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

Percentage Accurate: 99.8% → 99.8%

Time: 16.3s

Alternatives: 21

Speedup: 1.0×

• Unsound rule application detected in e-graph. Results may not be sound.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (fma y i (fma (+ b -0.5) (log c) (+ (fma x (log y) z) (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return fma(y, i, fma((b + -0.5), log(c), (fma(x, log(y), z) + (t + a))));
}

Julia

function code(x, y, z, t, a, b, c, i)
	return fma(y, i, fma(Float64(b + -0.5), log(c), Float64(fma(x, log(y), z) + Float64(t + a))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(y * i + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   2. fma-def 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   3. +-commutative 99.9%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)}\right) \]

   4. fma-def 99.9%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)}\right) \]

   5. sub-neg 99.9%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

   6. metadata-eval 99.9%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

   7. associate-+l+ 99.9%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{\left(x \cdot \log y + z\right) + \left(t + a\right)}\right)\right) \]

   8. fma-def 99.9%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{\mathsf{fma}\left(x, \log y, z\right)} + \left(t + a\right)\right)\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right)} \]

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right) \]

Alternative 2: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

2. Final simplification 99.9%

   \[\leadsto \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i \]

Alternative 3: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+206} \lor \neg \left(x \leq 2.55 \cdot 10^{+104}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(\log c \cdot \left(b - 0.5\right) + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.15e+206) (not (<= x 2.55e+104)))
   (+ (* y i) (+ (* x (log y)) (+ a (+ z t))))
   (fma y i (+ a (+ (* (log c) (- b 0.5)) (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.15e+206) || !(x <= 2.55e+104)) {
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	} else {
		tmp = fma(y, i, (a + ((log(c) * (b - 0.5)) + (z + t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.15e+206) || !(x <= 2.55e+104))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(a + Float64(z + t))));
	else
		tmp = fma(y, i, Float64(a + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(z + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.15e+206], N[Not[LessEqual[x, 2.55e+104]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15000000000000008e206 or 2.5500000000000001e104 < x

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 99.9%

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

   3. Taylor expanded in b around 0 96.1%

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

   if -1.15000000000000008e206 < x < 2.5500000000000001e104

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      2. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      3. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)}\right) \]

      4. fma-def 99.9%

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)}\right) \]

      5. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) \]

      7. associate-+l+ 99.9%

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{\left(x \cdot \log y + z\right) + \left(t + a\right)}\right)\right) \]

      8. fma-def 99.9%

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{\mathsf{fma}\left(x, \log y, z\right)} + \left(t + a\right)\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right)} \]

   4. Taylor expanded in x around 0 98.8%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a + \left(\log c \cdot \left(b - 0.5\right) + \left(t + z\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+206} \lor \neg \left(x \leq 2.55 \cdot 10^{+104}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(\log c \cdot \left(b - 0.5\right) + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 4: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* b (log c)))))

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + ((a + (t + (z + (x * Math.log(y))))) + (b * Math.log(c)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return (y * i) + ((a + (t + (z + (x * math.log(y))))) + (b * math.log(c)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(b * log(c))))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

2. Taylor expanded in b around inf 98.8%

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

3. Final simplification 98.8%

   \[\leadsto y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + b \cdot \log c\right) \]

Alternative 5: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+134} \lor \neg \left(b - 0.5 \leq 10^{+163}\right):\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -2e+134) (not (<= (- b 0.5) 1e+163)))
   (+ (* y i) (+ z (* b (log c))))
   (+ (* y i) (+ (* x (log y)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+134) || !((b - 0.5) <= 1e+163)) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-2d+134)) .or. (.not. ((b - 0.5d0) <= 1d+163))) then
        tmp = (y * i) + (z + (b * log(c)))
    else
        tmp = (y * i) + ((x * log(y)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+134) || !((b - 0.5) <= 1e+163)) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else {
		tmp = (y * i) + ((x * Math.log(y)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -2e+134) or not ((b - 0.5) <= 1e+163):
		tmp = (y * i) + (z + (b * math.log(c)))
	else:
		tmp = (y * i) + ((x * math.log(y)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -2e+134) || !(Float64(b - 0.5) <= 1e+163))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -2e+134) || ~(((b - 0.5) <= 1e+163)))
		tmp = (y * i) + (z + (b * log(c)));
	else
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+134], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+163]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -1.99999999999999984e134 or 9.9999999999999994e162 < (-.f64 b 1/2)

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 95.3%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 95.3%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 95.3%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 95.3%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 95.3%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 95.3%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 95.3%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in a around 0 93.0%

      \[\leadsto \left(\color{blue}{\left(t + z\right)} + \log c \cdot b\right) + y \cdot i \]

   7. Taylor expanded in t around 0 82.5%

      \[\leadsto \color{blue}{\left(\log c \cdot b + z\right)} + y \cdot i \]

   if -1.99999999999999984e134 < (-.f64 b 1/2) < 9.9999999999999994e162

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 98.5%

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

   3. Taylor expanded in b around 0 95.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+134} \lor \neg \left(b - 0.5 \leq 10^{+163}\right):\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 6: 94.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+206} \lor \neg \left(x \leq 1.5 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.45e+206) (not (<= x 1.5e+100)))
   (+ (* y i) (+ (* x (log y)) (+ a (+ z t))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ z (+ t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.45e+206) || !(x <= 1.5e+100)) {
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + (t + a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.45d+206)) .or. (.not. (x <= 1.5d+100))) then
        tmp = (y * i) + ((x * log(y)) + (a + (z + t)))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (z + (t + a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.45e+206) || !(x <= 1.5e+100)) {
		tmp = (y * i) + ((x * Math.log(y)) + (a + (z + t)));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (z + (t + a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.45e+206) or not (x <= 1.5e+100):
		tmp = (y * i) + ((x * math.log(y)) + (a + (z + t)))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (z + (t + a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.45e+206) || !(x <= 1.5e+100))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(z + Float64(t + a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.45e+206) || ~((x <= 1.5e+100)))
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + (t + a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.45e+206], N[Not[LessEqual[x, 1.5e+100]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e206 or 1.49999999999999993e100 < x

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 99.9%

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

   3. Taylor expanded in b around 0 96.1%

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

   if -1.45e206 < x < 1.49999999999999993e100

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 98.7%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 98.7%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 98.7%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 98.7%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 98.7%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 98.7%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+206} \lor \neg \left(x \leq 1.5 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \]

Alternative 7: 92.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+206} \lor \neg \left(x \leq 4.5 \cdot 10^{+101}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.15e+206) (not (<= x 4.5e+101)))
   (+ (* y i) (+ (* x (log y)) (+ a (+ z t))))
   (+ (* y i) (+ (* b (log c)) (+ z (+ t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.15e+206) || !(x <= 4.5e+101)) {
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	} else {
		tmp = (y * i) + ((b * log(c)) + (z + (t + a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.15d+206)) .or. (.not. (x <= 4.5d+101))) then
        tmp = (y * i) + ((x * log(y)) + (a + (z + t)))
    else
        tmp = (y * i) + ((b * log(c)) + (z + (t + a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.15e+206) || !(x <= 4.5e+101)) {
		tmp = (y * i) + ((x * Math.log(y)) + (a + (z + t)));
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + (z + (t + a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.15e+206) or not (x <= 4.5e+101):
		tmp = (y * i) + ((x * math.log(y)) + (a + (z + t)))
	else:
		tmp = (y * i) + ((b * math.log(c)) + (z + (t + a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.15e+206) || !(x <= 4.5e+101))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(z + Float64(t + a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.15e+206) || ~((x <= 4.5e+101)))
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	else
		tmp = (y * i) + ((b * log(c)) + (z + (t + a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.15e+206], N[Not[LessEqual[x, 4.5e+101]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15000000000000008e206 or 4.5000000000000002e101 < x

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 99.9%

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

   3. Taylor expanded in b around 0 96.1%

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

   if -1.15000000000000008e206 < x < 4.5000000000000002e101

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 98.7%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 98.7%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 98.7%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 98.7%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 98.7%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 98.7%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 97.2%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+206} \lor \neg \left(x \leq 4.5 \cdot 10^{+101}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \]

Alternative 8: 74.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + \left(a + \left(z + t\right)\right)\\ \mathbf{if}\;y \leq 7 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-55}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (+ a (+ z t)))))
   (if (<= y 7e-224)
     t_1
     (if (<= y 1.4e-55)
       (+ a (+ t (+ z (* b (log c)))))
       (if (<= y 1.4e+38) t_1 (+ (+ t a) (fma i y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + (a + (z + t));
	double tmp;
	if (y <= 7e-224) {
		tmp = t_1;
	} else if (y <= 1.4e-55) {
		tmp = a + (t + (z + (b * log(c))));
	} else if (y <= 1.4e+38) {
		tmp = t_1;
	} else {
		tmp = (t + a) + fma(i, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + Float64(a + Float64(z + t)))
	tmp = 0.0
	if (y <= 7e-224)
		tmp = t_1;
	elseif (y <= 1.4e-55)
		tmp = Float64(a + Float64(t + Float64(z + Float64(b * log(c)))));
	elseif (y <= 1.4e+38)
		tmp = t_1;
	else
		tmp = Float64(Float64(t + a) + fma(i, y, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 7e-224], t$95$1, If[LessEqual[y, 1.4e-55], N[(a + N[(t + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+38], t$95$1, N[(N[(t + a), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.00000000000000037e-224 or 1.39999999999999992e-55 < y < 1.4e38

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 97.0%

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

   3. Taylor expanded in b around 0 86.6%

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

   4. Taylor expanded in y around 0 81.8%

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

   if 7.00000000000000037e-224 < y < 1.39999999999999992e-55

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 92.8%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 92.8%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 92.8%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 92.8%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 92.8%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 92.8%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 91.4%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 82.9%

      \[\leadsto \color{blue}{a + \left(t + \left(\log c \cdot b + z\right)\right)} \]

   if 1.4e38 < y

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 92.1%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 92.1%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 92.1%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 92.1%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 92.1%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 92.1%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in b around 0 81.6%

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

      1. associate-+r+ 81.6%

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

      2. +-commutative 81.6%

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

      3. fma-udef 81.6%

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

   8. Simplified 81.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \log y + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-55}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \log y + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \]

Alternative 9: 72.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.6 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \log y + \left(t + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7.6e-280)
   (+ (* x (log y)) (+ t (+ z (* y i))))
   (if (<= a 1.2e+143)
     (+ (* y i) (+ (* b (log c)) (+ z t)))
     (+ (+ t a) (fma i y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.6e-280) {
		tmp = (x * log(y)) + (t + (z + (y * i)));
	} else if (a <= 1.2e+143) {
		tmp = (y * i) + ((b * log(c)) + (z + t));
	} else {
		tmp = (t + a) + fma(i, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 7.6e-280)
		tmp = Float64(Float64(x * log(y)) + Float64(t + Float64(z + Float64(y * i))));
	elseif (a <= 1.2e+143)
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(z + t)));
	else
		tmp = Float64(Float64(t + a) + fma(i, y, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 7.6e-280], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+143], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 7.6000000000000003e-280

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 98.0%

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

   3. Taylor expanded in b around 0 84.7%

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

   4. Taylor expanded in a around 0 71.9%

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

   if 7.6000000000000003e-280 < a < 1.1999999999999999e143

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 85.7%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 85.7%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 85.7%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 85.7%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 85.7%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 85.7%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 85.6%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in a around 0 85.5%

      \[\leadsto \left(\color{blue}{\left(t + z\right)} + \log c \cdot b\right) + y \cdot i \]

   if 1.1999999999999999e143 < a

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 88.3%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 88.3%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 88.3%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 88.3%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 88.3%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 88.3%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 88.3%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in b around 0 82.2%

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

      1. associate-+r+ 82.2%

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

      2. +-commutative 82.2%

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

      3. fma-udef 82.2%

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

   8. Simplified 82.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.6 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \log y + \left(t + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \]

Alternative 10: 67.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \log y + \left(t + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 9e-282)
   (+ (* x (log y)) (+ t (+ z (* y i))))
   (if (<= a 1.6e+143)
     (+ (* y i) (+ z (* b (log c))))
     (+ (+ t a) (fma i y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 9e-282) {
		tmp = (x * log(y)) + (t + (z + (y * i)));
	} else if (a <= 1.6e+143) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (t + a) + fma(i, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 9e-282)
		tmp = Float64(Float64(x * log(y)) + Float64(t + Float64(z + Float64(y * i))));
	elseif (a <= 1.6e+143)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(t + a) + fma(i, y, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 9e-282], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+143], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 9.00000000000000017e-282

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 98.0%

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

   3. Taylor expanded in b around 0 84.7%

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

   4. Taylor expanded in a around 0 71.9%

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

   if 9.00000000000000017e-282 < a < 1.60000000000000008e143

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 85.7%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 85.7%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 85.7%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 85.7%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 85.7%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 85.7%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 85.6%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in a around 0 85.5%

      \[\leadsto \left(\color{blue}{\left(t + z\right)} + \log c \cdot b\right) + y \cdot i \]

   7. Taylor expanded in t around 0 73.0%

      \[\leadsto \color{blue}{\left(\log c \cdot b + z\right)} + y \cdot i \]

   if 1.60000000000000008e143 < a

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 88.3%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 88.3%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 88.3%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 88.3%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 88.3%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 88.3%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 88.3%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in b around 0 82.2%

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

      1. associate-+r+ 82.2%

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

      2. +-commutative 82.2%

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

      3. fma-udef 82.2%

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

   8. Simplified 82.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \log y + \left(t + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \]

Alternative 11: 73.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+251} \lor \neg \left(b \leq 1.05 \cdot 10^{+194}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -3.6e+251) (not (<= b 1.05e+194)))
   (+ a (+ t (* b (log c))))
   (+ a (+ t (+ z (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -3.6e+251) || !(b <= 1.05e+194)) {
		tmp = a + (t + (b * log(c)));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-3.6d+251)) .or. (.not. (b <= 1.05d+194))) then
        tmp = a + (t + (b * log(c)))
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -3.6e+251) || !(b <= 1.05e+194)) {
		tmp = a + (t + (b * Math.log(c)));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -3.6e+251) or not (b <= 1.05e+194):
		tmp = a + (t + (b * math.log(c)))
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -3.6e+251) || !(b <= 1.05e+194))
		tmp = Float64(a + Float64(t + Float64(b * log(c))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -3.6e+251) || ~((b <= 1.05e+194)))
		tmp = a + (t + (b * log(c)));
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -3.6e+251], N[Not[LessEqual[b, 1.05e+194]], $MachinePrecision]], N[(a + N[(t + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.59999999999999997e251 or 1.05000000000000008e194 < b

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 97.5%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 97.5%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 97.5%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 97.5%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 97.5%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 97.5%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 97.5%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 86.7%

      \[\leadsto \color{blue}{a + \left(t + \left(\log c \cdot b + z\right)\right)} \]

   7. Taylor expanded in b around inf 81.3%

      \[\leadsto a + \left(t + \color{blue}{\log c \cdot b}\right) \]

   if -3.59999999999999997e251 < b < 1.05000000000000008e194

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 84.7%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 84.7%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 84.7%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 84.7%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 84.7%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 83.4%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in b around 0 77.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+251} \lor \neg \left(b \leq 1.05 \cdot 10^{+194}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]

Alternative 12: 73.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+251} \lor \neg \left(b \leq 2.4 \cdot 10^{+194}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.75e+251) (not (<= b 2.4e+194)))
   (+ a (+ t (* b (log c))))
   (+ (+ t a) (fma i y z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.75e+251) || !(b <= 2.4e+194)) {
		tmp = a + (t + (b * log(c)));
	} else {
		tmp = (t + a) + fma(i, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.75e+251) || !(b <= 2.4e+194))
		tmp = Float64(a + Float64(t + Float64(b * log(c))));
	else
		tmp = Float64(Float64(t + a) + fma(i, y, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.75e+251], N[Not[LessEqual[b, 2.4e+194]], $MachinePrecision]], N[(a + N[(t + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.75000000000000002e251 or 2.4e194 < b

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 97.5%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 97.5%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 97.5%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 97.5%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 97.5%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 97.5%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 97.5%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 86.7%

      \[\leadsto \color{blue}{a + \left(t + \left(\log c \cdot b + z\right)\right)} \]

   7. Taylor expanded in b around inf 81.3%

      \[\leadsto a + \left(t + \color{blue}{\log c \cdot b}\right) \]

   if -1.75000000000000002e251 < b < 2.4e194

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 84.7%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 84.7%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 84.7%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 84.7%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 84.7%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 83.4%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in b around 0 77.8%

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

      1. associate-+r+ 77.8%

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

      2. +-commutative 77.8%

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

      3. fma-udef 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+251} \lor \neg \left(b \leq 2.4 \cdot 10^{+194}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \]

Alternative 13: 73.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+50}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 6.5e+50) (+ a (+ t (+ z (* b (log c))))) (+ (+ t a) (fma i y z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 6.5e+50) {
		tmp = a + (t + (z + (b * log(c))));
	} else {
		tmp = (t + a) + fma(i, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 6.5e+50)
		tmp = Float64(a + Float64(t + Float64(z + Float64(b * log(c)))));
	else
		tmp = Float64(Float64(t + a) + fma(i, y, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 6.5e+50], N[(a + N[(t + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5000000000000003e50

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 82.5%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 82.5%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 82.5%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 82.5%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 82.5%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 82.5%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 80.5%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 72.4%

      \[\leadsto \color{blue}{a + \left(t + \left(\log c \cdot b + z\right)\right)} \]

   if 6.5000000000000003e50 < y

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 91.6%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 91.6%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 91.6%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 91.6%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 91.6%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 91.6%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 91.6%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in b around 0 84.0%

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

      1. associate-+r+ 84.0%

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

      2. +-commutative 84.0%

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

      3. fma-udef 84.0%

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

   8. Simplified 84.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+50}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \]

Alternative 14: 58.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.1 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.1e+143) (+ (* y i) (+ z (* b (log c)))) (+ (+ t a) (fma i y z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.1e+143) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (t + a) + fma(i, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.1e+143)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(t + a) + fma(i, y, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.1e+143], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.10000000000000007e143

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 86.3%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 86.3%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 86.3%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 86.3%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 86.3%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 85.0%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in a around 0 76.9%

      \[\leadsto \left(\color{blue}{\left(t + z\right)} + \log c \cdot b\right) + y \cdot i \]

   7. Taylor expanded in t around 0 61.8%

      \[\leadsto \color{blue}{\left(\log c \cdot b + z\right)} + y \cdot i \]

   if 1.10000000000000007e143 < a

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 88.3%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 88.3%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 88.3%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 88.3%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 88.3%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 88.3%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 88.3%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in b around 0 82.2%

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

      1. associate-+r+ 82.2%

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

      2. +-commutative 82.2%

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

      3. fma-udef 82.2%

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

   8. Simplified 82.2%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.1 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \mathsf{fma}\left(i, y, z\right)\\ \end{array} \]

Alternative 15: 71.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+255} \lor \neg \left(b \leq 2.85 \cdot 10^{+195}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.3e+255) (not (<= b 2.85e+195)))
   (* b (log c))
   (+ a (+ t (+ z (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.3e+255) || !(b <= 2.85e+195)) {
		tmp = b * log(c);
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-1.3d+255)) .or. (.not. (b <= 2.85d+195))) then
        tmp = b * log(c)
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.3e+255) || !(b <= 2.85e+195)) {
		tmp = b * Math.log(c);
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -1.3e+255) or not (b <= 2.85e+195):
		tmp = b * math.log(c)
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.3e+255) || !(b <= 2.85e+195))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -1.3e+255) || ~((b <= 2.85e+195)))
		tmp = b * log(c);
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.3e+255], N[Not[LessEqual[b, 2.85e+195]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.30000000000000005e255 or 2.8500000000000001e195 < b

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 99.6%

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

   3. Taylor expanded in b around inf 78.9%

      \[\leadsto \color{blue}{\log c \cdot b} \]

   if -1.30000000000000005e255 < b < 2.8500000000000001e195

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around 0 84.9%

      \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. +-commutative 84.9%

         \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. +-commutative 84.9%

         \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      3. associate-+l+ 84.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative 84.9%

         \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Simplified 84.9%

      \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in b around inf 83.6%

      \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

   6. Taylor expanded in b around 0 77.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+255} \lor \neg \left(b \leq 2.85 \cdot 10^{+195}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]

Alternative 16: 23.5% accurate, 14.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+156}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+53}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -240000000000:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-45}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-87}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-300}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3e+156)
   z
   (if (<= z -6.6e+53)
     (* y i)
     (if (<= z -240000000000.0)
       a
       (if (<= z -2.4e-45)
         (* y i)
         (if (<= z -3.7e-87) a (if (<= z -1.9e-300) (* y i) a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3e+156) {
		tmp = z;
	} else if (z <= -6.6e+53) {
		tmp = y * i;
	} else if (z <= -240000000000.0) {
		tmp = a;
	} else if (z <= -2.4e-45) {
		tmp = y * i;
	} else if (z <= -3.7e-87) {
		tmp = a;
	} else if (z <= -1.9e-300) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3d+156)) then
        tmp = z
    else if (z <= (-6.6d+53)) then
        tmp = y * i
    else if (z <= (-240000000000.0d0)) then
        tmp = a
    else if (z <= (-2.4d-45)) then
        tmp = y * i
    else if (z <= (-3.7d-87)) then
        tmp = a
    else if (z <= (-1.9d-300)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3e+156) {
		tmp = z;
	} else if (z <= -6.6e+53) {
		tmp = y * i;
	} else if (z <= -240000000000.0) {
		tmp = a;
	} else if (z <= -2.4e-45) {
		tmp = y * i;
	} else if (z <= -3.7e-87) {
		tmp = a;
	} else if (z <= -1.9e-300) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3e+156:
		tmp = z
	elif z <= -6.6e+53:
		tmp = y * i
	elif z <= -240000000000.0:
		tmp = a
	elif z <= -2.4e-45:
		tmp = y * i
	elif z <= -3.7e-87:
		tmp = a
	elif z <= -1.9e-300:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3e+156)
		tmp = z;
	elseif (z <= -6.6e+53)
		tmp = Float64(y * i);
	elseif (z <= -240000000000.0)
		tmp = a;
	elseif (z <= -2.4e-45)
		tmp = Float64(y * i);
	elseif (z <= -3.7e-87)
		tmp = a;
	elseif (z <= -1.9e-300)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3e+156)
		tmp = z;
	elseif (z <= -6.6e+53)
		tmp = y * i;
	elseif (z <= -240000000000.0)
		tmp = a;
	elseif (z <= -2.4e-45)
		tmp = y * i;
	elseif (z <= -3.7e-87)
		tmp = a;
	elseif (z <= -1.9e-300)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3e+156], z, If[LessEqual[z, -6.6e+53], N[(y * i), $MachinePrecision], If[LessEqual[z, -240000000000.0], a, If[LessEqual[z, -2.4e-45], N[(y * i), $MachinePrecision], If[LessEqual[z, -3.7e-87], a, If[LessEqual[z, -1.9e-300], N[(y * i), $MachinePrecision], a]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e156

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf 59.0%

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

   if -3e156 < z < -6.6000000000000004e53 or -2.4e11 < z < -2.3999999999999999e-45 or -3.7000000000000002e-87 < z < -1.90000000000000006e-300

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in y around inf 37.6%

      \[\leadsto \color{blue}{i \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 37.6%

         \[\leadsto \color{blue}{y \cdot i} \]

   4. Simplified 37.6%

      \[\leadsto \color{blue}{y \cdot i} \]

   if -6.6000000000000004e53 < z < -2.4e11 or -2.3999999999999999e-45 < z < -3.7000000000000002e-87 or -1.90000000000000006e-300 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in a around inf 17.5%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+156}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+53}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -240000000000:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-45}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-87}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-300}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17: 67.1% accurate, 24.3× speedup

Math

\[\begin{array}{l} \\ a + \left(t + \left(z + y \cdot i\right)\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

2. Taylor expanded in x around 0 86.5%

   \[\leadsto \left(\color{blue}{\left(a + \left(t + z\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Step-by-step derivation

   1. +-commutative 86.5%

      \[\leadsto \left(\color{blue}{\left(\left(t + z\right) + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. +-commutative 86.5%

      \[\leadsto \left(\left(\color{blue}{\left(z + t\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   3. associate-+l+ 86.5%

      \[\leadsto \left(\color{blue}{\left(z + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. +-commutative 86.5%

      \[\leadsto \left(\left(z + \color{blue}{\left(a + t\right)}\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

4. Simplified 86.5%

   \[\leadsto \left(\color{blue}{\left(z + \left(a + t\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

5. Taylor expanded in b around inf 85.4%

   \[\leadsto \left(\left(z + \left(a + t\right)\right) + \color{blue}{\log c \cdot b}\right) + y \cdot i \]

6. Taylor expanded in b around 0 70.2%

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

7. Final simplification 70.2%

   \[\leadsto a + \left(t + \left(z + y \cdot i\right)\right) \]

Alternative 18: 41.5% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+180}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6.2e+180) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.2e+180) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-6.2d+180)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.2e+180) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6.2e+180:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6.2e+180)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -6.2e+180)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6.2e+180], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999997e180

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf 70.4%

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

   if -6.19999999999999997e180 < z

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 98.6%

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

   3. Taylor expanded in b around 0 82.4%

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

   4. Taylor expanded in a around inf 42.3%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+180}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 19: 43.3% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+170}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.7e+170) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.7e+170) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3.7d+170)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.7e+170) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.7e+170:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.7e+170)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.7e+170)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.7e+170], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999987e170

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 100.0%

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

   3. Taylor expanded in b around 0 92.0%

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

   4. Taylor expanded in z around inf 75.6%

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

   if -3.69999999999999987e170 < z

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in b around inf 98.6%

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

   3. Taylor expanded in b around 0 82.2%

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

   4. Taylor expanded in a around inf 42.2%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+170}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 20: 20.9% accurate, 71.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -3e+170) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3e+170) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3d+170)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3e+170) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3e+170:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3e+170)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3e+170)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3e+170], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999997e170

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf 66.4%

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

   if -2.99999999999999997e170 < z

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in a around inf 14.5%

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

4. Final simplification 21.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 21: 16.2% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

2. Taylor expanded in a around inf 13.1%

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

3. Final simplification 13.1%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023171 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))