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

Percentage Accurate: 99.8% → 99.8%

Time: 12.8s

Alternatives: 23

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, 1.0× speedup

Math

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

FPCore

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

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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

NOTE: x, y, z, t, a, b, c, and i 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 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
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

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
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

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
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

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 92.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ t_2 := y \cdot i + \left(t\_1 + \left(z + a\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+163}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))) (t_2 (+ (* y i) (+ t_1 (+ z a)))))
   (if (<= t_1 -1e+65)
     t_2
     (if (<= t_1 2e+163) (+ (* y i) (+ (* x (log y)) (+ a (+ z t)))) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double t_2 = (y * i) + (t_1 + (z + a));
	double tmp;
	if (t_1 <= -1e+65) {
		tmp = t_2;
	} else if (t_1 <= 2e+163) {
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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) :: t_2
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    t_2 = (y * i) + (t_1 + (z + a))
    if (t_1 <= (-1d+65)) then
        tmp = t_2
    else if (t_1 <= 2d+163) then
        tmp = (y * i) + ((x * log(y)) + (a + (z + t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * Math.log(c);
	double t_2 = (y * i) + (t_1 + (z + a));
	double tmp;
	if (t_1 <= -1e+65) {
		tmp = t_2;
	} else if (t_1 <= 2e+163) {
		tmp = (y * i) + ((x * Math.log(y)) + (a + (z + t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	t_2 = (y * i) + (t_1 + (z + a))
	tmp = 0
	if t_1 <= -1e+65:
		tmp = t_2
	elif t_1 <= 2e+163:
		tmp = (y * i) + ((x * math.log(y)) + (a + (z + t)))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	t_2 = Float64(Float64(y * i) + Float64(t_1 + Float64(z + a)))
	tmp = 0.0
	if (t_1 <= -1e+65)
		tmp = t_2;
	elseif (t_1 <= 2e+163)
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(a + Float64(z + t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	t_2 = (y * i) + (t_1 + (z + a));
	tmp = 0.0;
	if (t_1 <= -1e+65)
		tmp = t_2;
	elseif (t_1 <= 2e+163)
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+65], t$95$2, If[LessEqual[t$95$1, 2e+163], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -9.9999999999999999e64 or 1.9999999999999999e163 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{z}, a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 87.8%

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

   if -9.9999999999999999e64 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 1.9999999999999999e163

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 97.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 97.1%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)}, \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a + \left(\left(t + z\right) + x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(a + \left(t + z\right)\right) + x \cdot \log y\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a + \left(t + z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(t + z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      7. log-lowering-log.f64 95.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 95.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b - 0.5\right) \cdot \log c \leq -1 \cdot 10^{+65}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{elif}\;\left(b - 0.5\right) \cdot \log c \leq 2 \cdot 10^{+163}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := a + \left(z + t\right)\\ t_3 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot i + \left(t\_1 + t\_2\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+137}:\\ \;\;\;\;y \cdot i + \left(t\_3 + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + t\_3\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i 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_2 (+ a (+ z t))) (t_3 (* (- b 0.5) (log c))))
   (if (<= x -1.5e+129)
     (+ (* y i) (+ t_1 t_2))
     (if (<= x 2.1e+137) (+ (* y i) (+ t_3 t_2)) (+ (* y i) (+ t_1 t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double t_2 = a + (z + t);
	double t_3 = (b - 0.5) * log(c);
	double tmp;
	if (x <= -1.5e+129) {
		tmp = (y * i) + (t_1 + t_2);
	} else if (x <= 2.1e+137) {
		tmp = (y * i) + (t_3 + t_2);
	} else {
		tmp = (y * i) + (t_1 + t_3);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = a + (z + t)
    t_3 = (b - 0.5d0) * log(c)
    if (x <= (-1.5d+129)) then
        tmp = (y * i) + (t_1 + t_2)
    else if (x <= 2.1d+137) then
        tmp = (y * i) + (t_3 + t_2)
    else
        tmp = (y * i) + (t_1 + t_3)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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);
	double t_2 = a + (z + t);
	double t_3 = (b - 0.5) * Math.log(c);
	double tmp;
	if (x <= -1.5e+129) {
		tmp = (y * i) + (t_1 + t_2);
	} else if (x <= 2.1e+137) {
		tmp = (y * i) + (t_3 + t_2);
	} else {
		tmp = (y * i) + (t_1 + t_3);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = a + (z + t)
	t_3 = (b - 0.5) * math.log(c)
	tmp = 0
	if x <= -1.5e+129:
		tmp = (y * i) + (t_1 + t_2)
	elif x <= 2.1e+137:
		tmp = (y * i) + (t_3 + t_2)
	else:
		tmp = (y * i) + (t_1 + t_3)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(a + Float64(z + t))
	t_3 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (x <= -1.5e+129)
		tmp = Float64(Float64(y * i) + Float64(t_1 + t_2));
	elseif (x <= 2.1e+137)
		tmp = Float64(Float64(y * i) + Float64(t_3 + t_2));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + t_3));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = a + (z + t);
	t_3 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (x <= -1.5e+129)
		tmp = (y * i) + (t_1 + t_2);
	elseif (x <= 2.1e+137)
		tmp = (y * i) + (t_3 + t_2);
	else
		tmp = (y * i) + (t_1 + t_3);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+129], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+137], N[(N[(y * i), $MachinePrecision] + N[(t$95$3 + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.50000000000000015e129

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)}, \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a + \left(\left(t + z\right) + x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(a + \left(t + z\right)\right) + x \cdot \log y\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a + \left(t + z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(t + z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      7. log-lowering-log.f64 91.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 91.9%

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

   if -1.50000000000000015e129 < x < 2.0999999999999999e137

   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. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{z}, t\right), a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 97.6%

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

   if 2.0999999999999999e137 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot \log y\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      2. log-lowering-log.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 93.0%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+137}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, b, c, and i 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) + (((((x * log(y)) + z) + t) + a) + (b * log(c)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf

   \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   3. log-lowering-log.f64 98.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 5: 59.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{-188}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-22}:\\ \;\;\;\;z + \log c \cdot \left(b + -0.5\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3e-188)
   (+ z (* y i))
   (if (<= a 4.8e-22)
     (+ z (* (log c) (+ b -0.5)))
     (if (<= a 2.05e+68)
       (+ (* y i) (* b (log c)))
       (if (<= a 3e+93) (* x (+ (log y) (/ z x))) (+ a (* y i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3e-188) {
		tmp = z + (y * i);
	} else if (a <= 4.8e-22) {
		tmp = z + (log(c) * (b + -0.5));
	} else if (a <= 2.05e+68) {
		tmp = (y * i) + (b * log(c));
	} else if (a <= 3e+93) {
		tmp = x * (log(y) + (z / x));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 <= 3d-188) then
        tmp = z + (y * i)
    else if (a <= 4.8d-22) then
        tmp = z + (log(c) * (b + (-0.5d0)))
    else if (a <= 2.05d+68) then
        tmp = (y * i) + (b * log(c))
    else if (a <= 3d+93) then
        tmp = x * (log(y) + (z / x))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3e-188) {
		tmp = z + (y * i);
	} else if (a <= 4.8e-22) {
		tmp = z + (Math.log(c) * (b + -0.5));
	} else if (a <= 2.05e+68) {
		tmp = (y * i) + (b * Math.log(c));
	} else if (a <= 3e+93) {
		tmp = x * (Math.log(y) + (z / x));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3e-188:
		tmp = z + (y * i)
	elif a <= 4.8e-22:
		tmp = z + (math.log(c) * (b + -0.5))
	elif a <= 2.05e+68:
		tmp = (y * i) + (b * math.log(c))
	elif a <= 3e+93:
		tmp = x * (math.log(y) + (z / x))
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3e-188)
		tmp = Float64(z + Float64(y * i));
	elseif (a <= 4.8e-22)
		tmp = Float64(z + Float64(log(c) * Float64(b + -0.5)));
	elseif (a <= 2.05e+68)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	elseif (a <= 3e+93)
		tmp = Float64(x * Float64(log(y) + Float64(z / x)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3e-188)
		tmp = z + (y * i);
	elseif (a <= 4.8e-22)
		tmp = z + (log(c) * (b + -0.5));
	elseif (a <= 2.05e+68)
		tmp = (y * i) + (b * log(c));
	elseif (a <= 3e+93)
		tmp = x * (log(y) + (z / x));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3e-188], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-22], N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e+68], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+93], N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < 3.00000000000000017e-188

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 44.8%

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

   if 3.00000000000000017e-188 < a < 4.80000000000000005e-22

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 72.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + \log c \cdot \left(b - \frac{1}{2}\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\log c, \color{blue}{\left(b - \frac{1}{2}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(\color{blue}{b} - \frac{1}{2}\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right)\right) \]

      6. +-lowering-+.f64 48.8%

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \color{blue}{\frac{-1}{2}}\right)\right)\right) \]

   8. Simplified 48.8%

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

   if 4.80000000000000005e-22 < a < 2.05e68

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(b \cdot \log c\right)}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\log c \cdot b\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\log c, b\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

      3. log-lowering-log.f64 36.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 36.8%

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

   if 2.05e68 < a < 2.99999999999999978e93

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. sum4-define N/A

         \[\leadsto \mathsf{sum4}\left(a, \color{blue}{t}, z, \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \left(\mathsf{neg}\left(\log c\right)\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. log-rec N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + \left(\mathsf{neg}\left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right) \]

      8. sum4-define N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right)} \]

      9. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \left(\left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) + \color{blue}{x \cdot \log y}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(\left(a + t\right) + \left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + \color{blue}{x \cdot \log y} \]

   5. Simplified 90.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 42.6%

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

   9. Taylor expanded in x around inf

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

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

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

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

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

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

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

       4. /-lowering-/.f64 35.6%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(z, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 35.6%

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

   if 2.99999999999999978e93 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 55.0%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{-188}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-22}:\\ \;\;\;\;z + \log c \cdot \left(b + -0.5\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 2.2 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;z + \log c \cdot \left(b + -0.5\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+147}:\\ \;\;\;\;a + \left(x \cdot \log y + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i 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 (<= a 2.2e-187)
     t_1
     (if (<= a 2.1e-104)
       (+ z (* (log c) (+ b -0.5)))
       (if (<= a 1.5e+77)
         t_1
         (if (<= a 8e+147) (+ a (+ (* x (log y)) t)) (+ a (* y i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 (a <= 2.2e-187) {
		tmp = t_1;
	} else if (a <= 2.1e-104) {
		tmp = z + (log(c) * (b + -0.5));
	} else if (a <= 1.5e+77) {
		tmp = t_1;
	} else if (a <= 8e+147) {
		tmp = a + ((x * log(y)) + t);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (a <= 2.2d-187) then
        tmp = t_1
    else if (a <= 2.1d-104) then
        tmp = z + (log(c) * (b + (-0.5d0)))
    else if (a <= 1.5d+77) then
        tmp = t_1
    else if (a <= 8d+147) then
        tmp = a + ((x * log(y)) + t)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 (a <= 2.2e-187) {
		tmp = t_1;
	} else if (a <= 2.1e-104) {
		tmp = z + (Math.log(c) * (b + -0.5));
	} else if (a <= 1.5e+77) {
		tmp = t_1;
	} else if (a <= 8e+147) {
		tmp = a + ((x * Math.log(y)) + t);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= 2.2e-187:
		tmp = t_1
	elif a <= 2.1e-104:
		tmp = z + (math.log(c) * (b + -0.5))
	elif a <= 1.5e+77:
		tmp = t_1
	elif a <= 8e+147:
		tmp = a + ((x * math.log(y)) + t)
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 2.2e-187)
		tmp = t_1;
	elseif (a <= 2.1e-104)
		tmp = Float64(z + Float64(log(c) * Float64(b + -0.5)));
	elseif (a <= 1.5e+77)
		tmp = t_1;
	elseif (a <= 8e+147)
		tmp = Float64(a + Float64(Float64(x * log(y)) + t));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= 2.2e-187)
		tmp = t_1;
	elseif (a <= 2.1e-104)
		tmp = z + (log(c) * (b + -0.5));
	elseif (a <= 1.5e+77)
		tmp = t_1;
	elseif (a <= 8e+147)
		tmp = a + ((x * log(y)) + t);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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[LessEqual[a, 2.2e-187], t$95$1, If[LessEqual[a, 2.1e-104], N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+77], t$95$1, If[LessEqual[a, 8e+147], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 2.20000000000000008e-187 or 2.09999999999999999e-104 < a < 1.4999999999999999e77

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 46.7%

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

   if 2.20000000000000008e-187 < a < 2.09999999999999999e-104

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 58.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + \log c \cdot \left(b - \frac{1}{2}\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\log c, \color{blue}{\left(b - \frac{1}{2}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(\color{blue}{b} - \frac{1}{2}\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right)\right) \]

      6. +-lowering-+.f64 48.9%

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \color{blue}{\frac{-1}{2}}\right)\right)\right) \]

   8. Simplified 48.9%

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

   if 1.4999999999999999e77 < a < 7.9999999999999998e147

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. sum4-define N/A

         \[\leadsto \mathsf{sum4}\left(a, \color{blue}{t}, z, \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \left(\mathsf{neg}\left(\log c\right)\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. log-rec N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + \left(\mathsf{neg}\left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right) \]

      8. sum4-define N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right)} \]

      9. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \left(\left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) + \color{blue}{x \cdot \log y}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(\left(a + t\right) + \left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + \color{blue}{x \cdot \log y} \]

   5. Simplified 97.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{a + \left(t + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(t + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\color{blue}{\log c} \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\log c, \color{blue}{\left(b - \frac{1}{2}\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(\color{blue}{b} - \frac{1}{2}\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right)\right)\right)\right) \]

      10. +-lowering-+.f64 86.1%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \color{blue}{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

   8. Simplified 86.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(x \cdot \log y\right)}\right)\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\log y}\right)\right)\right) \]

       2. log-lowering-log.f64 70.3%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right)\right) \]

   11. Simplified 70.3%

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

   if 7.9999999999999998e147 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 66.2%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{-187}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;z + \log c \cdot \left(b + -0.5\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+147}:\\ \;\;\;\;a + \left(x \cdot \log y + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+148}:\\ \;\;\;\;a + \left(x \cdot \log y + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i 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 (<= a 1.8e-175)
     t_1
     (if (<= a 1.7e-104)
       (+ a (* b (log c)))
       (if (<= a 4.8e+78)
         t_1
         (if (<= a 2.2e+148) (+ a (+ (* x (log y)) t)) (+ a (* y i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 (a <= 1.8e-175) {
		tmp = t_1;
	} else if (a <= 1.7e-104) {
		tmp = a + (b * log(c));
	} else if (a <= 4.8e+78) {
		tmp = t_1;
	} else if (a <= 2.2e+148) {
		tmp = a + ((x * log(y)) + t);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (a <= 1.8d-175) then
        tmp = t_1
    else if (a <= 1.7d-104) then
        tmp = a + (b * log(c))
    else if (a <= 4.8d+78) then
        tmp = t_1
    else if (a <= 2.2d+148) then
        tmp = a + ((x * log(y)) + t)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 (a <= 1.8e-175) {
		tmp = t_1;
	} else if (a <= 1.7e-104) {
		tmp = a + (b * Math.log(c));
	} else if (a <= 4.8e+78) {
		tmp = t_1;
	} else if (a <= 2.2e+148) {
		tmp = a + ((x * Math.log(y)) + t);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= 1.8e-175:
		tmp = t_1
	elif a <= 1.7e-104:
		tmp = a + (b * math.log(c))
	elif a <= 4.8e+78:
		tmp = t_1
	elif a <= 2.2e+148:
		tmp = a + ((x * math.log(y)) + t)
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 1.8e-175)
		tmp = t_1;
	elseif (a <= 1.7e-104)
		tmp = Float64(a + Float64(b * log(c)));
	elseif (a <= 4.8e+78)
		tmp = t_1;
	elseif (a <= 2.2e+148)
		tmp = Float64(a + Float64(Float64(x * log(y)) + t));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= 1.8e-175)
		tmp = t_1;
	elseif (a <= 1.7e-104)
		tmp = a + (b * log(c));
	elseif (a <= 4.8e+78)
		tmp = t_1;
	elseif (a <= 2.2e+148)
		tmp = a + ((x * log(y)) + t);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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[LessEqual[a, 1.8e-175], t$95$1, If[LessEqual[a, 1.7e-104], N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+78], t$95$1, If[LessEqual[a, 2.2e+148], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 1.8e-175 or 1.70000000000000008e-104 < a < 4.7999999999999997e78

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 46.4%

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

   if 1.8e-175 < a < 1.70000000000000008e-104

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 94.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 94.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 51.3%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + b \cdot \log c} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \log c\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(a, \left(\log c \cdot \color{blue}{b}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\log c, \color{blue}{b}\right)\right) \]

       4. log-lowering-log.f64 40.4%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right) \]

   11. Simplified 40.4%

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

   if 4.7999999999999997e78 < a < 2.1999999999999999e148

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. sum4-define N/A

         \[\leadsto \mathsf{sum4}\left(a, \color{blue}{t}, z, \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \left(\mathsf{neg}\left(\log c\right)\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. log-rec N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + \left(\mathsf{neg}\left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right) \]

      8. sum4-define N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right)} \]

      9. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \left(\left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) + \color{blue}{x \cdot \log y}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(\left(a + t\right) + \left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + \color{blue}{x \cdot \log y} \]

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{a + \left(t + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(t + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\color{blue}{\log c} \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\log c, \color{blue}{\left(b - \frac{1}{2}\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(\color{blue}{b} - \frac{1}{2}\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right)\right)\right)\right) \]

      10. +-lowering-+.f64 93.9%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \color{blue}{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

   8. Simplified 93.9%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(x \cdot \log y\right)}\right)\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\log y}\right)\right)\right) \]

       2. log-lowering-log.f64 76.6%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right)\right) \]

   11. Simplified 76.6%

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

   if 2.1999999999999999e148 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 66.2%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+78}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+148}:\\ \;\;\;\;a + \left(x \cdot \log y + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ a (* b (log c))))))
   (if (<= (- b 0.5) -2e+186)
     t_1
     (if (<= (- b 0.5) 5e+146)
       (+ (* y i) (+ (* x (log y)) (+ a (+ z t))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (b * log(c)));
	double tmp;
	if ((b - 0.5) <= -2e+186) {
		tmp = t_1;
	} else if ((b - 0.5) <= 5e+146) {
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 = (y * i) + (a + (b * log(c)))
    if ((b - 0.5d0) <= (-2d+186)) then
        tmp = t_1
    else if ((b - 0.5d0) <= 5d+146) then
        tmp = (y * i) + ((x * log(y)) + (a + (z + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (b * Math.log(c)));
	double tmp;
	if ((b - 0.5) <= -2e+186) {
		tmp = t_1;
	} else if ((b - 0.5) <= 5e+146) {
		tmp = (y * i) + ((x * Math.log(y)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (a + (b * math.log(c)))
	tmp = 0
	if (b - 0.5) <= -2e+186:
		tmp = t_1
	elif (b - 0.5) <= 5e+146:
		tmp = (y * i) + ((x * math.log(y)) + (a + (z + t)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))))
	tmp = 0.0
	if (Float64(b - 0.5) <= -2e+186)
		tmp = t_1;
	elseif (Float64(b - 0.5) <= 5e+146)
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(a + Float64(z + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (a + (b * log(c)));
	tmp = 0.0;
	if ((b - 0.5) <= -2e+186)
		tmp = t_1;
	elseif ((b - 0.5) <= 5e+146)
		tmp = (y * i) + ((x * log(y)) + (a + (z + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+186], t$95$1, If[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+146], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -1.99999999999999996e186 or 4.9999999999999999e146 < (-.f64 b #s(literal 1/2 binary64))

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 78.9%

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

   if -1.99999999999999996e186 < (-.f64 b #s(literal 1/2 binary64)) < 4.9999999999999999e146

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 97.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 97.4%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)}, \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a + \left(\left(t + z\right) + x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(a + \left(t + z\right)\right) + x \cdot \log y\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a + \left(t + z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(t + z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      7. log-lowering-log.f64 93.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 93.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+186}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 2.7 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-104}:\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i 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 (<= a 2.7e-175)
     t_1
     (if (<= a 1.8e-104)
       (+ a (* b (log c)))
       (if (<= a 4.1e+78)
         t_1
         (if (<= a 5.2e+146) (+ (* x (log y)) a) (+ a (* y i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 (a <= 2.7e-175) {
		tmp = t_1;
	} else if (a <= 1.8e-104) {
		tmp = a + (b * log(c));
	} else if (a <= 4.1e+78) {
		tmp = t_1;
	} else if (a <= 5.2e+146) {
		tmp = (x * log(y)) + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (a <= 2.7d-175) then
        tmp = t_1
    else if (a <= 1.8d-104) then
        tmp = a + (b * log(c))
    else if (a <= 4.1d+78) then
        tmp = t_1
    else if (a <= 5.2d+146) then
        tmp = (x * log(y)) + a
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 (a <= 2.7e-175) {
		tmp = t_1;
	} else if (a <= 1.8e-104) {
		tmp = a + (b * Math.log(c));
	} else if (a <= 4.1e+78) {
		tmp = t_1;
	} else if (a <= 5.2e+146) {
		tmp = (x * Math.log(y)) + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= 2.7e-175:
		tmp = t_1
	elif a <= 1.8e-104:
		tmp = a + (b * math.log(c))
	elif a <= 4.1e+78:
		tmp = t_1
	elif a <= 5.2e+146:
		tmp = (x * math.log(y)) + a
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 2.7e-175)
		tmp = t_1;
	elseif (a <= 1.8e-104)
		tmp = Float64(a + Float64(b * log(c)));
	elseif (a <= 4.1e+78)
		tmp = t_1;
	elseif (a <= 5.2e+146)
		tmp = Float64(Float64(x * log(y)) + a);
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= 2.7e-175)
		tmp = t_1;
	elseif (a <= 1.8e-104)
		tmp = a + (b * log(c));
	elseif (a <= 4.1e+78)
		tmp = t_1;
	elseif (a <= 5.2e+146)
		tmp = (x * log(y)) + a;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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[LessEqual[a, 2.7e-175], t$95$1, If[LessEqual[a, 1.8e-104], N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e+78], t$95$1, If[LessEqual[a, 5.2e+146], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 2.69999999999999999e-175 or 1.7999999999999999e-104 < a < 4.0999999999999997e78

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 46.4%

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

   if 2.69999999999999999e-175 < a < 1.7999999999999999e-104

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 94.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 94.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 51.3%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + b \cdot \log c} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \log c\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(a, \left(\log c \cdot \color{blue}{b}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\log c, \color{blue}{b}\right)\right) \]

       4. log-lowering-log.f64 40.4%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right) \]

   11. Simplified 40.4%

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

   if 4.0999999999999997e78 < a < 5.20000000000000028e146

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. sum4-define N/A

         \[\leadsto \mathsf{sum4}\left(a, \color{blue}{t}, z, \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \left(\mathsf{neg}\left(\log c\right)\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. log-rec N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + \left(\mathsf{neg}\left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right) \]

      8. sum4-define N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right)} \]

      9. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \left(\left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) + \color{blue}{x \cdot \log y}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(\left(a + t\right) + \left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + \color{blue}{x \cdot \log y} \]

   5. Simplified 99.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 41.7%

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

   if 5.20000000000000028e146 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 66.2%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.7 \cdot 10^{-175}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-104}:\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+78}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 2.7 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i 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 (<= a 2.7e-175)
     t_1
     (if (<= a 1.7e-104)
       (* b (log c))
       (if (<= a 1.15e+77)
         t_1
         (if (<= a 1.1e+148) (+ (* x (log y)) a) (+ a (* y i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 (a <= 2.7e-175) {
		tmp = t_1;
	} else if (a <= 1.7e-104) {
		tmp = b * log(c);
	} else if (a <= 1.15e+77) {
		tmp = t_1;
	} else if (a <= 1.1e+148) {
		tmp = (x * log(y)) + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (a <= 2.7d-175) then
        tmp = t_1
    else if (a <= 1.7d-104) then
        tmp = b * log(c)
    else if (a <= 1.15d+77) then
        tmp = t_1
    else if (a <= 1.1d+148) then
        tmp = (x * log(y)) + a
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 (a <= 2.7e-175) {
		tmp = t_1;
	} else if (a <= 1.7e-104) {
		tmp = b * Math.log(c);
	} else if (a <= 1.15e+77) {
		tmp = t_1;
	} else if (a <= 1.1e+148) {
		tmp = (x * Math.log(y)) + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= 2.7e-175:
		tmp = t_1
	elif a <= 1.7e-104:
		tmp = b * math.log(c)
	elif a <= 1.15e+77:
		tmp = t_1
	elif a <= 1.1e+148:
		tmp = (x * math.log(y)) + a
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 2.7e-175)
		tmp = t_1;
	elseif (a <= 1.7e-104)
		tmp = Float64(b * log(c));
	elseif (a <= 1.15e+77)
		tmp = t_1;
	elseif (a <= 1.1e+148)
		tmp = Float64(Float64(x * log(y)) + a);
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= 2.7e-175)
		tmp = t_1;
	elseif (a <= 1.7e-104)
		tmp = b * log(c);
	elseif (a <= 1.15e+77)
		tmp = t_1;
	elseif (a <= 1.1e+148)
		tmp = (x * log(y)) + a;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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[LessEqual[a, 2.7e-175], t$95$1, If[LessEqual[a, 1.7e-104], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+77], t$95$1, If[LessEqual[a, 1.1e+148], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 2.69999999999999999e-175 or 1.70000000000000008e-104 < a < 1.14999999999999997e77

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 46.1%

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

   if 2.69999999999999999e-175 < a < 1.70000000000000008e-104

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\log c, \color{blue}{b}\right) \]

      3. log-lowering-log.f64 40.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right) \]

   5. Simplified 40.5%

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

   if 1.14999999999999997e77 < a < 1.0999999999999999e148

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. sum4-define N/A

         \[\leadsto \mathsf{sum4}\left(a, \color{blue}{t}, z, \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \left(\mathsf{neg}\left(\log c\right)\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. log-rec N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + \left(\mathsf{neg}\left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right) \]

      8. sum4-define N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right)} \]

      9. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \left(\left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) + \color{blue}{x \cdot \log y}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(\left(a + t\right) + \left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + \color{blue}{x \cdot \log y} \]

   5. Simplified 97.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 38.6%

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

   if 1.0999999999999999e148 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 66.2%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.7 \cdot 10^{-175}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 95.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a + \left(z + t\right)\\ t_2 := y \cdot i + \left(x \cdot \log y + t\_1\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i 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))) (t_2 (+ (* y i) (+ (* x (log y)) t_1))))
   (if (<= x -1.7e+129)
     t_2
     (if (<= x 2.8e+63) (+ (* y i) (+ (* (- b 0.5) (log c)) t_1)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 t_2 = (y * i) + ((x * log(y)) + t_1);
	double tmp;
	if (x <= -1.7e+129) {
		tmp = t_2;
	} else if (x <= 2.8e+63) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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) :: t_2
    real(8) :: tmp
    t_1 = a + (z + t)
    t_2 = (y * i) + ((x * log(y)) + t_1)
    if (x <= (-1.7d+129)) then
        tmp = t_2
    else if (x <= 2.8d+63) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 t_2 = (y * i) + ((x * Math.log(y)) + t_1);
	double tmp;
	if (x <= -1.7e+129) {
		tmp = t_2;
	} else if (x <= 2.8e+63) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = a + (z + t)
	t_2 = (y * i) + ((x * math.log(y)) + t_1)
	tmp = 0
	if x <= -1.7e+129:
		tmp = t_2
	elif x <= 2.8e+63:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + t_1)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(z + t))
	t_2 = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t_1))
	tmp = 0.0
	if (x <= -1.7e+129)
		tmp = t_2;
	elseif (x <= 2.8e+63)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (z + t);
	t_2 = (y * i) + ((x * log(y)) + t_1);
	tmp = 0.0;
	if (x <= -1.7e+129)
		tmp = t_2;
	elseif (x <= 2.8e+63)
		tmp = (y * i) + (((b - 0.5) * log(c)) + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+129], t$95$2, If[LessEqual[x, 2.8e+63], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000009e129 or 2.79999999999999987e63 < x

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)}, \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a + \left(\left(t + z\right) + x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(a + \left(t + z\right)\right) + x \cdot \log y\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a + \left(t + z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(t + z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \left(x \cdot \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \log y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      7. log-lowering-log.f64 89.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 89.9%

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

   if -1.70000000000000009e129 < x < 2.79999999999999987e63

   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. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{z}, t\right), a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 99.0%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+129}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 8.2 \cdot 10^{-190}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;z + \log c \cdot \left(b + -0.5\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 8.2e-190)
   (+ z (* y i))
   (if (<= a 1.6e-64)
     (+ z (* (log c) (+ b -0.5)))
     (if (<= a 9.6e+95) (+ (* x (log y)) (* y i)) (+ a (* y i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 8.2e-190) {
		tmp = z + (y * i);
	} else if (a <= 1.6e-64) {
		tmp = z + (log(c) * (b + -0.5));
	} else if (a <= 9.6e+95) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 <= 8.2d-190) then
        tmp = z + (y * i)
    else if (a <= 1.6d-64) then
        tmp = z + (log(c) * (b + (-0.5d0)))
    else if (a <= 9.6d+95) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 8.2e-190) {
		tmp = z + (y * i);
	} else if (a <= 1.6e-64) {
		tmp = z + (Math.log(c) * (b + -0.5));
	} else if (a <= 9.6e+95) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 8.2e-190:
		tmp = z + (y * i)
	elif a <= 1.6e-64:
		tmp = z + (math.log(c) * (b + -0.5))
	elif a <= 9.6e+95:
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 8.2e-190)
		tmp = Float64(z + Float64(y * i));
	elseif (a <= 1.6e-64)
		tmp = Float64(z + Float64(log(c) * Float64(b + -0.5)));
	elseif (a <= 9.6e+95)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 8.2e-190)
		tmp = z + (y * i);
	elseif (a <= 1.6e-64)
		tmp = z + (log(c) * (b + -0.5));
	elseif (a <= 9.6e+95)
		tmp = (x * log(y)) + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 8.2e-190], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-64], N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e+95], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 8.2000000000000004e-190

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 44.8%

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

   if 8.2000000000000004e-190 < a < 1.59999999999999988e-64

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 68.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + \log c \cdot \left(b - \frac{1}{2}\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\log c, \color{blue}{\left(b - \frac{1}{2}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(\color{blue}{b} - \frac{1}{2}\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right)\right) \]

      6. +-lowering-+.f64 55.8%

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \color{blue}{\frac{-1}{2}}\right)\right)\right) \]

   8. Simplified 55.8%

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

   if 1.59999999999999988e-64 < a < 9.6000000000000002e95

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot \log y\right)}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

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

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

      2. log-lowering-log.f64 50.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 50.8%

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

   if 9.6000000000000002e95 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 55.0%

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

Alternative 13: 76.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+78}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 5e+78)
   (+ (* y i) (+ z (* (- b 0.5) (log c))))
   (if (<= a 1.15e+94) (+ (* x (log y)) z) (+ (* y i) (+ a (* b (log c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 5e+78) {
		tmp = (y * i) + (z + ((b - 0.5) * log(c)));
	} else if (a <= 1.15e+94) {
		tmp = (x * log(y)) + z;
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 <= 5d+78) then
        tmp = (y * i) + (z + ((b - 0.5d0) * log(c)))
    else if (a <= 1.15d+94) then
        tmp = (x * log(y)) + z
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 5e+78) {
		tmp = (y * i) + (z + ((b - 0.5) * Math.log(c)));
	} else if (a <= 1.15e+94) {
		tmp = (x * Math.log(y)) + z;
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 5e+78:
		tmp = (y * i) + (z + ((b - 0.5) * math.log(c)))
	elif a <= 1.15e+94:
		tmp = (x * math.log(y)) + z
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 5e+78)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	elseif (a <= 1.15e+94)
		tmp = Float64(Float64(x * log(y)) + z);
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 5e+78)
		tmp = (y * i) + (z + ((b - 0.5) * log(c)));
	elseif (a <= 1.15e+94)
		tmp = (x * log(y)) + z;
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 5e+78], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+94], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 4.99999999999999984e78

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 61.8%

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

   if 4.99999999999999984e78 < a < 1.15e94

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. sum4-define N/A

         \[\leadsto \mathsf{sum4}\left(a, \color{blue}{t}, z, \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \left(\mathsf{neg}\left(\log c\right)\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. log-rec N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + \left(\mathsf{neg}\left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right) \]

      8. sum4-define N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right)} \]

      9. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \left(\left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) + \color{blue}{x \cdot \log y}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(\left(a + t\right) + \left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + \color{blue}{x \cdot \log y} \]

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 26.3%

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

   if 1.15e94 < a

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 99.8%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 67.3%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+78}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;\left(a + \left(z + t\right)\right) + \log c \cdot \left(b + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 7.5e-11)
   (+ (+ a (+ z t)) (* (log c) (+ b -0.5)))
   (+ (* y i) (+ a (* b (log c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 7.5e-11) {
		tmp = (a + (z + t)) + (log(c) * (b + -0.5));
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (y <= 7.5d-11) then
        tmp = (a + (z + t)) + (log(c) * (b + (-0.5d0)))
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 7.5e-11) {
		tmp = (a + (z + t)) + (Math.log(c) * (b + -0.5));
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 7.5e-11:
		tmp = (a + (z + t)) + (math.log(c) * (b + -0.5))
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 7.5e-11)
		tmp = Float64(Float64(a + Float64(z + t)) + Float64(log(c) * Float64(b + -0.5)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 7.5e-11)
		tmp = (a + (z + t)) + (log(c) * (b + -0.5));
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 7.5e-11], N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.5e-11

   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. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. sum4-define N/A

         \[\leadsto \mathsf{sum4}\left(a, \color{blue}{t}, z, \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \left(\mathsf{neg}\left(\log c\right)\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. log-rec N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + \left(\mathsf{neg}\left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right) \]

      8. sum4-define N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right)} \]

      9. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \left(\left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) + \color{blue}{x \cdot \log y}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(\left(a + t\right) + \left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + \color{blue}{x \cdot \log y} \]

   5. Simplified 95.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto a + \left(\left(t + z\right) + \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)}\right) \]

      2. associate-+r+ N/A

         \[\leadsto \left(a + \left(t + z\right)\right) + \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(a + \left(t + z\right)\right), \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \left(t + z\right)\right), \left(\color{blue}{\log c} \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \left(\log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(\log c, \color{blue}{\left(b - \frac{1}{2}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(\color{blue}{b} - \frac{1}{2}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right)\right) \]

      10. +-lowering-+.f64 75.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \color{blue}{\frac{-1}{2}}\right)\right)\right) \]

   8. Simplified 75.9%

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

   if 7.5e-11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 61.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;\left(a + \left(z + t\right)\right) + \log c \cdot \left(b + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+251}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.45e+251) (+ z (* y i)) (+ (* y i) (+ a (* (- b 0.5) (log c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.45e+251) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (z <= (-2.45d+251)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a + ((b - 0.5d0) * log(c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.45e+251) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.45e+251:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.45e+251)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.45e+251)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.45e+251], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.44999999999999977e251

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 95.0%

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

   if -2.44999999999999977e251 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 54.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+251}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+251}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.45e+251) (+ z (* y i)) (+ (* y i) (+ a (* b (log c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.45e+251) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (z <= (-2.45d+251)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.45e+251) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.45e+251:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.45e+251)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.45e+251)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.45e+251], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.44999999999999977e251

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 95.0%

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

   if -2.44999999999999977e251 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \color{blue}{\left(b \cdot \log c\right)}\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \left(\log c \cdot b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\log c, b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), t\right), a\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 97.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 52.8%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+251}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 2.4 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i 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 (<= a 2.4e-175)
     t_1
     (if (<= a 1.7e-104)
       (* b (log c))
       (if (<= a 1.52e+90) t_1 (+ a (* y i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 (a <= 2.4e-175) {
		tmp = t_1;
	} else if (a <= 1.7e-104) {
		tmp = b * log(c);
	} else if (a <= 1.52e+90) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (a <= 2.4d-175) then
        tmp = t_1
    else if (a <= 1.7d-104) then
        tmp = b * log(c)
    else if (a <= 1.52d+90) then
        tmp = t_1
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 (a <= 2.4e-175) {
		tmp = t_1;
	} else if (a <= 1.7e-104) {
		tmp = b * Math.log(c);
	} else if (a <= 1.52e+90) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= 2.4e-175:
		tmp = t_1
	elif a <= 1.7e-104:
		tmp = b * math.log(c)
	elif a <= 1.52e+90:
		tmp = t_1
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 2.4e-175)
		tmp = t_1;
	elseif (a <= 1.7e-104)
		tmp = Float64(b * log(c));
	elseif (a <= 1.52e+90)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= 2.4e-175)
		tmp = t_1;
	elseif (a <= 1.7e-104)
		tmp = b * log(c);
	elseif (a <= 1.52e+90)
		tmp = t_1;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i 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[LessEqual[a, 2.4e-175], t$95$1, If[LessEqual[a, 1.7e-104], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.52e+90], t$95$1, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 2.4e-175 or 1.70000000000000008e-104 < a < 1.52000000000000009e90

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 45.9%

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

   if 2.4e-175 < a < 1.70000000000000008e-104

   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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\log c, \color{blue}{b}\right) \]

      3. log-lowering-log.f64 40.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), b\right) \]

   5. Simplified 40.5%

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

   if 1.52000000000000009e90 < a

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 52.3%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.4 \cdot 10^{-175}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{+90}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.8% accurate, 16.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-64}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+198}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2e-64) z (if (<= a 9.2e+198) (* y i) (+ t a))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2e-64) {
		tmp = z;
	} else if (a <= 9.2e+198) {
		tmp = y * i;
	} else {
		tmp = t + a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 <= 2d-64) then
        tmp = z
    else if (a <= 9.2d+198) then
        tmp = y * i
    else
        tmp = t + a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2e-64) {
		tmp = z;
	} else if (a <= 9.2e+198) {
		tmp = y * i;
	} else {
		tmp = t + a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2e-64:
		tmp = z
	elif a <= 9.2e+198:
		tmp = y * i
	else:
		tmp = t + a
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2e-64)
		tmp = z;
	elseif (a <= 9.2e+198)
		tmp = Float64(y * i);
	else
		tmp = Float64(t + a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2e-64)
		tmp = z;
	elseif (a <= 9.2e+198)
		tmp = y * i;
	else
		tmp = t + a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2e-64], z, If[LessEqual[a, 9.2e+198], N[(y * i), $MachinePrecision], N[(t + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.99999999999999993e-64

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Simplified 20.4%

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

   if 1.99999999999999993e-64 < a < 9.2000000000000002e198

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 32.2%

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

   5. Simplified 32.2%

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

   if 9.2000000000000002e198 < a

   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. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]

      2. sum4-define N/A

         \[\leadsto \mathsf{sum4}\left(a, \color{blue}{t}, z, \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \left(\mathsf{neg}\left(\log c\right)\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      4. log-rec N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y - \log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + \left(\mathsf{neg}\left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(x \cdot \log y + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{sum4}\left(a, t, z, \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right) \]

      8. sum4-define N/A

         \[\leadsto \left(a + t\right) + \color{blue}{\left(z + \left(-1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right) + x \cdot \log y\right)\right)} \]

      9. associate-+r+ N/A

         \[\leadsto \left(a + t\right) + \left(\left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right) + \color{blue}{x \cdot \log y}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \left(\left(a + t\right) + \left(z + -1 \cdot \left(\log \left(\frac{1}{c}\right) \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + \color{blue}{x \cdot \log y} \]

   5. Simplified 66.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{a + \left(t + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(t + \left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(x \cdot \log y + \log c \cdot \left(b - \frac{1}{2}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\left(x \cdot \log y\right), \color{blue}{\left(\log c \cdot \left(b - \frac{1}{2}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \log y\right), \left(\color{blue}{\log c} \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \left(\log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\log c, \color{blue}{\left(b - \frac{1}{2}\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(\color{blue}{b} - \frac{1}{2}\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right)\right)\right)\right) \]

      10. +-lowering-+.f64 60.5%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \color{blue}{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

   8. Simplified 60.5%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{t}\right) \]
   10. Step-by-step derivation

   11. Simplified 43.0%

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

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-64}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+198}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.5% accurate, 16.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.7 \cdot 10^{-64}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+199}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.7e-64) z (if (<= a 2.4e+199) (* y i) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.7e-64) {
		tmp = z;
	} else if (a <= 2.4e+199) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 <= 1.7d-64) then
        tmp = z
    else if (a <= 2.4d+199) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.7e-64) {
		tmp = z;
	} else if (a <= 2.4e+199) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.7e-64:
		tmp = z
	elif a <= 2.4e+199:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.7e-64)
		tmp = z;
	elseif (a <= 2.4e+199)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.7e-64)
		tmp = z;
	elseif (a <= 2.4e+199)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.7e-64], z, If[LessEqual[a, 2.4e+199], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if a < 1.70000000000000006e-64

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Simplified 20.4%

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

   if 1.70000000000000006e-64 < a < 2.40000000000000015e199

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 32.2%

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

   5. Simplified 32.2%

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

   if 2.40000000000000015e199 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Simplified 43.6%

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

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.7 \cdot 10^{-64}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+199}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 60.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.36 \cdot 10^{+90}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.36e+90) (+ z (* y i)) (+ a (* y i))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.36e+90) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 <= 1.36d+90) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.36e+90) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.36e+90:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.36e+90)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.36e+90)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.36e+90], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.3600000000000001e90

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 44.2%

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

   if 1.3600000000000001e90 < a

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 52.3%

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

Alternative 21: 51.4% accurate, 21.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+255}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -7.2e+255) z (+ a (* y i))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7.2e+255) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 (z <= (-7.2d+255)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7.2e+255) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -7.2e+255:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -7.2e+255)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -7.2e+255)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -7.2e+255], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999998e255

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Simplified 90.0%

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

   if -7.1999999999999998e255 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 37.7%

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

Alternative 22: 38.0% accurate, 36.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.8 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (if (<= a 1.8e+83) z a))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.8e+83) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i 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 <= 1.8d+83) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.8e+83) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.8e+83:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.8e+83)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.8e+83)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.8e+83], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 1.7999999999999999e83

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Simplified 20.2%

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

   if 1.7999999999999999e83 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Simplified 26.5%

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

Alternative 23: 22.9% accurate, 219.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ a \end{array} \]

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around inf

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

5. Simplified 12.3%

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

Reproduce

herbie shell --seed 2024140 
(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)))