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

Percentage Accurate: 60.2% → 91.9%

Time: 8.6s

Alternatives: 18

Speedup: 1.1×

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: 60.2% 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: 91.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+296}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;t\_2 \leq 10^{+269}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a + z\right) - b, y, \mathsf{fma}\left(a, t, z \cdot x\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - \frac{y}{\frac{t\_1}{b}}\\ \end{array} \end{array} \]

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 (<= t_2 -1e+296)
     (- (+ z a) (* y (/ b (+ (+ t x) y))))
     (if (<= t_2 1e+269)
       (/ (fma (- (+ a z) b) y (fma a t (* z x))) t_1)
       (- (+ z a) (/ y (/ t_1 b)))))))

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 <= -1e+296) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} else if (t_2 <= 1e+269) {
		tmp = fma(((a + z) - b), y, fma(a, t, (z * x))) / t_1;
	} else {
		tmp = (z + a) - (y / (t_1 / b));
	}
	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 <= -1e+296)
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	elseif (t_2 <= 1e+269)
		tmp = Float64(fma(Float64(Float64(a + z) - b), y, fma(a, t, Float64(z * x))) / t_1);
	else
		tmp = Float64(Float64(z + a) - Float64(y / Float64(t_1 / b)));
	end
	return 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[LessEqual[t$95$2, -1e+296], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+269], N[(N[(N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision] * y + N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - N[(y / N[(t$95$1 / b), $MachinePrecision]), $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)) < -9.99999999999999981e295

   1. Initial program 11.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 22.7%

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

   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. +-commutative N/A

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

      2. lower-+.f64 84.6

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

   7. Applied rewrites 84.6%

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

   if -9.99999999999999981e295 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e269

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 98.6

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

   5. Applied rewrites 98.6%

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

   if 1e269 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 11.7%

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

   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. +-commutative N/A

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

      2. lower-+.f64 85.2

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

   7. Applied rewrites 85.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. distribute-lft-neg-out N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-+.f64 N/A

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

      14. lower-/.f64 85.2

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

   9. Applied rewrites 85.2%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+296}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+269}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a + z\right) - b, y, \mathsf{fma}\left(a, t, z \cdot x\right)\right)}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - \frac{y}{\frac{\left(x + t\right) + y}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ t_4 := \left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+273}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_2}\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-195}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) t_2))
        (t_4 (- (+ z a) (* y (/ b (+ (+ t x) y))))))
   (if (<= t_3 -2e+273)
     t_4
     (if (<= t_3 -2e+134)
       (/ (fma z x (* y (- z b))) t_2)
       (if (<= t_3 -1e-195)
         (/ (- t_1 (* y b)) t_2)
         (if (<= t_3 10.0) (/ (fma a t (* z x)) (+ t x)) t_4))))))

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 + t) + y;
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	double t_4 = (z + a) - (y * (b / ((t + x) + y)));
	double tmp;
	if (t_3 <= -2e+273) {
		tmp = t_4;
	} else if (t_3 <= -2e+134) {
		tmp = fma(z, x, (y * (z - b))) / t_2;
	} else if (t_3 <= -1e-195) {
		tmp = (t_1 - (y * b)) / t_2;
	} else if (t_3 <= 10.0) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))))
	tmp = 0.0
	if (t_3 <= -2e+273)
		tmp = t_4;
	elseif (t_3 <= -2e+134)
		tmp = Float64(fma(z, x, Float64(y * Float64(z - b))) / t_2);
	elseif (t_3 <= -1e-195)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_2);
	elseif (t_3 <= 10.0)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_4;
	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[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+273], t$95$4, If[LessEqual[t$95$3, -2e+134], N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, -1e-195], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 10.0], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.99999999999999989e273 or 10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 33.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 38.7%

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

   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. +-commutative N/A

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

      2. lower-+.f64 79.0

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

   7. Applied rewrites 79.0%

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

   if -1.99999999999999989e273 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.99999999999999984e134

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. distribute-rgt-in N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 78.2

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

   5. Applied rewrites 78.2%

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

   if -1.99999999999999984e134 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.0000000000000001e-195

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -1.0000000000000001e-195 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 10

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 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 73.2

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

   5. Applied rewrites 73.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{+273}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{\left(x + t\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{-195}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot a - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - b\right)\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_2}\\ t_4 := \left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+273}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{+171}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, t\_1\right)}{t\_2}\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, t\_1\right)}{t + y}\\ \mathbf{elif}\;t\_3 \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z b)))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_2))
        (t_4 (- (+ z a) (* y (/ b (+ (+ t x) y))))))
   (if (<= t_3 -2e+273)
     t_4
     (if (<= t_3 -5e+171)
       (/ (fma z x t_1) t_2)
       (if (<= t_3 -2e-161)
         (/ (fma (+ t y) a t_1) (+ t y))
         (if (<= t_3 10.0) (/ (fma a t (* z x)) (+ t x)) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (z - b);
	double t_2 = (x + t) + y;
	double t_3 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_2;
	double t_4 = (z + a) - (y * (b / ((t + x) + y)));
	double tmp;
	if (t_3 <= -2e+273) {
		tmp = t_4;
	} else if (t_3 <= -5e+171) {
		tmp = fma(z, x, t_1) / t_2;
	} else if (t_3 <= -2e-161) {
		tmp = fma((t + y), a, t_1) / (t + y);
	} else if (t_3 <= 10.0) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(z - b))
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))))
	tmp = 0.0
	if (t_3 <= -2e+273)
		tmp = t_4;
	elseif (t_3 <= -5e+171)
		tmp = Float64(fma(z, x, t_1) / t_2);
	elseif (t_3 <= -2e-161)
		tmp = Float64(fma(Float64(t + y), a, t_1) / Float64(t + y));
	elseif (t_3 <= 10.0)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = 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$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+273], t$95$4, If[LessEqual[t$95$3, -5e+171], N[(N[(z * x + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, -2e-161], N[(N[(N[(t + y), $MachinePrecision] * a + t$95$1), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 10.0], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.99999999999999989e273 or 10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 33.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 38.7%

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

   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. +-commutative N/A

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

      2. lower-+.f64 79.0

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

   7. Applied rewrites 79.0%

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

   if -1.99999999999999989e273 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.0000000000000004e171

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. distribute-rgt-in N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 82.8

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

   5. Applied rewrites 82.8%

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

   if -5.0000000000000004e171 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.00000000000000006e-161

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 71.8

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

   5. Applied rewrites 71.8%

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

   if -2.00000000000000006e-161 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 10

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 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 72.2

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

   5. Applied rewrites 72.2%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{+273}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+171}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{\left(x + t\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, y \cdot \left(z - b\right)\right)}{t + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, y \cdot \left(z - b\right)\right)}{t + y}\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ z a) (* y (/ b (+ (+ t x) y))))))
   (if (<= t_1 -2e+134)
     t_2
     (if (<= t_1 -2e-161)
       (/ (fma (+ t y) a (* y (- z b))) (+ t y))
       (if (<= t_1 10.0) (/ (fma a t (* z x)) (+ t x)) t_2)))))

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 t_2 = (z + a) - (y * (b / ((t + x) + y)));
	double tmp;
	if (t_1 <= -2e+134) {
		tmp = t_2;
	} else if (t_1 <= -2e-161) {
		tmp = fma((t + y), a, (y * (z - b))) / (t + y);
	} else if (t_1 <= 10.0) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_2;
	}
	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))
	t_2 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))))
	tmp = 0.0
	if (t_1 <= -2e+134)
		tmp = t_2;
	elseif (t_1 <= -2e-161)
		tmp = Float64(fma(Float64(t + y), a, Float64(y * Float64(z - b))) / Float64(t + y));
	elseif (t_1 <= 10.0)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(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]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+134], t$95$2, If[LessEqual[t$95$1, -2e-161], N[(N[(N[(t + y), $MachinePrecision] * a + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10.0], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

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)) < -1.99999999999999984e134 or 10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 41.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 45.3%

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

   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. +-commutative N/A

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

      2. lower-+.f64 76.2

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

   7. Applied rewrites 76.2%

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

   if -1.99999999999999984e134 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.00000000000000006e-161

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if -2.00000000000000006e-161 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 10

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 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 72.2

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

   5. Applied rewrites 72.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, y \cdot \left(z - b\right)\right)}{t + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-195}:\\ \;\;\;\;\frac{a \cdot t - y \cdot b}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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))
        (t_3 (- (+ z a) (* y (/ b (+ (+ t x) y))))))
   (if (<= t_2 -5e+71)
     t_3
     (if (<= t_2 -1e-195)
       (/ (- (* a t) (* y b)) t_1)
       (if (<= t_2 10.0) (/ (fma a t (* z x)) (+ t x)) t_3)))))

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 t_3 = (z + a) - (y * (b / ((t + x) + y)));
	double tmp;
	if (t_2 <= -5e+71) {
		tmp = t_3;
	} else if (t_2 <= -1e-195) {
		tmp = ((a * t) - (y * b)) / t_1;
	} else if (t_2 <= 10.0) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_3;
	}
	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)
	t_3 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))))
	tmp = 0.0
	if (t_2 <= -5e+71)
		tmp = t_3;
	elseif (t_2 <= -1e-195)
		tmp = Float64(Float64(Float64(a * t) - Float64(y * b)) / t_1);
	elseif (t_2 <= 10.0)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_3;
	end
	return 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]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+71], t$95$3, If[LessEqual[t$95$2, -1e-195], N[(N[(N[(a * t), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 10.0], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

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)) < -4.99999999999999972e71 or 10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 46.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 49.5%

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

   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. +-commutative N/A

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

      2. lower-+.f64 74.7

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

   7. Applied rewrites 74.7%

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

   if -4.99999999999999972e71 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.0000000000000001e-195

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 83.7

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

   5. Applied rewrites 83.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.0%

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

   if -1.0000000000000001e-195 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 10

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 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 73.2

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

   5. Applied rewrites 73.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+71}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{-195}:\\ \;\;\;\;\frac{a \cdot t - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+76}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 10^{+210}:\\ \;\;\;\;\frac{t\_3 \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 -4e+76)
     t_3
     (if (<= t_2 10.0)
       (/ (fma a t (* z x)) (+ t x))
       (if (<= t_2 1e+210) (/ (* t_3 y) t_1) t_3)))))

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 t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -4e+76) {
		tmp = t_3;
	} else if (t_2 <= 10.0) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (t_2 <= 1e+210) {
		tmp = (t_3 * y) / t_1;
	} else {
		tmp = t_3;
	}
	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)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= -4e+76)
		tmp = t_3;
	elseif (t_2 <= 10.0)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (t_2 <= 1e+210)
		tmp = Float64(Float64(t_3 * y) / t_1);
	else
		tmp = t_3;
	end
	return 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]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+76], t$95$3, If[LessEqual[t$95$2, 10.0], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+210], N[(N[(t$95$3 * y), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]

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)) < -4.0000000000000002e76 or 9.99999999999999927e209 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 34.2%

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

   3. Taylor expanded in 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 67.8

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

   5. Applied rewrites 67.8%

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

   if -4.0000000000000002e76 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 10

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 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 68.1

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

   5. Applied rewrites 68.1%

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

   if 10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999927e209

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 69.4

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

   5. Applied rewrites 69.4%

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

Alternative 7: 57.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+41}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-69}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 10^{+44}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 -2e+41)
     t_3
     (if (<= t_2 1e-69)
       (/ (* (+ y t) a) t_1)
       (if (<= t_2 1e+44) (* (+ y x) (/ z (+ (+ y x) t))) t_3)))))

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 t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -2e+41) {
		tmp = t_3;
	} else if (t_2 <= 1e-69) {
		tmp = ((y + t) * a) / t_1;
	} else if (t_2 <= 1e+44) {
		tmp = (y + x) * (z / ((y + x) + t));
	} else {
		tmp = t_3;
	}
	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) :: tmp
    t_1 = (x + t) + y
    t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1
    t_3 = (a + z) - b
    if (t_2 <= (-2d+41)) then
        tmp = t_3
    else if (t_2 <= 1d-69) then
        tmp = ((y + t) * a) / t_1
    else if (t_2 <= 1d+44) then
        tmp = (y + x) * (z / ((y + x) + t))
    else
        tmp = t_3
    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 t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -2e+41) {
		tmp = t_3;
	} else if (t_2 <= 1e-69) {
		tmp = ((y + t) * a) / t_1;
	} else if (t_2 <= 1e+44) {
		tmp = (y + x) * (z / ((y + x) + t));
	} else {
		tmp = t_3;
	}
	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
	t_3 = (a + z) - b
	tmp = 0
	if t_2 <= -2e+41:
		tmp = t_3
	elif t_2 <= 1e-69:
		tmp = ((y + t) * a) / t_1
	elif t_2 <= 1e+44:
		tmp = (y + x) * (z / ((y + x) + t))
	else:
		tmp = t_3
	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)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= -2e+41)
		tmp = t_3;
	elseif (t_2 <= 1e-69)
		tmp = Float64(Float64(Float64(y + t) * a) / t_1);
	elseif (t_2 <= 1e+44)
		tmp = Float64(Float64(y + x) * Float64(z / Float64(Float64(y + x) + t)));
	else
		tmp = t_3;
	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;
	t_3 = (a + z) - b;
	tmp = 0.0;
	if (t_2 <= -2e+41)
		tmp = t_3;
	elseif (t_2 <= 1e-69)
		tmp = ((y + t) * a) / t_1;
	elseif (t_2 <= 1e+44)
		tmp = (y + x) * (z / ((y + x) + t));
	else
		tmp = t_3;
	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]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+41], t$95$3, If[LessEqual[t$95$2, 1e-69], N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e+44], N[(N[(y + x), $MachinePrecision] * N[(z / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

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)) < -2.00000000000000001e41 or 1.0000000000000001e44 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 44.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 64.0

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

   5. Applied rewrites 64.0%

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

   if -2.00000000000000001e41 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999996e-70

   1. Initial program 96.8%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 95.3%

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

   6. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. associate-+r+ N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 51.9

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

   8. Applied rewrites 51.9%

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

   if 9.9999999999999996e-70 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e44

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 55.2

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

   5. Applied rewrites 55.2%

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

Alternative 8: 76.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+213} \lor \neg \left(t\_2 \leq 5 \cdot 10^{+37}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{\left(y + x\right) + t}\\ \end{array} \end{array} \]

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 -4e+213) (not (<= t_2 5e+37)))
     (- (+ z a) (* y (/ b (+ (+ t x) y))))
     (/ (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 <= -4e+213) || !(t_2 <= 5e+37)) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} 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 <= -4e+213) || !(t_2 <= 5e+37))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	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, -4e+213], N[Not[LessEqual[t$95$2, 5e+37]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $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)) < -3.99999999999999994e213 or 4.99999999999999989e37 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 31.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 36.0%

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

   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. +-commutative N/A

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

      2. lower-+.f64 79.3

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

   7. Applied rewrites 79.3%

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

   if -3.99999999999999994e213 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999989e37

   1. Initial program 98.2%

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

   3. Taylor expanded in 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 83.1

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

   5. Applied rewrites 83.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -4 \cdot 10^{+213} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+37}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+76} \lor \neg \left(t\_1 \leq 10\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

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 -4e+76) (not (<= t_1 10.0)))
     (- (+ z a) (* y (/ b (+ (+ t 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 <= -4e+76) || !(t_1 <= 10.0)) {
		tmp = (z + a) - (y * (b / ((t + 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 <= -4e+76) || !(t_1 <= 10.0))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + 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, -4e+76], N[Not[LessEqual[t$95$1, 10.0]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + 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)) < -4.0000000000000002e76 or 10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 46.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 49.2%

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

   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. +-commutative N/A

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

      2. lower-+.f64 74.8

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

   7. Applied rewrites 74.8%

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

   if -4.0000000000000002e76 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 10

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 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 68.1

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

   5. Applied rewrites 68.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -4 \cdot 10^{+76} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;z - t \cdot \frac{z}{x + y}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+83}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+214}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.6e+104)
   (- z (* t (/ z (+ x y))))
   (if (<= x 8e+83)
     (- (+ a z) b)
     (if (<= x 3.2e+214)
       (* (+ y x) (/ z (+ (+ y x) t)))
       (- (+ z a) (* y (/ b x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.6e+104) {
		tmp = z - (t * (z / (x + y)));
	} else if (x <= 8e+83) {
		tmp = (a + z) - b;
	} else if (x <= 3.2e+214) {
		tmp = (y + x) * (z / ((y + x) + t));
	} else {
		tmp = (z + a) - (y * (b / 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 <= (-6.6d+104)) then
        tmp = z - (t * (z / (x + y)))
    else if (x <= 8d+83) then
        tmp = (a + z) - b
    else if (x <= 3.2d+214) then
        tmp = (y + x) * (z / ((y + x) + t))
    else
        tmp = (z + a) - (y * (b / 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 <= -6.6e+104) {
		tmp = z - (t * (z / (x + y)));
	} else if (x <= 8e+83) {
		tmp = (a + z) - b;
	} else if (x <= 3.2e+214) {
		tmp = (y + x) * (z / ((y + x) + t));
	} else {
		tmp = (z + a) - (y * (b / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.6e+104:
		tmp = z - (t * (z / (x + y)))
	elif x <= 8e+83:
		tmp = (a + z) - b
	elif x <= 3.2e+214:
		tmp = (y + x) * (z / ((y + x) + t))
	else:
		tmp = (z + a) - (y * (b / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.6e+104)
		tmp = Float64(z - Float64(t * Float64(z / Float64(x + y))));
	elseif (x <= 8e+83)
		tmp = Float64(Float64(a + z) - b);
	elseif (x <= 3.2e+214)
		tmp = Float64(Float64(y + x) * Float64(z / Float64(Float64(y + x) + t)));
	else
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.6e+104)
		tmp = z - (t * (z / (x + y)));
	elseif (x <= 8e+83)
		tmp = (a + z) - b;
	elseif (x <= 3.2e+214)
		tmp = (y + x) * (z / ((y + x) + t));
	else
		tmp = (z + a) - (y * (b / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.6e+104], N[(z - N[(t * N[(z / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+83], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 3.2e+214], N[(N[(y + x), $MachinePrecision] * N[(z / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.59999999999999969e104

   1. Initial program 55.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 52.2

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

   5. Applied rewrites 52.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 7.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 64.4%

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

   if -6.59999999999999969e104 < x < 8.00000000000000025e83

   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 57.9

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

   5. Applied rewrites 57.9%

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

   if 8.00000000000000025e83 < x < 3.19999999999999995e214

   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 z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 53.6

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

   5. Applied rewrites 53.6%

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

   if 3.19999999999999995e214 < x

   1. Initial program 28.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 46.0%

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

   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. +-commutative N/A

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

      2. lower-+.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 65.1

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

   10. Applied rewrites 65.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;z - t \cdot \frac{z}{x + y}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+83}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+214}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-113}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-18}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -6.2e-38)
     t_1
     (if (<= y 5.3e-113)
       (/ (fma a t (* z x)) (+ t x))
       (if (<= y 1.65e-18) (- (+ z a) (* y (/ b t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -6.2e-38) {
		tmp = t_1;
	} else if (y <= 5.3e-113) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (y <= 1.65e-18) {
		tmp = (z + a) - (y * (b / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -6.2e-38)
		tmp = t_1;
	elseif (y <= 5.3e-113)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (y <= 1.65e-18)
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.2e-38], t$95$1, If[LessEqual[y, 5.3e-113], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-18], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999966e-38 or 1.6500000000000001e-18 < y

   1. Initial program 45.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 71.3

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

   5. Applied rewrites 71.3%

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

   if -6.19999999999999966e-38 < y < 5.3000000000000004e-113

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 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 61.4

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

   5. Applied rewrites 61.4%

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

   if 5.3000000000000004e-113 < y < 1.6500000000000001e-18

   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. 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 68.5%

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

   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. +-commutative N/A

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

      2. lower-+.f64 74.7

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

   7. Applied rewrites 74.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 65.1

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

   10. Applied rewrites 65.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-38}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-113}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-18}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;z - t \cdot \frac{z}{x + y}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+140}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.6e+104)
   (- z (* t (/ z (+ x y))))
   (if (<= x 2.9e+140) (- (+ a z) b) (- (+ z a) (* y (/ b x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.6e+104) {
		tmp = z - (t * (z / (x + y)));
	} else if (x <= 2.9e+140) {
		tmp = (a + z) - b;
	} else {
		tmp = (z + a) - (y * (b / 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 <= (-6.6d+104)) then
        tmp = z - (t * (z / (x + y)))
    else if (x <= 2.9d+140) then
        tmp = (a + z) - b
    else
        tmp = (z + a) - (y * (b / 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 <= -6.6e+104) {
		tmp = z - (t * (z / (x + y)));
	} else if (x <= 2.9e+140) {
		tmp = (a + z) - b;
	} else {
		tmp = (z + a) - (y * (b / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.6e+104:
		tmp = z - (t * (z / (x + y)))
	elif x <= 2.9e+140:
		tmp = (a + z) - b
	else:
		tmp = (z + a) - (y * (b / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.6e+104)
		tmp = Float64(z - Float64(t * Float64(z / Float64(x + y))));
	elseif (x <= 2.9e+140)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.6e+104)
		tmp = z - (t * (z / (x + y)));
	elseif (x <= 2.9e+140)
		tmp = (a + z) - b;
	else
		tmp = (z + a) - (y * (b / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.6e+104], N[(z - N[(t * N[(z / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+140], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.59999999999999969e104

   1. Initial program 55.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 52.2

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

   5. Applied rewrites 52.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 7.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 64.4%

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

   if -6.59999999999999969e104 < x < 2.8999999999999999e140

   1. Initial program 67.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 56.7

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

   5. Applied rewrites 56.7%

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

   if 2.8999999999999999e140 < x

   1. Initial program 45.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 55.8%

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

   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. +-commutative N/A

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

      2. lower-+.f64 51.6

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

   7. Applied rewrites 51.6%

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

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 49.2

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

   10. Applied rewrites 49.2%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;z - t \cdot \frac{z}{x + y}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+140}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+110} \lor \neg \left(t \leq 4.4 \cdot 10^{+203}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.2e+110) (not (<= t 4.4e+203)))
   (* a (/ t (+ x t)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e+110) || !(t <= 4.4e+203)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (a + 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 ((t <= (-5.2d+110)) .or. (.not. (t <= 4.4d+203))) then
        tmp = a * (t / (x + t))
    else
        tmp = (a + 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 ((t <= -5.2e+110) || !(t <= 4.4e+203)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.2e+110) or not (t <= 4.4e+203):
		tmp = a * (t / (x + t))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.2e+110) || !(t <= 4.4e+203))
		tmp = Float64(a * Float64(t / Float64(x + t)));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.2e+110) || ~((t <= 4.4e+203)))
		tmp = a * (t / (x + t));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.2e+110], N[Not[LessEqual[t, 4.4e+203]], $MachinePrecision]], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e110 or 4.40000000000000009e203 < t

   1. Initial program 52.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 77.1%

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

   6. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 39.2

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

   8. Applied rewrites 39.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 64.9%

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

   if -5.2e110 < t < 4.40000000000000009e203

   1. Initial program 66.3%

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

   3. Taylor expanded in y around 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 54.2

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

   5. Applied rewrites 54.2%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+110} \lor \neg \left(t \leq 4.4 \cdot 10^{+203}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+66}:\\ \;\;\;\;a - a \cdot \frac{x}{y + t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+203}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.42e+66)
   (- a (* a (/ x (+ y t))))
   (if (<= t 4.4e+203) (- (+ a z) b) (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.42e+66) {
		tmp = a - (a * (x / (y + t)));
	} else if (t <= 4.4e+203) {
		tmp = (a + z) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.42d+66)) then
        tmp = a - (a * (x / (y + t)))
    else if (t <= 4.4d+203) then
        tmp = (a + z) - b
    else
        tmp = a * (t / (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.42e+66) {
		tmp = a - (a * (x / (y + t)));
	} else if (t <= 4.4e+203) {
		tmp = (a + z) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.42e+66:
		tmp = a - (a * (x / (y + t)))
	elif t <= 4.4e+203:
		tmp = (a + z) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.42e+66)
		tmp = Float64(a - Float64(a * Float64(x / Float64(y + t))));
	elseif (t <= 4.4e+203)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.42e+66)
		tmp = a - (a * (x / (y + t)));
	elseif (t <= 4.4e+203)
		tmp = (a + z) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.42e+66], N[(a - N[(a * N[(x / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+203], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4200000000000001e66

   1. Initial program 58.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 74.8%

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

   6. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. associate-+r+ N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 33.1

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

   8. Applied rewrites 33.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 53.7%

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

   if -1.4200000000000001e66 < t < 4.40000000000000009e203

   1. Initial program 66.3%

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

   3. Taylor expanded in y around 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 55.9

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

   5. Applied rewrites 55.9%

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

   if 4.40000000000000009e203 < t

   1. Initial program 50.3%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 33.8

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

   8. Applied rewrites 33.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 70.9%

       \[\leadsto a \cdot \color{blue}{\frac{t}{x + t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 46.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+111} \lor \neg \left(z \leq 4.4 \cdot 10^{+210}\right):\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e+111) (not (<= z 4.4e+210))) (- z b) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e+111) || !(z <= 4.4e+210)) {
		tmp = z - b;
	} else {
		tmp = a - 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 ((z <= (-3.2d+111)) .or. (.not. (z <= 4.4d+210))) then
        tmp = z - b
    else
        tmp = a - 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 ((z <= -3.2e+111) || !(z <= 4.4e+210)) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.2e+111) or not (z <= 4.4e+210):
		tmp = z - b
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.2e+111) || !(z <= 4.4e+210))
		tmp = Float64(z - b);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.2e+111) || ~((z <= 4.4e+210)))
		tmp = z - b;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.2e+111], N[Not[LessEqual[z, 4.4e+210]], $MachinePrecision]], N[(z - b), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000001e111 or 4.39999999999999974e210 < z

   1. Initial program 44.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 58.7

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

   5. Applied rewrites 58.7%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 3.1%

      \[\leadsto -b \]

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 53.1%

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

   if -3.2000000000000001e111 < z < 4.39999999999999974e210

   1. Initial program 70.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 47.9

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

   5. Applied rewrites 47.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 45.6%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+111} \lor \neg \left(z \leq 4.4 \cdot 10^{+210}\right):\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+91}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.8e+91) (- a b) (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.8e+91) {
		tmp = a - b;
	} else {
		tmp = (a + 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 (t <= (-1.8d+91)) then
        tmp = a - b
    else
        tmp = (a + 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 (t <= -1.8e+91) {
		tmp = a - b;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.8e+91:
		tmp = a - b
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.8e+91)
		tmp = Float64(a - b);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.8e+91)
		tmp = a - b;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.8e+91], N[(a - b), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e91

   1. Initial program 56.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 38.3

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

   5. Applied rewrites 38.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 54.3%

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

   if -1.8e91 < t

   1. Initial program 64.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 53.1

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

   5. Applied rewrites 53.1%

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

Alternative 17: 36.8% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.4%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
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 50.8

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

5. Applied rewrites 50.8%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 38.8%

   \[\leadsto a - \color{blue}{b} \]
9. Add Preprocessing

Alternative 18: 13.9% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.4%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
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 50.8

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

5. Applied rewrites 50.8%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 11.4%

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

Developer Target 1: 81.2% 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 2024307 
(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)))