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

Percentage Accurate: 69.5% → 99.4%

Time: 12.8s

Alternatives: 12

Speedup: 2.1×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

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 + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Python

def code(x, y, z):
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

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 + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Python

def code(x, y, z):
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)\\ t_1 := 0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\\ \mathbf{if}\;\frac{y \cdot t\_1}{t\_0} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{t\_0}{t\_1}} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 3.350343815022304 (* z (+ z 6.012459259764103))))
        (t_1
         (+
          0.279195317918525
          (* z (+ (* z 0.0692910599291889) 0.4917317610505968)))))
   (if (<= (/ (* y t_1) t_0) INFINITY)
     (+ (/ y (/ t_0 t_1)) x)
     (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	double t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	double tmp;
	if (((y * t_1) / t_0) <= ((double) INFINITY)) {
		tmp = (y / (t_0 / t_1)) + x;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	double t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	double tmp;
	if (((y * t_1) / t_0) <= Double.POSITIVE_INFINITY) {
		tmp = (y / (t_0 / t_1)) + x;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 3.350343815022304 + (z * (z + 6.012459259764103))
	t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968))
	tmp = 0
	if ((y * t_1) / t_0) <= math.inf:
		tmp = (y / (t_0 / t_1)) + x
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(3.350343815022304 + Float64(z * Float64(z + 6.012459259764103)))
	t_1 = Float64(0.279195317918525 + Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)))
	tmp = 0.0
	if (Float64(Float64(y * t_1) / t_0) <= Inf)
		tmp = Float64(Float64(y / Float64(t_0 / t_1)) + x);
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	tmp = 0.0;
	if (((y * t_1) / t_0) <= Inf)
		tmp = (y / (t_0 / t_1)) + x;
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(3.350343815022304 + N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.279195317918525 + N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], Infinity], N[(N[(y / N[(t$95$0 / t$95$1), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))) < +inf.0

   1. Initial program 94.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), \color{blue}{x}\right) \]

   4. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525}} + x} \]

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))

   1. Initial program 0.0%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)}{0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)}} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)\\ t_1 := 0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\\ \mathbf{if}\;\frac{y \cdot t\_1}{t\_0} \leq \infty:\\ \;\;\;\;x + t\_1 \cdot \frac{y}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 3.350343815022304 (* z (+ z 6.012459259764103))))
        (t_1
         (+
          0.279195317918525
          (* z (+ (* z 0.0692910599291889) 0.4917317610505968)))))
   (if (<= (/ (* y t_1) t_0) INFINITY)
     (+ x (* t_1 (/ y t_0)))
     (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	double t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	double tmp;
	if (((y * t_1) / t_0) <= ((double) INFINITY)) {
		tmp = x + (t_1 * (y / t_0));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	double t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	double tmp;
	if (((y * t_1) / t_0) <= Double.POSITIVE_INFINITY) {
		tmp = x + (t_1 * (y / t_0));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 3.350343815022304 + (z * (z + 6.012459259764103))
	t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968))
	tmp = 0
	if ((y * t_1) / t_0) <= math.inf:
		tmp = x + (t_1 * (y / t_0))
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(3.350343815022304 + Float64(z * Float64(z + 6.012459259764103)))
	t_1 = Float64(0.279195317918525 + Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)))
	tmp = 0.0
	if (Float64(Float64(y * t_1) / t_0) <= Inf)
		tmp = Float64(x + Float64(t_1 * Float64(y / t_0)));
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	tmp = 0.0;
	if (((y * t_1) / t_0) <= Inf)
		tmp = x + (t_1 * (y / t_0));
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(3.350343815022304 + N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.279195317918525 + N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], Infinity], N[(x + N[(t$95$1 * N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))) < +inf.0

   1. Initial program 94.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot y}{\color{blue}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z} + \frac{104698244219447}{31250000000000}}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot \color{blue}{\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right), \color{blue}{\left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{\color{blue}{y}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}\right)}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z\right), \color{blue}{\frac{104698244219447}{31250000000000}}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right)\right) \]

      13. +-lowering-+.f64 98.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right)\right) \]

   4. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{\left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right) \cdot \frac{y}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}} \]

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))

   1. Initial program 0.0%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)} \leq \infty:\\ \;\;\;\;x + \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right) \cdot \frac{y}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 0.0692910599291889\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0 + \frac{\frac{y \cdot -0.4046220386999212}{z} - y \cdot -0.07512208616047561}{z}\\ \mathbf{elif}\;z \leq 4.1:\\ \;\;\;\;x + \left(z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right) + y \cdot 0.08333333333333323\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 0.0692910599291889))))
   (if (<= z -5.4)
     (+
      t_0
      (/ (- (/ (* y -0.4046220386999212) z) (* y -0.07512208616047561)) z))
     (if (<= z 4.1)
       (+
        x
        (+
         (* z (+ (* y -0.00277777777751721) (* z (* y 0.0007936505811533442))))
         (* y 0.08333333333333323)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0 + ((((y * -0.4046220386999212) / z) - (y * -0.07512208616047561)) / z);
	} else if (z <= 4.1) {
		tmp = x + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + (y * 0.08333333333333323));
	} 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 = x + (y * 0.0692910599291889d0)
    if (z <= (-5.4d0)) then
        tmp = t_0 + ((((y * (-0.4046220386999212d0)) / z) - (y * (-0.07512208616047561d0))) / z)
    else if (z <= 4.1d0) then
        tmp = x + ((z * ((y * (-0.00277777777751721d0)) + (z * (y * 0.0007936505811533442d0)))) + (y * 0.08333333333333323d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0 + ((((y * -0.4046220386999212) / z) - (y * -0.07512208616047561)) / z);
	} else if (z <= 4.1) {
		tmp = x + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + (y * 0.08333333333333323));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 0.0692910599291889)
	tmp = 0
	if z <= -5.4:
		tmp = t_0 + ((((y * -0.4046220386999212) / z) - (y * -0.07512208616047561)) / z)
	elif z <= 4.1:
		tmp = x + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + (y * 0.08333333333333323))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 0.0692910599291889))
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(t_0 + Float64(Float64(Float64(Float64(y * -0.4046220386999212) / z) - Float64(y * -0.07512208616047561)) / z));
	elseif (z <= 4.1)
		tmp = Float64(x + Float64(Float64(z * Float64(Float64(y * -0.00277777777751721) + Float64(z * Float64(y * 0.0007936505811533442)))) + Float64(y * 0.08333333333333323)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 0.0692910599291889);
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0 + ((((y * -0.4046220386999212) / z) - (y * -0.07512208616047561)) / z);
	elseif (z <= 4.1)
		tmp = x + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + (y * 0.08333333333333323));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], N[(t$95$0 + N[(N[(N[(N[(y * -0.4046220386999212), $MachinePrecision] / z), $MachinePrecision] - N[(y * -0.07512208616047561), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1], N[(x + N[(N[(z * N[(N[(y * -0.00277777777751721), $MachinePrecision] + N[(z * N[(y * 0.0007936505811533442), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 39.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-1 \cdot \frac{\frac{11167812716741}{40000000000000} \cdot y - \left(\frac{-6012459259764103}{1000000000000000} \cdot \left(\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y\right) + \frac{72546523146905574025723165383}{312500000000000000000000000000} \cdot y\right)}{z} + \frac{-307332350656623}{625000000000000} \cdot y\right) - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)} \]

   5. Simplified 98.0%

      \[\leadsto \color{blue}{\left(x + y \cdot 0.0692910599291889\right) - \frac{y \cdot -0.07512208616047561 - \frac{y \cdot -0.4046220386999212}{z}}{z}} \]

   if -5.4000000000000004 < z < 4.0999999999999996

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(y \cdot 0.08333333333333323 + z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right)\right)} \]

   if 4.0999999999999996 < z

   1. Initial program 41.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;\left(x + y \cdot 0.0692910599291889\right) + \frac{\frac{y \cdot -0.4046220386999212}{z} - y \cdot -0.07512208616047561}{z}\\ \mathbf{elif}\;z \leq 4.1:\\ \;\;\;\;x + \left(z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right) + y \cdot 0.08333333333333323\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x - y \cdot \left(\frac{-0.07512208616047561}{z} - 0.0692910599291889\right)\\ \mathbf{elif}\;z \leq 4.4:\\ \;\;\;\;x + \left(z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right) + y \cdot 0.08333333333333323\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (- x (* y (- (/ -0.07512208616047561 z) 0.0692910599291889)))
   (if (<= z 4.4)
     (+
      x
      (+
       (* z (+ (* y -0.00277777777751721) (* z (* y 0.0007936505811533442))))
       (* y 0.08333333333333323)))
     (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	} else if (z <= 4.4) {
		tmp = x + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + (y * 0.08333333333333323));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	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 (z <= (-5.4d0)) then
        tmp = x - (y * (((-0.07512208616047561d0) / z) - 0.0692910599291889d0))
    else if (z <= 4.4d0) then
        tmp = x + ((z * ((y * (-0.00277777777751721d0)) + (z * (y * 0.0007936505811533442d0)))) + (y * 0.08333333333333323d0))
    else
        tmp = x + (y * 0.0692910599291889d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	} else if (z <= 4.4) {
		tmp = x + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + (y * 0.08333333333333323));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4:
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889))
	elif z <= 4.4:
		tmp = x + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + (y * 0.08333333333333323))
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(x - Float64(y * Float64(Float64(-0.07512208616047561 / z) - 0.0692910599291889)));
	elseif (z <= 4.4)
		tmp = Float64(x + Float64(Float64(z * Float64(Float64(y * -0.00277777777751721) + Float64(z * Float64(y * 0.0007936505811533442)))) + Float64(y * 0.08333333333333323)));
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4)
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	elseif (z <= 4.4)
		tmp = x + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + (y * 0.08333333333333323));
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(x - N[(y * N[(N[(-0.07512208616047561 / z), $MachinePrecision] - 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4], N[(x + N[(N[(z * N[(N[(y * -0.00277777777751721), $MachinePrecision] + N[(z * N[(y * 0.0007936505811533442), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 39.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      2. associate--l+ N/A

         \[\leadsto x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto x + \left(\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right) + \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y}\right) \]

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

         \[\leadsto x + \left(\frac{y}{z} \cdot \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right) + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      5. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{751220861604756070699018739433}{10000000000000000000000000000000} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      6. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-751220861604756070699018739433}{10000000000000000000000000000000}}{-1} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{-1} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      8. times-frac N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{z \cdot -1} + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      9. *-commutative N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{-1 \cdot z} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

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

          \[\leadsto x + \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{-1 \cdot z} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      12. distribute-neg-frac2 N/A

          \[\leadsto x + \left(\left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right) + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      13. mul-1-neg N/A

          \[\leadsto x + \left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      17. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

   5. Simplified 97.7%

      \[\leadsto \color{blue}{x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)} \]

   if -5.4000000000000004 < z < 4.4000000000000004

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(y \cdot 0.08333333333333323 + z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right)\right)} \]

   if 4.4000000000000004 < z

   1. Initial program 41.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x - y \cdot \left(\frac{-0.07512208616047561}{z} - 0.0692910599291889\right)\\ \mathbf{elif}\;z \leq 4.4:\\ \;\;\;\;x + \left(z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right) + y \cdot 0.08333333333333323\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x - y \cdot \left(\frac{-0.07512208616047561}{z} - 0.0692910599291889\right)\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;y \cdot 0.08333333333333323 + \left(x + z \cdot \left(y \cdot -0.00277777777751721\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (- x (* y (- (/ -0.07512208616047561 z) 0.0692910599291889)))
   (if (<= z 5.0)
     (+ (* y 0.08333333333333323) (+ x (* z (* y -0.00277777777751721))))
     (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	} else if (z <= 5.0) {
		tmp = (y * 0.08333333333333323) + (x + (z * (y * -0.00277777777751721)));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	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 (z <= (-5.4d0)) then
        tmp = x - (y * (((-0.07512208616047561d0) / z) - 0.0692910599291889d0))
    else if (z <= 5.0d0) then
        tmp = (y * 0.08333333333333323d0) + (x + (z * (y * (-0.00277777777751721d0))))
    else
        tmp = x + (y * 0.0692910599291889d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	} else if (z <= 5.0) {
		tmp = (y * 0.08333333333333323) + (x + (z * (y * -0.00277777777751721)));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4:
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889))
	elif z <= 5.0:
		tmp = (y * 0.08333333333333323) + (x + (z * (y * -0.00277777777751721)))
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(x - Float64(y * Float64(Float64(-0.07512208616047561 / z) - 0.0692910599291889)));
	elseif (z <= 5.0)
		tmp = Float64(Float64(y * 0.08333333333333323) + Float64(x + Float64(z * Float64(y * -0.00277777777751721))));
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4)
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	elseif (z <= 5.0)
		tmp = (y * 0.08333333333333323) + (x + (z * (y * -0.00277777777751721)));
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(x - N[(y * N[(N[(-0.07512208616047561 / z), $MachinePrecision] - 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.0], N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(x + N[(z * N[(y * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 39.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      2. associate--l+ N/A

         \[\leadsto x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto x + \left(\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right) + \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y}\right) \]

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

         \[\leadsto x + \left(\frac{y}{z} \cdot \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right) + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      5. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{751220861604756070699018739433}{10000000000000000000000000000000} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      6. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-751220861604756070699018739433}{10000000000000000000000000000000}}{-1} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{-1} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      8. times-frac N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{z \cdot -1} + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      9. *-commutative N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{-1 \cdot z} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

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

          \[\leadsto x + \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{-1 \cdot z} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      12. distribute-neg-frac2 N/A

          \[\leadsto x + \left(\left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right) + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      13. mul-1-neg N/A

          \[\leadsto x + \left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      17. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

   5. Simplified 97.7%

      \[\leadsto \color{blue}{x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)} \]

   if -5.4000000000000004 < z < 5

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}}\right)\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{1}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \cdot \color{blue}{\left(y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\frac{1}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{1}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \cdot y\right), \color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), y\right), \left(\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z} + \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}\right)\right), y\right), \left(\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)} \cdot z + \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \color{blue}{\frac{307332350656623}{625000000000000}}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(z \cdot \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \mathsf{+.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right), \color{blue}{\frac{11167812716741}{40000000000000}}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \mathsf{+.f64}\left(\left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right)\right)\right) \]

      15. *-lowering-*.f64 99.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right), y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right)\right)\right) \]

   4. Applied egg-rr 99.4%

      \[\leadsto x + \color{blue}{\left(\frac{1}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \cdot y\right) \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(\frac{279195317918525}{3350343815022304} \cdot y + x\right) + \color{blue}{z} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \]

      3. associate-+l+ N/A

         \[\leadsto \frac{279195317918525}{3350343815022304} \cdot y + \color{blue}{\left(x + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{279195317918525}{3350343815022304} \cdot y\right), \color{blue}{\left(x + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, y\right), \left(\color{blue}{x} + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, y\right), \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, y\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, y\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, y\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right)\right)\right)\right) \]

      10. metadata-eval 99.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, y\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-155900051080628738716045985239}{56124018394291031809500087342080}\right)\right)\right)\right) \]

   7. Simplified 99.2%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y + \left(x + z \cdot \left(y \cdot -0.00277777777751721\right)\right)} \]

   if 5 < z

   1. Initial program 41.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x - y \cdot \left(\frac{-0.07512208616047561}{z} - 0.0692910599291889\right)\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;y \cdot 0.08333333333333323 + \left(x + z \cdot \left(y \cdot -0.00277777777751721\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x - y \cdot \left(\frac{-0.07512208616047561}{z} - 0.0692910599291889\right)\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (- x (* y (- (/ -0.07512208616047561 z) 0.0692910599291889)))
   (if (<= z 5.0)
     (+ x (* y (+ 0.08333333333333323 (* z -0.00277777777751721))))
     (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	} else if (z <= 5.0) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	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 (z <= (-5.4d0)) then
        tmp = x - (y * (((-0.07512208616047561d0) / z) - 0.0692910599291889d0))
    else if (z <= 5.0d0) then
        tmp = x + (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0))))
    else
        tmp = x + (y * 0.0692910599291889d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	} else if (z <= 5.0) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4:
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889))
	elif z <= 5.0:
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)))
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(x - Float64(y * Float64(Float64(-0.07512208616047561 / z) - 0.0692910599291889)));
	elseif (z <= 5.0)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))));
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4)
		tmp = x - (y * ((-0.07512208616047561 / z) - 0.0692910599291889));
	elseif (z <= 5.0)
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(x - N[(y * N[(N[(-0.07512208616047561 / z), $MachinePrecision] - 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.0], N[(x + N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 39.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      2. associate--l+ N/A

         \[\leadsto x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto x + \left(\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right) + \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y}\right) \]

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

         \[\leadsto x + \left(\frac{y}{z} \cdot \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right) + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      5. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{751220861604756070699018739433}{10000000000000000000000000000000} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      6. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-751220861604756070699018739433}{10000000000000000000000000000000}}{-1} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{-1} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      8. times-frac N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{z \cdot -1} + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      9. *-commutative N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{-1 \cdot z} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

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

          \[\leadsto x + \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{-1 \cdot z} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} + \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      12. distribute-neg-frac2 N/A

          \[\leadsto x + \left(\left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right) + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      13. mul-1-neg N/A

          \[\leadsto x + \left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \color{blue}{\frac{692910599291889}{10000000000000000}} \cdot y\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      17. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

   5. Simplified 97.7%

      \[\leadsto \color{blue}{x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)} \]

   if -5.4000000000000004 < z < 5

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \color{blue}{z} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(y \cdot \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right) \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + y \cdot \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right), \color{blue}{z}\right)\right)\right)\right) \]

      10. metadata-eval 99.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(\frac{-155900051080628738716045985239}{56124018394291031809500087342080}, z\right)\right)\right)\right) \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{x + y \cdot \left(0.08333333333333323 + -0.00277777777751721 \cdot z\right)} \]

   if 5 < z

   1. Initial program 41.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x - y \cdot \left(\frac{-0.07512208616047561}{z} - 0.0692910599291889\right)\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 0.0692910599291889\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 0.0692910599291889))))
   (if (<= z -5.4)
     t_0
     (if (<= z 5.0)
       (+ x (* y (+ 0.08333333333333323 (* z -0.00277777777751721))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.0) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} 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 = x + (y * 0.0692910599291889d0)
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 5.0d0) then
        tmp = x + (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.0) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 0.0692910599291889)
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 5.0:
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 0.0692910599291889))
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.0)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 0.0692910599291889);
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.0)
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 5.0], N[(x + N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5 < z

   1. Initial program 40.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]

   if -5.4000000000000004 < z < 5

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \color{blue}{z} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(y \cdot \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right) \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + y \cdot \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right), \color{blue}{z}\right)\right)\right)\right) \]

      10. metadata-eval 99.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(\frac{-155900051080628738716045985239}{56124018394291031809500087342080}, z\right)\right)\right)\right) \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{x + y \cdot \left(0.08333333333333323 + -0.00277777777751721 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 0.0692910599291889\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 0.0692910599291889))))
   (if (<= z -5.4) t_0 (if (<= z 6.0) (+ x (* y 0.08333333333333323)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 6.0) {
		tmp = x + (y * 0.08333333333333323);
	} 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 = x + (y * 0.0692910599291889d0)
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 6.0d0) then
        tmp = x + (y * 0.08333333333333323d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 6.0) {
		tmp = x + (y * 0.08333333333333323);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 0.0692910599291889)
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 6.0:
		tmp = x + (y * 0.08333333333333323)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 0.0692910599291889))
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 6.0)
		tmp = Float64(x + Float64(y * 0.08333333333333323));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 0.0692910599291889);
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 6.0)
		tmp = x + (y * 0.08333333333333323);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 6.0], N[(x + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 6 < z

   1. Initial program 40.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]

   if -5.4000000000000004 < z < 6

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

      3. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

   5. Simplified 98.8%

      \[\leadsto \color{blue}{x + y \cdot 0.08333333333333323} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 61.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-59}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.9e-120) x (if (<= x 3.9e-59) (* y 0.08333333333333323) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.9e-120) {
		tmp = x;
	} else if (x <= 3.9e-59) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = 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 <= (-2.9d-120)) then
        tmp = x
    else if (x <= 3.9d-59) then
        tmp = y * 0.08333333333333323d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.9e-120) {
		tmp = x;
	} else if (x <= 3.9e-59) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.9e-120:
		tmp = x
	elif x <= 3.9e-59:
		tmp = y * 0.08333333333333323
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.9e-120)
		tmp = x;
	elseif (x <= 3.9e-59)
		tmp = Float64(y * 0.08333333333333323);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.9e-120)
		tmp = x;
	elseif (x <= 3.9e-59)
		tmp = y * 0.08333333333333323;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.9e-120], x, If[LessEqual[x, 3.9e-59], N[(y * 0.08333333333333323), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e-120 or 3.90000000000000019e-59 < x

   1. Initial program 68.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 73.4%

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

   if -2.9e-120 < x < 3.90000000000000019e-59

   1. Initial program 77.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

      3. *-lowering-*.f64 71.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

   5. Simplified 71.1%

      \[\leadsto \color{blue}{x + y \cdot 0.08333333333333323} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{279195317918525}{3350343815022304} \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 57.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{y}\right) \]

   8. Simplified 57.5%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-59}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e-39) x (if (<= x 4.9e-17) (* y 0.0692910599291889) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-39) {
		tmp = x;
	} else if (x <= 4.9e-17) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = 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 <= (-2.1d-39)) then
        tmp = x
    else if (x <= 4.9d-17) then
        tmp = y * 0.0692910599291889d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-39) {
		tmp = x;
	} else if (x <= 4.9e-17) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-39:
		tmp = x
	elif x <= 4.9e-17:
		tmp = y * 0.0692910599291889
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-39)
		tmp = x;
	elseif (x <= 4.9e-17)
		tmp = Float64(y * 0.0692910599291889);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e-39)
		tmp = x;
	elseif (x <= 4.9e-17)
		tmp = y * 0.0692910599291889;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-39], x, If[LessEqual[x, 4.9e-17], N[(y * 0.0692910599291889), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999993e-39 or 4.90000000000000012e-17 < x

   1. Initial program 69.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 78.6%

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

   if -2.09999999999999993e-39 < x < 4.90000000000000012e-17

   1. Initial program 75.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 62.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 62.6%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 46.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{692910599291889}{10000000000000000}, \color{blue}{y}\right) \]

   8. Simplified 46.5%

      \[\leadsto \color{blue}{0.0692910599291889 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+239}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8e+239) (+ x (* y 0.0692910599291889)) (* y 0.08333333333333323)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e+239) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = y * 0.08333333333333323;
	}
	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 (y <= 8d+239) then
        tmp = x + (y * 0.0692910599291889d0)
    else
        tmp = y * 0.08333333333333323d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e+239) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = y * 0.08333333333333323;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8e+239:
		tmp = x + (y * 0.0692910599291889)
	else:
		tmp = y * 0.08333333333333323
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8e+239)
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	else
		tmp = Float64(y * 0.08333333333333323);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8e+239)
		tmp = x + (y * 0.0692910599291889);
	else
		tmp = y * 0.08333333333333323;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8e+239], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], N[(y * 0.08333333333333323), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.99999999999999993e239

   1. Initial program 70.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 80.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 80.7%

      \[\leadsto \color{blue}{x + y \cdot 0.0692910599291889} \]

   if 7.99999999999999993e239 < y

   1. Initial program 91.0%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

      3. *-lowering-*.f64 79.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

   5. Simplified 79.7%

      \[\leadsto \color{blue}{x + y \cdot 0.08333333333333323} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{279195317918525}{3350343815022304} \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 79.7%

         \[\leadsto \mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{y}\right) \]

   8. Simplified 79.7%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+239}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.3% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

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
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 71.9%

   \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 52.9%

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

Developer Target 1: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{if}\;z < -8120153.652456675:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z < 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y)
          (- (/ (* 0.40462203869992125 y) (* z z)) x))))
   (if (< z -8120153.652456675)
     t_0
     (if (< z 6.576118972787377e+20)
       (+
        x
        (*
         (*
          y
          (+
           (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
           0.279195317918525))
         (/ 1.0 (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	double tmp;
	if (z < -8120153.652456675) {
		tmp = t_0;
	} else if (z < 6.576118972787377e+20) {
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	} 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 = (((0.07512208616047561d0 / z) + 0.0692910599291889d0) * y) - (((0.40462203869992125d0 * y) / (z * z)) - x)
    if (z < (-8120153.652456675d0)) then
        tmp = t_0
    else if (z < 6.576118972787377d+20) then
        tmp = x + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) * (1.0d0 / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	double tmp;
	if (z < -8120153.652456675) {
		tmp = t_0;
	} else if (z < 6.576118972787377e+20) {
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x)
	tmp = 0
	if z < -8120153.652456675:
		tmp = t_0
	elif z < 6.576118972787377e+20:
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(0.07512208616047561 / z) + 0.0692910599291889) * y) - Float64(Float64(Float64(0.40462203869992125 * y) / Float64(z * z)) - x))
	tmp = 0.0
	if (z < -8120153.652456675)
		tmp = t_0;
	elseif (z < 6.576118972787377e+20)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * Float64(1.0 / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	tmp = 0.0;
	if (z < -8120153.652456675)
		tmp = t_0;
	elseif (z < 6.576118972787377e+20)
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(0.07512208616047561 / z), $MachinePrecision] + 0.0692910599291889), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(0.40462203869992125 * y), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -8120153.652456675], t$95$0, If[Less[z, 6.576118972787377e+20], N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024158 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -324806146098267/40000000) (- (* (+ (/ 7512208616047561/100000000000000000 z) 692910599291889/10000000000000000) y) (- (/ (* 323697630959937/800000000000000 y) (* z z)) x)) (if (< z 657611897278737700000) (+ x (* (* y (+ (* (+ (* z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (/ 1 (+ (* (+ z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))) (- (* (+ (/ 7512208616047561/100000000000000000 z) 692910599291889/10000000000000000) y) (- (/ (* 323697630959937/800000000000000 y) (* z z)) x)))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))