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

Percentage Accurate: 99.8% → 99.8%

Time: 17.1s

Alternatives: 16

Speedup: 1.0×

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, 0.7× speedup

Math

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

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (fma x (log y) z) (+ t a)) (+ (* (+ b -0.5) (log c)) (* y i))))

C

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

Julia

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

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(x * N[Log[y], $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. associate-+l+ 99.5%

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

   2. associate-+l+ 99.5%

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

   3. fma-def 99.5%

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

   4. sub-neg 99.5%

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

   5. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5)))))

C

assert(z < t && t < a);
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))))) + (log(c) * (b - 0.5)));
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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))))) + (log(c) * (b - 0.5d0)))
end function

Java

assert z < t && t < a;
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))))) + (Math.log(c) * (b - 0.5)));
}

Python

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

Julia

z, t, a = sort([z, t, a])
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(log(c) * Float64(b - 0.5))))
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5)));
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

2. Final simplification 99.5%

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

Alternative 3: 95.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := a + \left(z + t\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+129} \lor \neg \left(x \leq 9.6 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ z t))))
   (if (or (<= x -2e+129) (not (<= x 9.6e+100)))
     (+ (* y i) (+ (* x (log y)) t_1))
     (+ (* y i) (+ (* (log c) (- b 0.5)) t_1)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (z + t);
	double tmp;
	if ((x <= -2e+129) || !(x <= 9.6e+100)) {
		tmp = (y * i) + ((x * log(y)) + t_1);
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + t_1);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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) :: t_1
    real(8) :: tmp
    t_1 = a + (z + t)
    if ((x <= (-2d+129)) .or. (.not. (x <= 9.6d+100))) then
        tmp = (y * i) + ((x * log(y)) + t_1)
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + t_1)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (z + t);
	double tmp;
	if ((x <= -2e+129) || !(x <= 9.6e+100)) {
		tmp = (y * i) + ((x * Math.log(y)) + t_1);
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + t_1);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = a + (z + t)
	tmp = 0
	if (x <= -2e+129) or not (x <= 9.6e+100):
		tmp = (y * i) + ((x * math.log(y)) + t_1)
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + t_1)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(z + t))
	tmp = 0.0
	if ((x <= -2e+129) || !(x <= 9.6e+100))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + t_1));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (z + t);
	tmp = 0.0;
	if ((x <= -2e+129) || ~((x <= 9.6e+100)))
		tmp = (y * i) + ((x * log(y)) + t_1);
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2e+129], N[Not[LessEqual[x, 9.6e+100]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2e129 or 9.60000000000000046e100 < x

   1. Initial program 98.7%

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

      1. sub-neg 46.4%

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

      2. metadata-eval 46.4%

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

      3. add-cube-cbrt 46.4%

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

      4. pow3 46.4%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 46.4%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   3. Applied egg-rr 98.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   4. Taylor expanded in b around inf 92.9%

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

   if -2e129 < x < 9.60000000000000046e100

   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 99.9%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+129} \lor \neg \left(x \leq 9.6 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 4: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \log y + \left(t + \left(z + y \cdot i\right)\right)\\ \mathbf{if}\;a \leq 5.8 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-86}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (+ t (+ z (* y i))))))
   (if (<= a 5.8e-124)
     t_1
     (if (<= a 1.15e-86)
       (+ a (+ z (* (log c) (- b 0.5))))
       (if (<= a 1.1e+124) t_1 (+ (* y i) (+ z a)))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + (t + (z + (y * i)));
	double tmp;
	if (a <= 5.8e-124) {
		tmp = t_1;
	} else if (a <= 1.15e-86) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else if (a <= 1.1e+124) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) + (t + (z + (y * i)))
    if (a <= 5.8d-124) then
        tmp = t_1
    else if (a <= 1.15d-86) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else if (a <= 1.1d+124) then
        tmp = t_1
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * Math.log(y)) + (t + (z + (y * i)));
	double tmp;
	if (a <= 5.8e-124) {
		tmp = t_1;
	} else if (a <= 1.15e-86) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else if (a <= 1.1e+124) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + (t + (z + (y * i)))
	tmp = 0
	if a <= 5.8e-124:
		tmp = t_1
	elif a <= 1.15e-86:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	elif a <= 1.1e+124:
		tmp = t_1
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + Float64(t + Float64(z + Float64(y * i))))
	tmp = 0.0
	if (a <= 5.8e-124)
		tmp = t_1;
	elseif (a <= 1.15e-86)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	elseif (a <= 1.1e+124)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + (t + (z + (y * i)));
	tmp = 0.0;
	if (a <= 5.8e-124)
		tmp = t_1;
	elseif (a <= 1.15e-86)
		tmp = a + (z + (log(c) * (b - 0.5)));
	elseif (a <= 1.1e+124)
		tmp = t_1;
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 5.8e-124], t$95$1, If[LessEqual[a, 1.15e-86], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+124], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 5.8000000000000004e-124 or 1.14999999999999998e-86 < a < 1.1e124

   1. Initial program 99.3%

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

      1. sub-neg 76.7%

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

      2. metadata-eval 76.7%

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

      3. add-cube-cbrt 76.6%

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

      4. pow3 76.6%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 76.6%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   3. Applied egg-rr 99.2%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   4. Taylor expanded in b around inf 88.3%

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

   5. Taylor expanded in a around 0 82.2%

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

   if 5.8000000000000004e-124 < a < 1.14999999999999998e-86

   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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. associate-+l+ 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 84.2%

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

      1. +-commutative 84.2%

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

      2. +-commutative 84.2%

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

      3. associate-+l+ 84.2%

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

      4. *-commutative 84.2%

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

      5. fma-def 84.2%

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

      6. sub-neg 84.2%

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

      7. metadata-eval 84.2%

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

      8. fma-def 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in x around 0 81.7%

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

   8. Taylor expanded in i around 0 32.7%

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

   if 1.1e124 < 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 88.2%

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

      1. sub-neg 88.2%

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

      2. metadata-eval 88.2%

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

      3. add-cube-cbrt 88.1%

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

      4. pow3 88.1%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 88.1%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 88.1%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-+r+ 81.2%

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

   7. Simplified 81.2%

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

   8. Taylor expanded in t around 0 67.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.8 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \log y + \left(t + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-86}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \log y + \left(t + \left(z + y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]

Alternative 5: 91.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+177} \lor \neg \left(x \leq 2.05 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \log y + \left(t + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\log c \cdot \left(b - 0.5\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y i))))
   (if (or (<= x -1.02e+177) (not (<= x 2.05e+103)))
     (+ (* x (log y)) (+ t t_1))
     (+ a (+ (* (log c) (- b 0.5)) t_1)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if ((x <= -1.02e+177) || !(x <= 2.05e+103)) {
		tmp = (x * log(y)) + (t + t_1);
	} else {
		tmp = a + ((log(c) * (b - 0.5)) + t_1);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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) :: t_1
    real(8) :: tmp
    t_1 = z + (y * i)
    if ((x <= (-1.02d+177)) .or. (.not. (x <= 2.05d+103))) then
        tmp = (x * log(y)) + (t + t_1)
    else
        tmp = a + ((log(c) * (b - 0.5d0)) + t_1)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if ((x <= -1.02e+177) || !(x <= 2.05e+103)) {
		tmp = (x * Math.log(y)) + (t + t_1);
	} else {
		tmp = a + ((Math.log(c) * (b - 0.5)) + t_1);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if (x <= -1.02e+177) or not (x <= 2.05e+103):
		tmp = (x * math.log(y)) + (t + t_1)
	else:
		tmp = a + ((math.log(c) * (b - 0.5)) + t_1)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if ((x <= -1.02e+177) || !(x <= 2.05e+103))
		tmp = Float64(Float64(x * log(y)) + Float64(t + t_1));
	else
		tmp = Float64(a + Float64(Float64(log(c) * Float64(b - 0.5)) + t_1));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if ((x <= -1.02e+177) || ~((x <= 2.05e+103)))
		tmp = (x * log(y)) + (t + t_1);
	else
		tmp = a + ((log(c) * (b - 0.5)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.02e+177], N[Not[LessEqual[x, 2.05e+103]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e177 or 2.0500000000000001e103 < x

   1. Initial program 98.6%

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

      1. sub-neg 42.3%

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

      2. metadata-eval 42.3%

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

      3. add-cube-cbrt 42.3%

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

      4. pow3 42.3%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 42.3%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   3. Applied egg-rr 98.5%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   4. Taylor expanded in b around inf 95.0%

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

   5. Taylor expanded in a around 0 89.7%

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

   if -1.02e177 < x < 2.0500000000000001e103

   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 t around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. +-commutative 76.6%

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

      3. associate-+l+ 76.6%

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

      4. *-commutative 76.6%

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

      5. fma-def 76.6%

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

      6. sub-neg 76.6%

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

      7. metadata-eval 76.6%

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

      8. fma-def 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in x around 0 74.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+177} \lor \neg \left(x \leq 2.05 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \log y + \left(t + \left(z + y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\log c \cdot \left(b - 0.5\right) + \left(z + y \cdot i\right)\right)\\ \end{array} \]

Alternative 6: 94.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+130} \lor \neg \left(x \leq 1.06 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\log c \cdot \left(b - 0.5\right) + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -6.4e+130) (not (<= x 1.06e+102)))
   (+ (* y i) (+ (* x (log y)) (+ a (+ z t))))
   (+ a (+ (* (log c) (- b 0.5)) (+ z (* y i))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.4e+130) || !(x <= 1.06e+102)) {
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	} else {
		tmp = a + ((log(c) * (b - 0.5)) + (z + (y * i)));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= (-6.4d+130)) .or. (.not. (x <= 1.06d+102))) then
        tmp = (y * i) + ((x * log(y)) + (a + (z + t)))
    else
        tmp = a + ((log(c) * (b - 0.5d0)) + (z + (y * i)))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.4e+130) || !(x <= 1.06e+102)) {
		tmp = (y * i) + ((x * Math.log(y)) + (a + (z + t)));
	} else {
		tmp = a + ((Math.log(c) * (b - 0.5)) + (z + (y * i)));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -6.4e+130) or not (x <= 1.06e+102):
		tmp = (y * i) + ((x * math.log(y)) + (a + (z + t)))
	else:
		tmp = a + ((math.log(c) * (b - 0.5)) + (z + (y * i)))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -6.4e+130) || !(x <= 1.06e+102))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(a + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -6.4e+130) || ~((x <= 1.06e+102)))
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	else
		tmp = a + ((log(c) * (b - 0.5)) + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -6.4e+130], N[Not[LessEqual[x, 1.06e+102]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4e130 or 1.06000000000000001e102 < x

   1. Initial program 98.7%

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

      1. sub-neg 46.4%

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

      2. metadata-eval 46.4%

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

      3. add-cube-cbrt 46.4%

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

      4. pow3 46.4%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 46.4%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   3. Applied egg-rr 98.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   4. Taylor expanded in b around inf 92.9%

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

   if -6.4e130 < x < 1.06000000000000001e102

   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 t around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. +-commutative 75.2%

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

      3. associate-+l+ 75.2%

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

      4. *-commutative 75.2%

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

      5. fma-def 75.2%

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

      6. sub-neg 75.2%

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

      7. metadata-eval 75.2%

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

      8. fma-def 75.2%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in x around 0 75.2%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+130} \lor \neg \left(x \leq 1.06 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\log c \cdot \left(b - 0.5\right) + \left(z + y \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 73.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+53} \lor \neg \left(i \leq 1.6 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.55e+53) (not (<= i 1.6e-34)))
   (+ (* y i) (+ z a))
   (+ (* x (log y)) (+ a (+ z t)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.55e+53) || !(i <= 1.6e-34)) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = (x * log(y)) + (a + (z + t));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 ((i <= (-1.55d+53)) .or. (.not. (i <= 1.6d-34))) then
        tmp = (y * i) + (z + a)
    else
        tmp = (x * log(y)) + (a + (z + t))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.55e+53) || !(i <= 1.6e-34)) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = (x * Math.log(y)) + (a + (z + t));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.55e+53) or not (i <= 1.6e-34):
		tmp = (y * i) + (z + a)
	else:
		tmp = (x * math.log(y)) + (a + (z + t))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.55e+53) || !(i <= 1.6e-34))
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(Float64(x * log(y)) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1.55e+53) || ~((i <= 1.6e-34)))
		tmp = (y * i) + (z + a);
	else
		tmp = (x * log(y)) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.55e+53], N[Not[LessEqual[i, 1.6e-34]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.5500000000000001e53 or 1.60000000000000001e-34 < i

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0 87.3%

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

      1. sub-neg 87.3%

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

      2. metadata-eval 87.3%

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

      3. add-cube-cbrt 87.3%

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

      4. pow3 87.3%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 87.3%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 87.3%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-+r+ 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in t around 0 65.0%

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

   if -1.5500000000000001e53 < i < 1.60000000000000001e-34

   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. sub-neg 71.7%

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

      2. metadata-eval 71.7%

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

      3. add-cube-cbrt 71.6%

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

      4. pow3 71.5%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 71.5%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   3. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   4. Taylor expanded in b around inf 87.6%

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

   5. Taylor expanded in y around 0 84.1%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+53} \lor \neg \left(i \leq 1.6 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 8: 75.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{elif}\;i \leq 215:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -9e-57)
   (+ (* y i) (+ t (+ z a)))
   (if (<= i 215.0) (+ a (+ z (* (log c) (- b 0.5)))) (+ (* y i) (+ z a)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -9e-57) {
		tmp = (y * i) + (t + (z + a));
	} else if (i <= 215.0) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 (i <= (-9d-57)) then
        tmp = (y * i) + (t + (z + a))
    else if (i <= 215.0d0) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -9e-57) {
		tmp = (y * i) + (t + (z + a));
	} else if (i <= 215.0) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -9e-57:
		tmp = (y * i) + (t + (z + a))
	elif i <= 215.0:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -9e-57)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	elseif (i <= 215.0)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -9e-57)
		tmp = (y * i) + (t + (z + a));
	elseif (i <= 215.0)
		tmp = a + (z + (log(c) * (b - 0.5)));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -9e-57], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 215.0], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.99999999999999945e-57

   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 84.4%

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

      1. sub-neg 84.4%

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

      2. metadata-eval 84.4%

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

      3. add-cube-cbrt 84.4%

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

      4. pow3 84.4%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 84.4%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 84.4%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-+r+ 83.1%

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

   7. Simplified 83.1%

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

   if -8.99999999999999945e-57 < i < 215

   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 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. +-commutative 77.7%

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

      3. associate-+l+ 77.7%

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

      4. *-commutative 77.7%

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

      5. fma-def 77.7%

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

      6. sub-neg 77.7%

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

      7. metadata-eval 77.7%

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

      8. fma-def 77.7%

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

   6. Simplified 77.7%

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

   7. Taylor expanded in x around 0 51.8%

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

   8. Taylor expanded in i around 0 49.7%

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

   if 215 < i

   1. Initial program 97.9%

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

   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. sub-neg 86.3%

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

      2. metadata-eval 86.3%

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

      3. add-cube-cbrt 86.3%

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

      4. pow3 86.3%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 86.3%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 86.3%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-+r+ 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in t around 0 61.2%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{elif}\;i \leq 215:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]

Alternative 9: 70.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+243} \lor \neg \left(x \leq 2 \cdot 10^{+153}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -9.8e+243) (not (<= x 2e+153)))
   (* x (log y))
   (+ (* y i) (+ t (+ z a)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -9.8e+243) || !(x <= 2e+153)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= (-9.8d+243)) .or. (.not. (x <= 2d+153))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -9.8e+243) || !(x <= 2e+153)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -9.8e+243) or not (x <= 2e+153):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -9.8e+243) || !(x <= 2e+153))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -9.8e+243) || ~((x <= 2e+153)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -9.8e+243], N[Not[LessEqual[x, 2e+153]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.79999999999999967e243 or 2e153 < x

   1. Initial program 97.9%

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

      1. +-commutative 97.9%

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

      2. fma-def 97.9%

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

      3. +-commutative 97.9%

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

      4. fma-def 97.9%

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

      5. sub-neg 97.9%

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

      6. metadata-eval 97.9%

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

      7. associate-+l+ 97.9%

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

      8. fma-def 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in t around 0 96.1%

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

      1. +-commutative 96.1%

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

      2. +-commutative 96.1%

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

      3. associate-+l+ 96.1%

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

      4. *-commutative 96.1%

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

      5. fma-def 96.1%

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

      6. sub-neg 96.1%

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

      7. metadata-eval 96.1%

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

      8. fma-def 96.1%

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

   6. Simplified 96.1%

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

   7. Taylor expanded in x around inf 65.2%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -9.79999999999999967e243 < x < 2e153

   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 93.6%

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

      1. sub-neg 93.6%

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

      2. metadata-eval 93.6%

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

      3. add-cube-cbrt 93.5%

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

      4. pow3 93.5%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 93.5%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 93.5%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-+r+ 80.2%

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

   7. Simplified 80.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+243} \lor \neg \left(x \leq 2 \cdot 10^{+153}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]

Alternative 10: 69.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+229}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -3e+229) (* b (log c)) (+ (* y i) (+ t (+ z a)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -3e+229) {
		tmp = b * log(c);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 <= (-3d+229)) then
        tmp = b * log(c)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -3e+229) {
		tmp = b * Math.log(c);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -3e+229:
		tmp = b * math.log(c)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -3e+229)
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -3e+229)
		tmp = b * log(c);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -3e+229], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.99999999999999998e229

   1. Initial program 99.3%

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

   2. Taylor expanded in b around inf 58.8%

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

   if -2.99999999999999998e229 < b

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 79.2%

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

      1. sub-neg 79.2%

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

      2. metadata-eval 79.2%

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

      3. add-cube-cbrt 79.1%

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

      4. pow3 79.1%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 79.1%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 79.1%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-+r+ 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+229}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]

Alternative 11: 51.7% accurate, 24.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+102}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.6e+122) (* y i) (if (<= i 2.9e+102) (+ a (+ z t)) (* y i))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.6e+122) {
		tmp = y * i;
	} else if (i <= 2.9e+102) {
		tmp = a + (z + t);
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 (i <= (-1.6d+122)) then
        tmp = y * i
    else if (i <= 2.9d+102) then
        tmp = a + (z + t)
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.6e+122) {
		tmp = y * i;
	} else if (i <= 2.9e+102) {
		tmp = a + (z + t);
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.6e+122:
		tmp = y * i
	elif i <= 2.9e+102:
		tmp = a + (z + t)
	else:
		tmp = y * i
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.6e+122)
		tmp = Float64(y * i);
	elseif (i <= 2.9e+102)
		tmp = Float64(a + Float64(z + t));
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -1.6e+122)
		tmp = y * i;
	elseif (i <= 2.9e+102)
		tmp = a + (z + t);
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.6e+122], N[(y * i), $MachinePrecision], If[LessEqual[i, 2.9e+102], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(y * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.60000000000000006e122 or 2.9000000000000002e102 < i

   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 60.6%

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

      1. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   if -1.60000000000000006e122 < i < 2.9000000000000002e102

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 75.7%

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

      1. sub-neg 75.7%

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

      2. metadata-eval 75.7%

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

      3. add-cube-cbrt 75.6%

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

      4. pow3 75.6%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 75.6%

         \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

   4. Applied egg-rr 75.6%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

   5. Taylor expanded in b around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. associate-+r+ 62.8%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in y around 0 54.7%

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

      1. +-commutative 54.7%

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

   10. Simplified 54.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+102}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]

Alternative 12: 67.5% accurate, 24.3× speedup

Math

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

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (+ (* y i) (+ t (+ z a))))

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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) + (t + (z + a))
end function

Java

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

Python

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

Julia

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

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (t + (z + a));
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in x around 0 79.0%

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

   1. sub-neg 79.0%

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

   2. metadata-eval 79.0%

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

   3. add-cube-cbrt 78.9%

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

   4. pow3 78.9%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

   5. *-commutative 78.9%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

4. Applied egg-rr 78.9%

   \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

5. Taylor expanded in b around inf 68.3%

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

   1. +-commutative 68.3%

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

   2. associate-+r+ 68.3%

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

7. Simplified 68.3%

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

8. Final simplification 68.3%

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

Alternative 13: 37.9% accurate, 30.7× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{-110}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+193}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 4.5e-110) z (if (<= a 2.5e+193) (* y i) a)))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.5e-110) {
		tmp = z;
	} else if (a <= 2.5e+193) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 (a <= 4.5d-110) then
        tmp = z
    else if (a <= 2.5d+193) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.5e-110) {
		tmp = z;
	} else if (a <= 2.5e+193) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.5e-110:
		tmp = z
	elif a <= 2.5e+193:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.5e-110)
		tmp = z;
	elseif (a <= 2.5e+193)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4.5e-110)
		tmp = z;
	elseif (a <= 2.5e+193)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.5e-110], z, If[LessEqual[a, 2.5e+193], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if a < 4.5000000000000001e-110

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 19.8%

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

   if 4.5000000000000001e-110 < a < 2.49999999999999986e193

   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 y around inf 27.5%

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

      1. *-commutative 27.5%

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

   4. Simplified 27.5%

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

   if 2.49999999999999986e193 < a

   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 40.9%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{-110}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+193}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14: 66.9% accurate, 31.3× speedup

Math

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

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (+ (* y i) (+ z a)))

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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) + (z + a)
end function

Java

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

Python

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

Julia

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

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (z + a);
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in x around 0 79.0%

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

   1. sub-neg 79.0%

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

   2. metadata-eval 79.0%

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

   3. add-cube-cbrt 78.9%

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

   4. pow3 78.9%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

   5. *-commutative 78.9%

      \[\leadsto \left(\left(a + \left(t + z\right)\right) + {\left(\sqrt[3]{\color{blue}{\log c \cdot \left(b + -0.5\right)}}\right)}^{3}\right) + y \cdot i \]

4. Applied egg-rr 78.9%

   \[\leadsto \left(\left(a + \left(t + z\right)\right) + \color{blue}{{\left(\sqrt[3]{\log c \cdot \left(b + -0.5\right)}\right)}^{3}}\right) + y \cdot i \]

5. Taylor expanded in b around inf 68.3%

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

   1. +-commutative 68.3%

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

   2. associate-+r+ 68.3%

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

7. Simplified 68.3%

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

8. Taylor expanded in t around 0 51.6%

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

9. Final simplification 51.6%

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

Alternative 15: 37.1% accurate, 71.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.35 \cdot 10^{+168}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (if (<= a 1.35e+168) z a))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.35e+168) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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 (a <= 1.35d+168) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.35e+168) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.35e+168:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.35e+168)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.35e+168)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.35e+168], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 1.35000000000000008e168

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 20.4%

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

   if 1.35000000000000008e168 < 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 a around inf 36.7%

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

4. Final simplification 22.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.35 \cdot 10^{+168}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 22.6% accurate, 219.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ a \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 a)

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
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

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

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	return a

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in a around inf 11.8%

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

3. Final simplification 11.8%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023238 
(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)))