= 1e+226)
		tmp = t_1;
	else
		tmp = fma(Float64(Float64(-y) / Float64(Float64(x + y) + t)), b, Float64(a + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+226], t$95$1, N[(N[((-y) / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * b + N[(a + z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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

   1. Initial program 6.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 16.1%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 84.8

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

   7. Applied rewrites 84.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999961e225

   1. Initial program 99.1%

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

   if 9.99999999999999961e225 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 12.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 18.7%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 80.4

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

   7. Applied rewrites 80.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

   9. Applied rewrites 81.9%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+226}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{\left(x + y\right) + t}, b, a + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-20} \lor \neg \left(t\_2 \leq 5 \cdot 10^{+125}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{\left(x + y\right) + t}, b, a + z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{\left(y + x\right) + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_2 -2e-20) (not (<= t_2 5e+125)))
     (fma (/ (- y) (+ (+ x y) t)) b (+ a z))
     (/ (fma (+ y x) z t_1) (+ (+ y x) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = ((((x + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_2 <= -2e-20) || !(t_2 <= 5e+125)) {
		tmp = fma((-y / ((x + y) + t)), b, (a + z));
	} else {
		tmp = fma((y + x), z, t_1) / ((y + x) + t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_2 <= -2e-20) || !(t_2 <= 5e+125))
		tmp = fma(Float64(Float64(-y) / Float64(Float64(x + y) + t)), b, Float64(a + z));
	else
		tmp = Float64(fma(Float64(y + x), z, t_1) / Float64(Float64(y + x) + t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e-20], N[Not[LessEqual[t$95$2, 5e+125]], $MachinePrecision]], N[(N[((-y) / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * b + N[(a + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]]]

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)) < -1.99999999999999989e-20 or 4.99999999999999962e125 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 41.0%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 43.2%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 79.1

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

   7. Applied rewrites 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

   9. Applied rewrites 82.0%

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

   if -1.99999999999999989e-20 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999962e125

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 77.8

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

   5. Applied rewrites 77.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{-20} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+125}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{\left(x + y\right) + t}, b, a + z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-44} \lor \neg \left(t\_1 \leq 10^{+25}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{\left(x + y\right) + t}, b, a + z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -2e-44) (not (<= t_1 1e+25)))
     (fma (/ (- y) (+ (+ x y) t)) b (+ a z))
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -2e-44) || !(t_1 <= 1e+25)) {
		tmp = fma((-y / ((x + y) + t)), b, (a + z));
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -2e-44) || !(t_1 <= 1e+25))
		tmp = fma(Float64(Float64(-y) / Float64(Float64(x + y) + t)), b, Float64(a + z));
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, -2e-44], N[Not[LessEqual[t$95$1, 1e+25]], $MachinePrecision]], N[(N[((-y) / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * b + N[(a + z), $MachinePrecision]), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]]

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)) < -1.99999999999999991e-44 or 1.00000000000000009e25 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 51.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 53.1%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 76.8

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

   7. Applied rewrites 76.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

   9. Applied rewrites 79.3%

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

   if -1.99999999999999991e-44 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000009e25

   1. Initial program 98.3%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 65.6

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

   5. Applied rewrites 65.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{-44} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+25}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{\left(x + y\right) + t}, b, a + z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-41} \lor \neg \left(t\_1 \leq 10^{+135}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e-41) (not (<= t_1 1e+135)))
     (- (+ a z) (* y (/ b (+ x y))))
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e-41) || !(t_1 <= 1e+135)) {
		tmp = (a + z) - (y * (b / (x + y)));
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e-41) || !(t_1 <= 1e+135))
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / Float64(x + y))));
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, -5e-41], N[Not[LessEqual[t$95$1, 1e+135]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]]

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)) < -4.9999999999999996e-41 or 9.99999999999999962e134 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 42.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 44.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 78.9

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

   7. Applied rewrites 78.9%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 70.9

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

   10. Applied rewrites 70.9%

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

   if -4.9999999999999996e-41 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999962e134

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 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. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 64.0

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

   5. Applied rewrites 64.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{-41} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+135}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+49} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+125}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e+49) (not (<= t_1 5e+125)))
     (- (+ a z) b)
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+49) || !(t_1 <= 5e+125)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e+49) || !(t_1 <= 5e+125))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, -5e+49], N[Not[LessEqual[t$95$1, 5e+125]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]]

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)) < -5.0000000000000004e49 or 4.99999999999999962e125 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 35.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 70.4

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

   5. Applied rewrites 70.4%

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

   if -5.0000000000000004e49 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999962e125

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 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. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 62.3

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

   5. Applied rewrites 62.3%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+49} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+125}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-41} \lor \neg \left(t\_2 \leq 4 \cdot 10^{+26}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{t\_1}\\ \end{array} \end{array} \]

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_1)))
   (if (or (<= t_2 -5e-41) (not (<= t_2 4e+26)))
     (- (+ a z) b)
     (/ (* a t) t_1))))

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)) / t_1;
	double tmp;
	if ((t_2 <= -5e-41) || !(t_2 <= 4e+26)) {
		tmp = (a + z) - b;
	} else {
		tmp = (a * t) / 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) :: t_2
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1
    if ((t_2 <= (-5d-41)) .or. (.not. (t_2 <= 4d+26))) then
        tmp = (a + z) - b
    else
        tmp = (a * t) / 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 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -5e-41) || !(t_2 <= 4e+26)) {
		tmp = (a + z) - b;
	} else {
		tmp = (a * t) / t_1;
	}
	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_1
	tmp = 0
	if (t_2 <= -5e-41) or not (t_2 <= 4e+26):
		tmp = (a + z) - b
	else:
		tmp = (a * t) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= -5e-41) || !(t_2 <= 4e+26))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(a * t) / t_1);
	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_1;
	tmp = 0.0;
	if ((t_2 <= -5e-41) || ~((t_2 <= 4e+26)))
		tmp = (a + z) - b;
	else
		tmp = (a * t) / t_1;
	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[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e-41], N[Not[LessEqual[t$95$2, 4e+26]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * t), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

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)) < -4.9999999999999996e-41 or 4.00000000000000019e26 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 50.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 64.2

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

   5. Applied rewrites 64.2%

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

   if -4.9999999999999996e-41 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000019e26

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 44.4

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

   5. Applied rewrites 44.4%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{-41} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 4 \cdot 10^{+26}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{-78} \lor \neg \left(z \leq 6.5 \cdot 10^{-43}\right):\\ \;\;\;\;z \cdot \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{t\_2}, \frac{x + y}{t\_2}\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t\_1} + \frac{y}{t\_1}, a, \frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (+ t (+ x y))))
   (if (or (<= z -1.52e-78) (not (<= z 6.5e-43)))
     (-
      (* z (fma (/ a z) (/ (+ t y) t_2) (/ (+ x y) t_2)))
      (* y (/ b (+ (+ t x) y))))
     (fma (+ (/ t t_1) (/ y t_1)) a (/ (fma z x (* y (- z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = t + (x + y);
	double tmp;
	if ((z <= -1.52e-78) || !(z <= 6.5e-43)) {
		tmp = (z * fma((a / z), ((t + y) / t_2), ((x + y) / t_2))) - (y * (b / ((t + x) + y)));
	} else {
		tmp = fma(((t / t_1) + (y / t_1)), a, (fma(z, x, (y * (z - b))) / t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if ((z <= -1.52e-78) || !(z <= 6.5e-43))
		tmp = Float64(Float64(z * fma(Float64(a / z), Float64(Float64(t + y) / t_2), Float64(Float64(x + y) / t_2))) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = fma(Float64(Float64(t / t_1) + Float64(y / t_1)), a, Float64(fma(z, x, Float64(y * Float64(z - b))) / t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.52e-78], N[Not[LessEqual[z, 6.5e-43]], $MachinePrecision]], N[(N[(z * N[(N[(a / z), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] * a + N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.52e-78 or 6.50000000000000001e-43 < z

   1. Initial program 57.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 57.7%

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

   5. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. times-frac N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower-+.f64 N/A

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

      16. lower-+.f64 N/A

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

      17. lower-+.f64 96.0

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

   7. Applied rewrites 96.0%

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

   if -1.52e-78 < z < 6.50000000000000001e-43

   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 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

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

   5. Applied rewrites 90.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-78} \lor \neg \left(z \leq 6.5 \cdot 10^{-43}\right):\\ \;\;\;\;z \cdot \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{t + \left(x + y\right)}, \frac{x + y}{t + \left(x + y\right)}\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\left(y + x\right) + t} + \frac{y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{\left(y + x\right) + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{a}{\left(y + x\right) + t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+58}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.3e+55)
   (* (+ t y) (/ a (+ (+ y x) t)))
   (if (<= t 8e+58) (- (+ a z) b) (- (+ a z) (* y (/ b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.3e+55) {
		tmp = (t + y) * (a / ((y + x) + t));
	} else if (t <= 8e+58) {
		tmp = (a + z) - b;
	} else {
		tmp = (a + z) - (y * (b / 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 (t <= (-1.3d+55)) then
        tmp = (t + y) * (a / ((y + x) + t))
    else if (t <= 8d+58) then
        tmp = (a + z) - b
    else
        tmp = (a + z) - (y * (b / 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 (t <= -1.3e+55) {
		tmp = (t + y) * (a / ((y + x) + t));
	} else if (t <= 8e+58) {
		tmp = (a + z) - b;
	} else {
		tmp = (a + z) - (y * (b / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.3e+55:
		tmp = (t + y) * (a / ((y + x) + t))
	elif t <= 8e+58:
		tmp = (a + z) - b
	else:
		tmp = (a + z) - (y * (b / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.3e+55)
		tmp = Float64(Float64(t + y) * Float64(a / Float64(Float64(y + x) + t)));
	elseif (t <= 8e+58)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.3e+55)
		tmp = (t + y) * (a / ((y + x) + t));
	elseif (t <= 8e+58)
		tmp = (a + z) - b;
	else
		tmp = (a + z) - (y * (b / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.3e+55], N[(N[(t + y), $MachinePrecision] * N[(a / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+58], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e55

   1. Initial program 53.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 68.4

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

   5. Applied rewrites 68.4%

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

   if -1.3e55 < t < 7.99999999999999955e58

   1. Initial program 68.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 60.5

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

   5. Applied rewrites 60.5%

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

   if 7.99999999999999955e58 < t

   1. Initial program 56.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 65.6

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

   7. Applied rewrites 65.6%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 63.4

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

   10. Applied rewrites 63.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{a}{\left(y + x\right) + t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+58}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+50}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+58}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.7e+50)
   (+ a z)
   (if (<= t 8e+58) (- (+ a z) b) (- (+ a z) (* y (/ b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.7e+50) {
		tmp = a + z;
	} else if (t <= 8e+58) {
		tmp = (a + z) - b;
	} else {
		tmp = (a + z) - (y * (b / 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 (t <= (-5.7d+50)) then
        tmp = a + z
    else if (t <= 8d+58) then
        tmp = (a + z) - b
    else
        tmp = (a + z) - (y * (b / 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 (t <= -5.7e+50) {
		tmp = a + z;
	} else if (t <= 8e+58) {
		tmp = (a + z) - b;
	} else {
		tmp = (a + z) - (y * (b / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.7e+50:
		tmp = a + z
	elif t <= 8e+58:
		tmp = (a + z) - b
	else:
		tmp = (a + z) - (y * (b / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.7e+50)
		tmp = Float64(a + z);
	elseif (t <= 8e+58)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.7e+50)
		tmp = a + z;
	elseif (t <= 8e+58)
		tmp = (a + z) - b;
	else
		tmp = (a + z) - (y * (b / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.7e+50], N[(a + z), $MachinePrecision], If[LessEqual[t, 8e+58], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7000000000000002e50

   1. Initial program 53.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 44.5

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

   5. Applied rewrites 44.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 49.1%

      \[\leadsto a - \color{blue}{b} \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 54.0%

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

   if -5.7000000000000002e50 < t < 7.99999999999999955e58

   1. Initial program 68.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 60.5

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

   5. Applied rewrites 60.5%

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

   if 7.99999999999999955e58 < t

   1. Initial program 56.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 65.6

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

   7. Applied rewrites 65.6%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 63.4

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

   10. Applied rewrites 63.4%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+50}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+58}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+82}:\\ \;\;\;\;z - \frac{y \cdot \left(b - a\right)}{x}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+17}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.7e+82)
   (- z (/ (* y (- b a)) x))
   (if (<= x 1.02e+17) (- (+ 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 <= -1.7e+82) {
		tmp = z - ((y * (b - a)) / x);
	} else if (x <= 1.02e+17) {
		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 <= (-1.7d+82)) then
        tmp = z - ((y * (b - a)) / x)
    else if (x <= 1.02d+17) 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 <= -1.7e+82) {
		tmp = z - ((y * (b - a)) / x);
	} else if (x <= 1.02e+17) {
		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 <= -1.7e+82:
		tmp = z - ((y * (b - a)) / x)
	elif x <= 1.02e+17:
		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 <= -1.7e+82)
		tmp = Float64(z - Float64(Float64(y * Float64(b - a)) / x));
	elseif (x <= 1.02e+17)
		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 <= -1.7e+82)
		tmp = z - ((y * (b - a)) / x);
	elseif (x <= 1.02e+17)
		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, -1.7e+82], N[(z - N[(N[(y * N[(b - a), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+17], 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 < -1.69999999999999997e82

   1. Initial program 49.0%

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

   3. Taylor expanded in 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 51.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 55.4%

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

   if -1.69999999999999997e82 < x < 1.02e17

   1. Initial program 66.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 61.4

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

   5. Applied rewrites 61.4%

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

   if 1.02e17 < x

   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 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 50.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 52.6%

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

Alternative 13: 55.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+58}:\\ \;\;\;\;z - \frac{t \cdot \left(z - a\right)}{x}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+17}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.2e+58)
   (- z (/ (* t (- z a)) x))
   (if (<= x 1.02e+17) (- (+ 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 <= -8.2e+58) {
		tmp = z - ((t * (z - a)) / x);
	} else if (x <= 1.02e+17) {
		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 <= (-8.2d+58)) then
        tmp = z - ((t * (z - a)) / x)
    else if (x <= 1.02d+17) 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 <= -8.2e+58) {
		tmp = z - ((t * (z - a)) / x);
	} else if (x <= 1.02e+17) {
		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 <= -8.2e+58:
		tmp = z - ((t * (z - a)) / x)
	elif x <= 1.02e+17:
		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 <= -8.2e+58)
		tmp = Float64(z - Float64(Float64(t * Float64(z - a)) / x));
	elseif (x <= 1.02e+17)
		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 <= -8.2e+58)
		tmp = z - ((t * (z - a)) / x);
	elseif (x <= 1.02e+17)
		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, -8.2e+58], N[(z - N[(N[(t * N[(z - a), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+17], 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 < -8.2e58

   1. Initial program 48.3%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 50.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 52.7%

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

   if -8.2e58 < x < 1.02e17

   1. Initial program 66.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 61.9

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

   5. Applied rewrites 61.9%

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

   if 1.02e17 < x

   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 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 50.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 52.6%

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

Alternative 14: 55.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{+17}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.02e+17) (- (+ 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 <= 1.02e+17) {
		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 <= 1.02d+17) 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 <= 1.02e+17) {
		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 <= 1.02e+17:
		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 <= 1.02e+17)
		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 <= 1.02e+17)
		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, 1.02e+17], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z - N[(N[(b * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.02e17

   1. Initial program 61.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 57.4

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

   5. Applied rewrites 57.4%

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

   if 1.02e17 < x

   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 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 50.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 52.6%

      \[\leadsto z - \frac{b \cdot y}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 58.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-128} \lor \neg \left(y \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.7e-128) (not (<= y 1.65e-9))) (- (+ a z) b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.7e-128) || !(y <= 1.65e-9)) {
		tmp = (a + z) - b;
	} else {
		tmp = a + z;
	}
	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 <= (-3.7d-128)) .or. (.not. (y <= 1.65d-9))) then
        tmp = (a + z) - b
    else
        tmp = a + z
    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 <= -3.7e-128) || !(y <= 1.65e-9)) {
		tmp = (a + z) - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.7e-128) or not (y <= 1.65e-9):
		tmp = (a + z) - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.7e-128) || !(y <= 1.65e-9))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.7e-128) || ~((y <= 1.65e-9)))
		tmp = (a + z) - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.7e-128], N[Not[LessEqual[y, 1.65e-9]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e-128 or 1.65000000000000009e-9 < y

   1. Initial program 53.4%

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

   3. Taylor expanded in 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. lower-+.f64 65.7

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

   5. Applied rewrites 65.7%

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

   if -3.7e-128 < y < 1.65000000000000009e-9

   1. Initial program 78.4%

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

   3. Taylor expanded in 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. lower-+.f64 32.7

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

   5. Applied rewrites 32.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 21.1%

      \[\leadsto a - \color{blue}{b} \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 45.1%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-128} \lor \neg \left(y \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+27} \lor \neg \left(a \leq 6.4 \cdot 10^{-116}\right):\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.1e+27) (not (<= a 6.4e-116))) (+ a z) (- z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.1e+27) || !(a <= 6.4e-116)) {
		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 ((a <= (-4.1d+27)) .or. (.not. (a <= 6.4d-116))) 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 ((a <= -4.1e+27) || !(a <= 6.4e-116)) {
		tmp = a + z;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.1e+27) or not (a <= 6.4e-116):
		tmp = a + z
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.1e+27) || !(a <= 6.4e-116))
		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 ((a <= -4.1e+27) || ~((a <= 6.4e-116)))
		tmp = a + z;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.1e+27], N[Not[LessEqual[a, 6.4e-116]], $MachinePrecision]], N[(a + z), $MachinePrecision], N[(z - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1000000000000002e27 or 6.40000000000000019e-116 < a

   1. Initial program 55.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 51.5

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

   5. Applied rewrites 51.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 42.4%

      \[\leadsto a - \color{blue}{b} \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 56.9%

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

   if -4.1000000000000002e27 < a < 6.40000000000000019e-116

   1. Initial program 73.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 26.7%

      \[\leadsto a - \color{blue}{b} \]

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 51.9%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+27} \lor \neg \left(a \leq 6.4 \cdot 10^{-116}\right):\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.8% 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 62.9%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
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. lower-+.f64 53.2

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

5. Applied rewrites 53.2%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 35.7%

   \[\leadsto a - \color{blue}{b} \]

9. Taylor expanded in b around 0

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

11. Applied rewrites 50.2%

    \[\leadsto a + \color{blue}{z} \]
12. Add Preprocessing

Alternative 18: 13.0% 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 62.9%

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

3. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

   2. associate-*l/ N/A

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

   3. associate-*l* N/A

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

   4. lower-*.f64 N/A

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

   5. associate-*r/ N/A

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

   6. lower-/.f64 N/A

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

   7. mul-1-neg N/A

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

   8. lower-neg.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-+.f64 21.6

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

5. Applied rewrites 21.6%

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

6. Taylor expanded in y around inf

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

8. Applied rewrites 12.7%

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

Developer Target 1: 81.7% 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 2024318 
(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)))