Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C

Percentage Accurate: 57.5% → 98.7%

Time: 15.8s

Alternatives: 20

Speedup: 2.8×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

Initial Program: 57.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{t\_0}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \frac{6193.6101064416025 - \left(x \cdot x\right) \cdot 17.342137594641823}{78.6994924154 + x \cdot -4.16438922228}\right)\right)\right)}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (/
          (*
           (- x 2.0)
           (+
            (*
             x
             (+
              (*
               x
               (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
              y))
            z))
          t_0)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+305)))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/
        (+
         101.7851458539211
         (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
        x)))
     (/
      (*
       (- x 2.0)
       (+
        z
        (*
         x
         (+
          y
          (*
           x
           (+
            137.519416416
            (*
             x
             (/
              (- 6193.6101064416025 (* (* x x) 17.342137594641823))
              (+ 78.6994924154 (* x -4.16438922228))))))))))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+305)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((6193.6101064416025 - ((x * x) * 17.342137594641823)) / (78.6994924154 + (x * -4.16438922228)))))))))) / t_0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+305)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((6193.6101064416025 - ((x * x) * 17.342137594641823)) / (78.6994924154 + (x * -4.16438922228)))))))))) / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+305):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x))
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((6193.6101064416025 - ((x * x) * 17.342137594641823)) / (78.6994924154 + (x * -4.16438922228)))))))))) / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+305))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(6193.6101064416025 - Float64(Float64(x * x) * 17.342137594641823)) / Float64(78.6994924154 + Float64(x * -4.16438922228)))))))))) / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+305)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((6193.6101064416025 - ((x * x) * 17.342137594641823)) / (78.6994924154 + (x * -4.16438922228)))))))))) / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+305]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(6193.6101064416025 - N[(N[(x * x), $MachinePrecision] * 17.342137594641823), $MachinePrecision]), $MachinePrecision] / N[(78.6994924154 + N[(x * -4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < -inf.0 or 5.00000000000000009e305 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 7.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 7.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 7.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 7.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 7.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 5.00000000000000009e305

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot 4.16438922228} \cdot \sqrt[3]{x \cdot 4.16438922228}\right) \cdot \sqrt[3]{x \cdot 4.16438922228}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      2. pow3 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot 4.16438922228}\right)}^{3}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot 4.16438922228}\right)}^{3}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   5. Step-by-step derivation

      1. rem-cube-cbrt 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{x \cdot 4.16438922228} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      2. *-commutative 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{4.16438922228 \cdot x} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. +-commutative 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\left(78.6994924154 + 4.16438922228 \cdot x\right)} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. flip-+ 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{78.6994924154 \cdot 78.6994924154 - \left(4.16438922228 \cdot x\right) \cdot \left(4.16438922228 \cdot x\right)}{78.6994924154 - 4.16438922228 \cdot x}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. metadata-eval 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{\color{blue}{6193.6101064416025} - \left(4.16438922228 \cdot x\right) \cdot \left(4.16438922228 \cdot x\right)}{78.6994924154 - 4.16438922228 \cdot x} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. *-commutative 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - \color{blue}{\left(x \cdot 4.16438922228\right)} \cdot \left(4.16438922228 \cdot x\right)}{78.6994924154 - 4.16438922228 \cdot x} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. *-commutative 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - \left(x \cdot 4.16438922228\right) \cdot \color{blue}{\left(x \cdot 4.16438922228\right)}}{78.6994924154 - 4.16438922228 \cdot x} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. pow2 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - \color{blue}{{\left(x \cdot 4.16438922228\right)}^{2}}}{78.6994924154 - 4.16438922228 \cdot x} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      9. *-commutative 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - {\left(x \cdot 4.16438922228\right)}^{2}}{78.6994924154 - \color{blue}{x \cdot 4.16438922228}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Applied egg-rr 99.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{6193.6101064416025 - {\left(x \cdot 4.16438922228\right)}^{2}}{78.6994924154 - x \cdot 4.16438922228}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   7. Step-by-step derivation

      1. unpow2 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - \color{blue}{\left(x \cdot 4.16438922228\right) \cdot \left(x \cdot 4.16438922228\right)}}{78.6994924154 - x \cdot 4.16438922228} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      2. swap-sqr 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - \color{blue}{\left(x \cdot x\right) \cdot \left(4.16438922228 \cdot 4.16438922228\right)}}{78.6994924154 - x \cdot 4.16438922228} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. unpow2 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - \color{blue}{{x}^{2}} \cdot \left(4.16438922228 \cdot 4.16438922228\right)}{78.6994924154 - x \cdot 4.16438922228} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. metadata-eval 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - {x}^{2} \cdot \color{blue}{17.342137594641823}}{78.6994924154 - x \cdot 4.16438922228} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. *-commutative 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - {x}^{2} \cdot 17.342137594641823}{78.6994924154 - \color{blue}{4.16438922228 \cdot x}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. cancel-sign-sub-inv 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - {x}^{2} \cdot 17.342137594641823}{\color{blue}{78.6994924154 + \left(-4.16438922228\right) \cdot x}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. metadata-eval 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - {x}^{2} \cdot 17.342137594641823}{78.6994924154 + \color{blue}{-4.16438922228} \cdot x} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. rem-cube-cbrt 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - {x}^{2} \cdot 17.342137594641823}{78.6994924154 + \color{blue}{{\left(\sqrt[3]{-4.16438922228}\right)}^{3}} \cdot x} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      9. *-commutative 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - {x}^{2} \cdot 17.342137594641823}{78.6994924154 + \color{blue}{x \cdot {\left(\sqrt[3]{-4.16438922228}\right)}^{3}}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      10. rem-cube-cbrt 99.6%

          \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - {x}^{2} \cdot 17.342137594641823}{78.6994924154 + x \cdot \color{blue}{-4.16438922228}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   8. Simplified 99.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{6193.6101064416025 - {x}^{2} \cdot 17.342137594641823}{78.6994924154 + x \cdot -4.16438922228}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   9. Step-by-step derivation

      1. unpow2 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - \color{blue}{\left(x \cdot x\right)} \cdot 17.342137594641823}{78.6994924154 + x \cdot -4.16438922228} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   10. Applied egg-rr 99.6%

       \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\frac{6193.6101064416025 - \color{blue}{\left(x \cdot x\right)} \cdot 17.342137594641823}{78.6994924154 + x \cdot -4.16438922228} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty \lor \neg \left(\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \frac{6193.6101064416025 - \left(x \cdot x\right) \cdot 17.342137594641823}{78.6994924154 + x \cdot -4.16438922228}\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      5e+305)
   (*
    (+ x -2.0)
    (/
     (fma
      (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma
      (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
      x
      47.066876606)))
   (*
    (+ x -2.0)
    (-
     4.16438922228
     (/
      (+
       101.7851458539211
       (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
      x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 5e+305) {
		tmp = (x + -2.0) * (fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((x + 43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 5e+305)
		tmp = Float64(Float64(x + -2.0) * Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(x + 43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 5e+305], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 5.00000000000000009e305

   1. Initial program 96.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.0%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.0%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.0%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.0%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   if 5.00000000000000009e305 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 2.3%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 2.3%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 2.3%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 2.3%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 2.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot t\_0 + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, t\_0, y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)))
   (if (<=
        (/
         (* (- x 2.0) (+ (* x (+ (* x t_0) y)) z))
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        5e+305)
     (*
      (fma x (fma x t_0 y) z)
      (/
       (+ x -2.0)
       (fma
        x
        (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
        47.066876606)))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/
        (+
         101.7851458539211
         (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
        x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416;
	double tmp;
	if ((((x - 2.0) * ((x * ((x * t_0) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 5e+305) {
		tmp = fma(x, fma(x, t_0, y), z) * ((x + -2.0) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * t_0) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 5e+305)
		tmp = Float64(fma(x, fma(x, t_0, y), z) * Float64(Float64(x + -2.0) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * t$95$0), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 5e+305], N[(N[(x * N[(x * t$95$0 + y), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x + -2.0), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 5.00000000000000009e305

   1. Initial program 96.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 98.8%

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{137.519416416 + x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)}, y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

   if 5.00000000000000009e305 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 2.3%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 2.3%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 2.3%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 2.3%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 2.3%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 2.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416, y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{t\_0}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot \left(4.16438922228 + \frac{78.6994924154}{x}\right)\right)\right)\right)\right)}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (/
          (*
           (- x 2.0)
           (+
            (*
             x
             (+
              (*
               x
               (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
              y))
            z))
          t_0)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+305)))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/
        (+
         101.7851458539211
         (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
        x)))
     (/
      (*
       (- x 2.0)
       (+
        z
        (*
         x
         (+
          y
          (*
           x
           (+
            137.519416416
            (* x (* x (+ 4.16438922228 (/ 78.6994924154 x))))))))))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+305)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * (x * (4.16438922228 + (78.6994924154 / x)))))))))) / t_0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+305)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * (x * (4.16438922228 + (78.6994924154 / x)))))))))) / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+305):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x))
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * (x * (4.16438922228 + (78.6994924154 / x)))))))))) / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+305))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(x * Float64(4.16438922228 + Float64(78.6994924154 / x)))))))))) / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+305)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * (x * (4.16438922228 + (78.6994924154 / x)))))))))) / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+305]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(x * N[(4.16438922228 + N[(78.6994924154 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < -inf.0 or 5.00000000000000009e305 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 7.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 7.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 7.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 7.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 7.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 5.00000000000000009e305

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot 4.16438922228} \cdot \sqrt[3]{x \cdot 4.16438922228}\right) \cdot \sqrt[3]{x \cdot 4.16438922228}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      2. pow3 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot 4.16438922228}\right)}^{3}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot 4.16438922228}\right)}^{3}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Taylor expanded in x around inf 99.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\left(x \cdot \left(78.6994924154 \cdot \frac{1}{x} + {\left(\sqrt[3]{4.16438922228}\right)}^{3}\right)\right)} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   6. Step-by-step derivation

      1. rem-cube-cbrt 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \left(78.6994924154 \cdot \frac{1}{x} + \color{blue}{4.16438922228}\right)\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      2. +-commutative 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \color{blue}{\left(4.16438922228 + 78.6994924154 \cdot \frac{1}{x}\right)}\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. associate-*r/ 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \left(4.16438922228 + \color{blue}{\frac{78.6994924154 \cdot 1}{x}}\right)\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. metadata-eval 99.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \left(4.16438922228 + \frac{\color{blue}{78.6994924154}}{x}\right)\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   7. Simplified 99.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\left(x \cdot \left(4.16438922228 + \frac{78.6994924154}{x}\right)\right)} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty \lor \neg \left(\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot \left(4.16438922228 + \frac{78.6994924154}{x}\right)\right)\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           (- x 2.0)
           (+
            (*
             x
             (+
              (*
               x
               (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
              y))
            z))
          (+
           (*
            x
            (+
             (* x (+ (* x (+ x 43.3400022514)) 263.505074721))
             313.399215894))
           47.066876606))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+305)))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/
        (+
         101.7851458539211
         (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
        x)))
     t_0)))

C

double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 5e+305)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if ((t_0 <= -Double.POSITIVE_INFINITY) || !(t_0 <= 5e+305)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0
	if (t_0 <= -math.inf) or not (t_0 <= 5e+305):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606))
	tmp = 0.0
	if ((t_0 <= Float64(-Inf)) || !(t_0 <= 5e+305))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	tmp = 0.0;
	if ((t_0 <= -Inf) || ~((t_0 <= 5e+305)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 5e+305]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < -inf.0 or 5.00000000000000009e305 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 7.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 7.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 7.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 7.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 7.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 7.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 99.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 99.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 5.00000000000000009e305

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty \lor \neg \left(\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+33}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{elif}\;x \leq 114000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414 + \left(\frac{y}{x} + 130977.50649958357 \cdot \frac{-1}{x}\right)}{x} - 110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e+33)
   (*
    (+ x -2.0)
    (-
     4.16438922228
     (/
      (+
       101.7851458539211
       (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
      x)))
   (if (<= x 114000.0)
     (/
      (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
      (+
       (*
        x
        (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
       47.066876606))
     (*
      x
      (+
       4.16438922228
       (/
        (-
         (/
          (+ 3655.1204654076414 (+ (/ y x) (* 130977.50649958357 (/ -1.0 x))))
          x)
         110.1139242984811)
        x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e+33) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else if (x <= 114000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = x * (4.16438922228 + ((((3655.1204654076414 + ((y / x) + (130977.50649958357 * (-1.0 / x)))) / x) - 110.1139242984811) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.6d+33)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((((124074.40615218398d0 - y) / x) - 3451.550173699799d0) / x)) / x))
    else if (x <= 114000.0d0) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else
        tmp = x * (4.16438922228d0 + ((((3655.1204654076414d0 + ((y / x) + (130977.50649958357d0 * ((-1.0d0) / x)))) / x) - 110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e+33) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else if (x <= 114000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = x * (4.16438922228 + ((((3655.1204654076414 + ((y / x) + (130977.50649958357 * (-1.0 / x)))) / x) - 110.1139242984811) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e+33:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x))
	elif x <= 114000.0:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	else:
		tmp = x * (4.16438922228 + ((((3655.1204654076414 + ((y / x) + (130977.50649958357 * (-1.0 / x)))) / x) - 110.1139242984811) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e+33)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	elseif (x <= 114000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3655.1204654076414 + Float64(Float64(y / x) + Float64(130977.50649958357 * Float64(-1.0 / x)))) / x) - 110.1139242984811) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e+33)
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	elseif (x <= 114000.0)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = x * (4.16438922228 + ((((3655.1204654076414 + ((y / x) + (130977.50649958357 * (-1.0 / x)))) / x) - 110.1139242984811) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e+33], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 114000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(N[(N[(N[(3655.1204654076414 + N[(N[(y / x), $MachinePrecision] + N[(130977.50649958357 * N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.60000000000000009e33

   1. Initial program 10.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 20.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 20.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 20.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 20.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 20.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 20.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 20.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 20.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 20.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 20.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 97.4%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 97.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 97.4%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 97.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 97.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 97.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 97.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 97.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 97.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 97.4%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -1.60000000000000009e33 < x < 114000

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.8%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{137.519416416 \cdot x} + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   4. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot 137.519416416} + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Simplified 97.8%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot 137.519416416} + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   if 114000 < x

   1. Initial program 19.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 21.1%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 21.1%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 21.1%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 21.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 21.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 21.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 21.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 21.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 21.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 21.1%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 21.1%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 97.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+33}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{elif}\;x \leq 114000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414 + \left(\frac{y}{x} + 130977.50649958357 \cdot \frac{-1}{x}\right)}{x} - 110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -53 \lor \neg \left(x \leq 48\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -53.0) (not (<= x 48.0)))
   (*
    (+ x -2.0)
    (-
     4.16438922228
     (/
      (+
       101.7851458539211
       (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
      x)))
   (/
    (* (- x 2.0) (+ z (* x (+ y (* x (+ 137.519416416 (* x 78.6994924154)))))))
    (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -53.0) || !(x <= 48.0)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-53.0d0)) .or. (.not. (x <= 48.0d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((((124074.40615218398d0 - y) / x) - 3451.550173699799d0) / x)) / x))
    else
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * (137.519416416d0 + (x * 78.6994924154d0))))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -53.0) || !(x <= 48.0)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -53.0) or not (x <= 48.0):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x))
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -53.0) || !(x <= 48.0))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * 78.6994924154))))))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -53.0) || ~((x <= 48.0)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -53.0], N[Not[LessEqual[x, 48.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -53 or 48 < x

   1. Initial program 20.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 26.1%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 26.1%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 26.1%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 26.1%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 26.1%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 94.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 94.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -53 < x < 48

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{263.505074721 \cdot x} + 313.399215894\right) \cdot x + 47.066876606} \]
   4. Step-by-step derivation

      1. *-commutative 98.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{x \cdot 263.505074721} + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Simplified 98.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{x \cdot 263.505074721} + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0 98.5%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot \left(137.519416416 + 78.6994924154 \cdot x\right)} + y\right) \cdot x + z\right)}{\left(x \cdot 263.505074721 + 313.399215894\right) \cdot x + 47.066876606} \]
   7. Step-by-step derivation

      1. *-commutative 98.5%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(x \cdot \left(137.519416416 + \color{blue}{x \cdot 78.6994924154}\right) + y\right) \cdot x + z\right)}{\left(x \cdot 263.505074721 + 313.399215894\right) \cdot x + 47.066876606} \]

   8. Simplified 98.5%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)} + y\right) \cdot x + z\right)}{\left(x \cdot 263.505074721 + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -53 \lor \neg \left(x \leq 48\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -116 \lor \neg \left(x \leq 110\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -116.0) (not (<= x 110.0)))
   (*
    (+ x -2.0)
    (-
     4.16438922228
     (/
      (+
       101.7851458539211
       (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
      x)))
   (/
    (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
    (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -116.0) || !(x <= 110.0)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-116.0d0)) .or. (.not. (x <= 110.0d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((((124074.40615218398d0 - y) / x) - 3451.550173699799d0) / x)) / x))
    else
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -116.0) || !(x <= 110.0)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -116.0) or not (x <= 110.0):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x))
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -116.0) || !(x <= 110.0))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -116.0) || ~((x <= 110.0)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -116.0], N[Not[LessEqual[x, 110.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -116 or 110 < x

   1. Initial program 20.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 26.1%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 26.1%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 26.1%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 26.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 26.1%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 26.1%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 94.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 94.3%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 94.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -116 < x < 110

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{263.505074721 \cdot x} + 313.399215894\right) \cdot x + 47.066876606} \]
   4. Step-by-step derivation

      1. *-commutative 98.6%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{x \cdot 263.505074721} + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Simplified 98.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{x \cdot 263.505074721} + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0 98.0%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{137.519416416 \cdot x} + y\right) \cdot x + z\right)}{\left(x \cdot 263.505074721 + 313.399215894\right) \cdot x + 47.066876606} \]
   7. Step-by-step derivation

      1. *-commutative 99.0%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot 137.519416416} + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   8. Simplified 98.0%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot 137.519416416} + y\right) \cdot x + z\right)}{\left(x \cdot 263.505074721 + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -116 \lor \neg \left(x \leq 110\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 0.212\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 - x \cdot \left(z \cdot 0.14147091005106402 - y \cdot 0.0212463641547976\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5) (not (<= x 0.212)))
   (*
    (+ x -2.0)
    (-
     4.16438922228
     (/
      (+
       101.7851458539211
       (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
      x)))
   (*
    (+ x -2.0)
    (-
     (* z 0.0212463641547976)
     (* x (- (* z 0.14147091005106402) (* y 0.0212463641547976)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 0.212)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) - (x * ((z * 0.14147091005106402) - (y * 0.0212463641547976))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.5d0)) .or. (.not. (x <= 0.212d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((((124074.40615218398d0 - y) / x) - 3451.550173699799d0) / x)) / x))
    else
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) - (x * ((z * 0.14147091005106402d0) - (y * 0.0212463641547976d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 0.212)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	} else {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) - (x * ((z * 0.14147091005106402) - (y * 0.0212463641547976))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5) or not (x <= 0.212):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x))
	else:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) - (x * ((z * 0.14147091005106402) - (y * 0.0212463641547976))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5) || !(x <= 0.212))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) - Float64(x * Float64(Float64(z * 0.14147091005106402) - Float64(y * 0.0212463641547976)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5) || ~((x <= 0.212)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	else
		tmp = (x + -2.0) * ((z * 0.0212463641547976) - (x * ((z * 0.14147091005106402) - (y * 0.0212463641547976))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5], N[Not[LessEqual[x, 0.212]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] - N[(x * N[(N[(z * 0.14147091005106402), $MachinePrecision] - N[(y * 0.0212463641547976), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 0.211999999999999994 < x

   1. Initial program 21.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 26.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 26.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 26.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 26.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 26.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 93.5%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 93.5%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 93.5%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 93.5%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 93.5%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 93.5%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 93.5%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 93.5%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 93.5%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 93.5%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -5.5 < x < 0.211999999999999994

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 91.8%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z + x \cdot \left(0.0212463641547976 \cdot y - 0.14147091005106402 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 0.212\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 - x \cdot \left(z \cdot 0.14147091005106402 - y \cdot 0.0212463641547976\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -42000 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 - x \cdot \left(z \cdot 0.14147091005106402 - y \cdot 0.0212463641547976\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -42000.0) (not (<= x 5200.0)))
   (*
    (+ x -2.0)
    (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x)))
   (*
    (+ x -2.0)
    (-
     (* z 0.0212463641547976)
     (* x (- (* z 0.14147091005106402) (* y 0.0212463641547976)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42000.0) || !(x <= 5200.0)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) - (x * ((z * 0.14147091005106402) - (y * 0.0212463641547976))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-42000.0d0)) .or. (.not. (x <= 5200.0d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    else
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) - (x * ((z * 0.14147091005106402d0) - (y * 0.0212463641547976d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42000.0) || !(x <= 5200.0)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) - (x * ((z * 0.14147091005106402) - (y * 0.0212463641547976))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -42000.0) or not (x <= 5200.0):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	else:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) - (x * ((z * 0.14147091005106402) - (y * 0.0212463641547976))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -42000.0) || !(x <= 5200.0))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) - Float64(x * Float64(Float64(z * 0.14147091005106402) - Float64(y * 0.0212463641547976)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -42000.0) || ~((x <= 5200.0)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	else
		tmp = (x + -2.0) * ((z * 0.0212463641547976) - (x * ((z * 0.14147091005106402) - (y * 0.0212463641547976))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -42000.0], N[Not[LessEqual[x, 5200.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] - N[(x * N[(N[(z * 0.14147091005106402), $MachinePrecision] - N[(y * 0.0212463641547976), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -42000 or 5200 < x

   1. Initial program 19.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 24.8%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 24.8%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 24.8%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 24.8%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 24.8%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 24.8%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 24.8%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 24.8%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 24.8%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 24.8%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 24.8%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 87.8%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 87.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)}\right) \]

      2. unsub-neg 87.8%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

      3. sub-neg 87.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 + \left(-3451.550173699799 \cdot \frac{1}{x}\right)}}{x}\right) \]

      4. associate-*r/ 87.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\color{blue}{\frac{3451.550173699799 \cdot 1}{x}}\right)}{x}\right) \]

      5. metadata-eval 87.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\frac{\color{blue}{3451.550173699799}}{x}\right)}{x}\right) \]

      6. distribute-neg-frac 87.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\frac{-3451.550173699799}{x}}}{x}\right) \]

      7. metadata-eval 87.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\color{blue}{-3451.550173699799}}{x}}{x}\right) \]

   7. Simplified 87.8%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)} \]

   if -42000 < x < 5200

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 90.0%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z + x \cdot \left(0.0212463641547976 \cdot y - 0.14147091005106402 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -42000 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 - x \cdot \left(z \cdot 0.14147091005106402 - y \cdot 0.0212463641547976\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -42000 \lor \neg \left(x \leq 0.00037\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 - y \cdot -0.0424927283095952\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -42000.0) (not (<= x 0.00037)))
   (*
    (+ x -2.0)
    (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x)))
   (-
    (* z -0.0424927283095952)
    (* x (- (* z -0.28294182010212804) (* y -0.0424927283095952))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42000.0) || !(x <= 0.00037)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else {
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (y * -0.0424927283095952)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-42000.0d0)) .or. (.not. (x <= 0.00037d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    else
        tmp = (z * (-0.0424927283095952d0)) - (x * ((z * (-0.28294182010212804d0)) - (y * (-0.0424927283095952d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42000.0) || !(x <= 0.00037)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else {
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (y * -0.0424927283095952)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -42000.0) or not (x <= 0.00037):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	else:
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (y * -0.0424927283095952)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -42000.0) || !(x <= 0.00037))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	else
		tmp = Float64(Float64(z * -0.0424927283095952) - Float64(x * Float64(Float64(z * -0.28294182010212804) - Float64(y * -0.0424927283095952))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -42000.0) || ~((x <= 0.00037)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	else
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (y * -0.0424927283095952)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -42000.0], N[Not[LessEqual[x, 0.00037]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * -0.0424927283095952), $MachinePrecision] - N[(x * N[(N[(z * -0.28294182010212804), $MachinePrecision] - N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -42000 or 3.6999999999999999e-4 < x

   1. Initial program 21.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 26.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 26.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 26.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 26.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 26.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 26.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 85.7%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 85.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)}\right) \]

      2. unsub-neg 85.7%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

      3. sub-neg 85.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 + \left(-3451.550173699799 \cdot \frac{1}{x}\right)}}{x}\right) \]

      4. associate-*r/ 85.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\color{blue}{\frac{3451.550173699799 \cdot 1}{x}}\right)}{x}\right) \]

      5. metadata-eval 85.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\frac{\color{blue}{3451.550173699799}}{x}\right)}{x}\right) \]

      6. distribute-neg-frac 85.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\frac{-3451.550173699799}{x}}}{x}\right) \]

      7. metadata-eval 85.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\color{blue}{-3451.550173699799}}{x}}{x}\right) \]

   7. Simplified 85.7%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)} \]

   if -42000 < x < 3.6999999999999999e-4

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 91.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   6. Taylor expanded in z around 0 91.9%

      \[\leadsto -0.0424927283095952 \cdot z + x \cdot \left(\color{blue}{-0.0424927283095952 \cdot y} - -0.28294182010212804 \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -42000 \lor \neg \left(x \leq 0.00037\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 - y \cdot -0.0424927283095952\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -45000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right) + z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -45000.0) (not (<= x 2.0)))
   (*
    (+ x -2.0)
    (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x)))
   (+ (* -0.0424927283095952 (* x y)) (* z -0.0424927283095952))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -45000.0) || !(x <= 2.0)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else {
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-45000.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    else
        tmp = ((-0.0424927283095952d0) * (x * y)) + (z * (-0.0424927283095952d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -45000.0) || !(x <= 2.0)) {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else {
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -45000.0) or not (x <= 2.0):
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	else:
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -45000.0) || !(x <= 2.0))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	else
		tmp = Float64(Float64(-0.0424927283095952 * Float64(x * y)) + Float64(z * -0.0424927283095952));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -45000.0) || ~((x <= 2.0)))
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	else
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -45000.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -45000 or 2 < x

   1. Initial program 19.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 25.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 25.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 25.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 25.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 87.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 87.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)}\right) \]

      2. unsub-neg 87.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

      3. sub-neg 87.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 + \left(-3451.550173699799 \cdot \frac{1}{x}\right)}}{x}\right) \]

      4. associate-*r/ 87.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\color{blue}{\frac{3451.550173699799 \cdot 1}{x}}\right)}{x}\right) \]

      5. metadata-eval 87.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\frac{\color{blue}{3451.550173699799}}{x}\right)}{x}\right) \]

      6. distribute-neg-frac 87.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\frac{-3451.550173699799}{x}}}{x}\right) \]

      7. metadata-eval 87.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\color{blue}{-3451.550173699799}}{x}}{x}\right) \]

   7. Simplified 87.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)} \]

   if -45000 < x < 2

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 90.6%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   6. Taylor expanded in z around 0 90.6%

      \[\leadsto -0.0424927283095952 \cdot z + \color{blue}{-0.0424927283095952 \cdot \left(x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -45000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right) + z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -42000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(\frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x} - -4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right) + z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -42000.0) (not (<= x 2.0)))
   (*
    x
    (- (/ (+ (/ 3655.1204654076414 x) -110.1139242984811) x) -4.16438922228))
   (+ (* -0.0424927283095952 (* x y)) (* z -0.0424927283095952))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42000.0) || !(x <= 2.0)) {
		tmp = x * ((((3655.1204654076414 / x) + -110.1139242984811) / x) - -4.16438922228);
	} else {
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-42000.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = x * ((((3655.1204654076414d0 / x) + (-110.1139242984811d0)) / x) - (-4.16438922228d0))
    else
        tmp = ((-0.0424927283095952d0) * (x * y)) + (z * (-0.0424927283095952d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42000.0) || !(x <= 2.0)) {
		tmp = x * ((((3655.1204654076414 / x) + -110.1139242984811) / x) - -4.16438922228);
	} else {
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -42000.0) or not (x <= 2.0):
		tmp = x * ((((3655.1204654076414 / x) + -110.1139242984811) / x) - -4.16438922228)
	else:
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -42000.0) || !(x <= 2.0))
		tmp = Float64(x * Float64(Float64(Float64(Float64(3655.1204654076414 / x) + -110.1139242984811) / x) - -4.16438922228));
	else
		tmp = Float64(Float64(-0.0424927283095952 * Float64(x * y)) + Float64(z * -0.0424927283095952));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -42000.0) || ~((x <= 2.0)))
		tmp = x * ((((3655.1204654076414 / x) + -110.1139242984811) / x) - -4.16438922228);
	else
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -42000.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(x * N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + -110.1139242984811), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision], N[(N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -42000 or 2 < x

   1. Initial program 19.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 25.5%

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{137.519416416 + x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)}, y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

   6. Taylor expanded in x around -inf 87.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   8. Simplified 87.1%

      \[\leadsto \color{blue}{x \cdot \left(-\left(-4.16438922228 - \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\right)} \]

   if -42000 < x < 2

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 90.6%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   6. Taylor expanded in z around 0 90.6%

      \[\leadsto -0.0424927283095952 \cdot z + \color{blue}{-0.0424927283095952 \cdot \left(x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -42000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(\frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x} - -4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right) + z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 89.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -42000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right) + z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -42000.0) (not (<= x 2.0)))
   (* (+ x -2.0) (- 4.16438922228 (/ 101.7851458539211 x)))
   (+ (* -0.0424927283095952 (* x y)) (* z -0.0424927283095952))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42000.0) || !(x <= 2.0)) {
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else {
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-42000.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - (101.7851458539211d0 / x))
    else
        tmp = ((-0.0424927283095952d0) * (x * y)) + (z * (-0.0424927283095952d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -42000.0) || !(x <= 2.0)) {
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else {
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -42000.0) or not (x <= 2.0):
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x))
	else:
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -42000.0) || !(x <= 2.0))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	else
		tmp = Float64(Float64(-0.0424927283095952 * Float64(x * y)) + Float64(z * -0.0424927283095952));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -42000.0) || ~((x <= 2.0)))
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	else
		tmp = (-0.0424927283095952 * (x * y)) + (z * -0.0424927283095952);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -42000.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -42000 or 2 < x

   1. Initial program 19.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 25.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 25.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 25.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 25.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 86.6%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{101.7851458539211 \cdot 1}{x}}\right) \]

      2. metadata-eval 86.6%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211}}{x}\right) \]

   7. Simplified 86.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211}{x}\right)} \]

   if -42000 < x < 2

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 90.6%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   6. Taylor expanded in z around 0 90.6%

      \[\leadsto -0.0424927283095952 \cdot z + \color{blue}{-0.0424927283095952 \cdot \left(x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -42000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right) + z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.16 \lor \neg \left(x \leq 5800\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.16) (not (<= x 5800.0)))
   (* (+ x -2.0) (- 4.16438922228 (/ 101.7851458539211 x)))
   (* (+ x -2.0) (* z 0.0212463641547976))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.16) || !(x <= 5800.0)) {
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.16d0)) .or. (.not. (x <= 5800.0d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - (101.7851458539211d0 / x))
    else
        tmp = (x + (-2.0d0)) * (z * 0.0212463641547976d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.16) || !(x <= 5800.0)) {
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.16) or not (x <= 5800.0):
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x))
	else:
		tmp = (x + -2.0) * (z * 0.0212463641547976)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.16) || !(x <= 5800.0))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(z * 0.0212463641547976));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.16) || ~((x <= 5800.0)))
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	else
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.16], N[Not[LessEqual[x, 5800.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.160000000000000003 or 5800 < x

   1. Initial program 19.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 25.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 25.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 25.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 25.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 86.6%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{101.7851458539211 \cdot 1}{x}}\right) \]

      2. metadata-eval 86.6%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211}}{x}\right) \]

   7. Simplified 86.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211}{x}\right)} \]

   if -0.160000000000000003 < x < 5800

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.7%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.16 \lor \neg \left(x \leq 5800\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.192 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.192) (not (<= x 5200.0)))
   (* x (- 4.16438922228 (/ 110.1139242984811 x)))
   (* (+ x -2.0) (* z 0.0212463641547976))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.192) || !(x <= 5200.0)) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.192d0)) .or. (.not. (x <= 5200.0d0))) then
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    else
        tmp = (x + (-2.0d0)) * (z * 0.0212463641547976d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.192) || !(x <= 5200.0)) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.192) or not (x <= 5200.0):
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	else:
		tmp = (x + -2.0) * (z * 0.0212463641547976)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.192) || !(x <= 5200.0))
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(z * 0.0212463641547976));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.192) || ~((x <= 5200.0)))
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	else
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.192], N[Not[LessEqual[x, 5200.0]], $MachinePrecision]], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.192 or 5200 < x

   1. Initial program 19.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 25.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 25.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 25.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 25.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.6%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 86.6%

         \[\leadsto x \cdot \left(4.16438922228 - \color{blue}{\frac{110.1139242984811 \cdot 1}{x}}\right) \]

      2. metadata-eval 86.6%

         \[\leadsto x \cdot \left(4.16438922228 - \frac{\color{blue}{110.1139242984811}}{x}\right) \]

   7. Simplified 86.6%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]

   if -0.192 < x < 5200

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.7%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.192 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 76.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -60 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -60.0) (not (<= x 5200.0)))
   (* x (- 4.16438922228 (/ 110.1139242984811 x)))
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -60.0) || !(x <= 5200.0)) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-60.0d0)) .or. (.not. (x <= 5200.0d0))) then
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -60.0) || !(x <= 5200.0)) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -60.0) or not (x <= 5200.0):
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -60.0) || !(x <= 5200.0))
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -60.0) || ~((x <= 5200.0)))
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -60.0], N[Not[LessEqual[x, 5200.0]], $MachinePrecision]], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -60 or 5200 < x

   1. Initial program 19.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 25.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 25.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 25.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 25.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.6%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 86.6%

         \[\leadsto x \cdot \left(4.16438922228 - \color{blue}{\frac{110.1139242984811 \cdot 1}{x}}\right) \]

      2. metadata-eval 86.6%

         \[\leadsto x \cdot \left(4.16438922228 - \frac{\color{blue}{110.1139242984811}}{x}\right) \]

   7. Simplified 86.6%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]

   if -60 < x < 5200

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.7%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 66.7%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   7. Simplified 66.7%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -60 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 76.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5) (not (<= x 5200.0)))
   (* 4.16438922228 (+ x -2.0))
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 5200.0)) {
		tmp = 4.16438922228 * (x + -2.0);
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.5d0)) .or. (.not. (x <= 5200.0d0))) then
        tmp = 4.16438922228d0 * (x + (-2.0d0))
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 5200.0)) {
		tmp = 4.16438922228 * (x + -2.0);
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5) or not (x <= 5200.0):
		tmp = 4.16438922228 * (x + -2.0)
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5) || !(x <= 5200.0))
		tmp = Float64(4.16438922228 * Float64(x + -2.0));
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5) || ~((x <= 5200.0)))
		tmp = 4.16438922228 * (x + -2.0);
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5], N[Not[LessEqual[x, 5200.0]], $MachinePrecision]], N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 5200 < x

   1. Initial program 19.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 25.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 25.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 25.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 25.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{4.16438922228} \]

   if -5.5 < x < 5200

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.7%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 66.7%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   7. Simplified 66.7%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 76.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -470 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -470.0) (not (<= x 5200.0)))
   (* x 4.16438922228)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -470.0) || !(x <= 5200.0)) {
		tmp = x * 4.16438922228;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-470.0d0)) .or. (.not. (x <= 5200.0d0))) then
        tmp = x * 4.16438922228d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -470.0) || !(x <= 5200.0)) {
		tmp = x * 4.16438922228;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -470.0) or not (x <= 5200.0):
		tmp = x * 4.16438922228
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -470.0) || !(x <= 5200.0))
		tmp = Float64(x * 4.16438922228);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -470.0) || ~((x <= 5200.0)))
		tmp = x * 4.16438922228;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -470.0], N[Not[LessEqual[x, 5200.0]], $MachinePrecision]], N[(x * 4.16438922228), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -470 or 5200 < x

   1. Initial program 19.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 25.5%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 25.5%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 25.5%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 25.5%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 25.5%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.1%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative 86.1%

         \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -470 < x < 5200

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.7%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 66.7%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   7. Simplified 66.7%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -470 \lor \neg \left(x \leq 5200\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 45.8% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 4.16438922228 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 4.16438922228))

C

double code(double x, double y, double z) {
	return x * 4.16438922228;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * 4.16438922228d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 4.16438922228;
}

Python

def code(x, y, z):
	return x * 4.16438922228

Julia

function code(x, y, z)
	return Float64(x * 4.16438922228)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 4.16438922228;
end

Wolfram

code[x_, y_, z_] := N[(x * 4.16438922228), $MachinePrecision]

Derivation

1. Initial program 63.2%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
2. Step-by-step derivation

   1. associate-/l* 65.8%

      \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

   2. sub-neg 65.8%

      \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   3. metadata-eval 65.8%

      \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   4. fma-define 65.8%

      \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. fma-define 65.8%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. fma-define 65.8%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   7. fma-define 65.8%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   8. fma-define 65.8%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

   9. fma-define 65.8%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

   10. fma-define 65.8%

       \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

3. Simplified 65.8%

   \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 41.2%

   \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
6. Step-by-step derivation

   1. *-commutative 41.2%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

7. Simplified 41.2%

   \[\leadsto \color{blue}{x \cdot 4.16438922228} \]
8. Add Preprocessing

Developer Target 1: 98.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))
   (if (< x -3.326128725870005e+62)
     t_0
     (if (< x 9.429991714554673e+55)
       (*
        (/ (- x 2.0) 1.0)
        (/
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z)
         (+
          (*
           (+
            (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x))))
            313.399215894)
           x)
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * x)))) + 313.399215894d0) * x) + 47.066876606d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811
	tmp = 0
	if x < -3.326128725870005e+62:
		tmp = t_0
	elif x < 9.429991714554673e+55:
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / Float64(Float64(Float64(Float64(Float64(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -332612872587000500000000000000000000000000000000000000000000000) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000) (if (< x 94299917145546730000000000000000000000000000000000000000) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (+ (* (+ (+ (* 263505074721/1000000000 x) (+ (* 216700011257/5000000000 (* x x)) (* x (* x x)))) 156699607947/500000000) x) 23533438303/500000000))) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000))))

  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))