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

Percentage Accurate: 99.8% → 99.8%

Time: 16.3s

Alternatives: 22

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. fma-def 99.9%

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

   7. associate-+l+ 99.9%

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

   8. fma-def 99.9%

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

   9. +-commutative 99.9%

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

   10. associate-+l+ 99.9%

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

   11. fma-def 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 92.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := x \cdot \log y\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+173} \lor \neg \left(t_1 \leq 2 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot i + \left(t_1 + \left(a + t_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t_2 + \left(t + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (* x (log y))))
   (if (or (<= t_1 -5e+173) (not (<= t_1 2e+43)))
     (+ (* y i) (+ t_1 (+ a t_2)))
     (+ a (+ t_2 (+ t (+ z (+ (* y i) (* -0.5 (log c))))))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double t_2 = x * log(y);
	double tmp;
	if ((t_1 <= -5e+173) || !(t_1 <= 2e+43)) {
		tmp = (y * i) + (t_1 + (a + t_2));
	} else {
		tmp = a + (t_2 + (t + (z + ((y * i) + (-0.5 * log(c))))));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = x * log(y)
    if ((t_1 <= (-5d+173)) .or. (.not. (t_1 <= 2d+43))) then
        tmp = (y * i) + (t_1 + (a + t_2))
    else
        tmp = a + (t_2 + (t + (z + ((y * i) + ((-0.5d0) * log(c))))))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double t_2 = x * Math.log(y);
	double tmp;
	if ((t_1 <= -5e+173) || !(t_1 <= 2e+43)) {
		tmp = (y * i) + (t_1 + (a + t_2));
	} else {
		tmp = a + (t_2 + (t + (z + ((y * i) + (-0.5 * Math.log(c))))));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = x * math.log(y)
	tmp = 0
	if (t_1 <= -5e+173) or not (t_1 <= 2e+43):
		tmp = (y * i) + (t_1 + (a + t_2))
	else:
		tmp = a + (t_2 + (t + (z + ((y * i) + (-0.5 * math.log(c))))))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(x * log(y))
	tmp = 0.0
	if ((t_1 <= -5e+173) || !(t_1 <= 2e+43))
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + t_2)));
	else
		tmp = Float64(a + Float64(t_2 + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(-0.5 * log(c)))))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = x * log(y);
	tmp = 0.0;
	if ((t_1 <= -5e+173) || ~((t_1 <= 2e+43)))
		tmp = (y * i) + (t_1 + (a + t_2));
	else
		tmp = a + (t_2 + (t + (z + ((y * i) + (-0.5 * log(c))))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+173], N[Not[LessEqual[t$95$1, 2e+43]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t$95$2 + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b 1/2) (log.f64 c)) < -5.00000000000000034e173 or 2.00000000000000003e43 < (*.f64 (-.f64 b 1/2) (log.f64 c))

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 98.4%

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

   3. Taylor expanded in z around 0 85.3%

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

   if -5.00000000000000034e173 < (*.f64 (-.f64 b 1/2) (log.f64 c)) < 2.00000000000000003e43

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around 0 98.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -5 \cdot 10^{+173} \lor \neg \left(\log c \cdot \left(b - 0.5\right) \leq 2 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + \left(t + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\right)\right)\\ \end{array} \]

Alternative 3: 77.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+173} \lor \neg \left(t_1 \leq 2 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot i + \left(a + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (or (<= t_1 -5e+173) (not (<= t_1 2e+43)))
     (+ (* y i) (+ a t_1))
     (+ a (+ z (+ (* y i) (* -0.5 (log c))))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if ((t_1 <= -5e+173) || !(t_1 <= 2e+43)) {
		tmp = (y * i) + (a + t_1);
	} else {
		tmp = a + (z + ((y * i) + (-0.5 * log(c))));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if ((t_1 <= (-5d+173)) .or. (.not. (t_1 <= 2d+43))) then
        tmp = (y * i) + (a + t_1)
    else
        tmp = a + (z + ((y * i) + ((-0.5d0) * log(c))))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if ((t_1 <= -5e+173) || !(t_1 <= 2e+43)) {
		tmp = (y * i) + (a + t_1);
	} else {
		tmp = a + (z + ((y * i) + (-0.5 * Math.log(c))));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if (t_1 <= -5e+173) or not (t_1 <= 2e+43):
		tmp = (y * i) + (a + t_1)
	else:
		tmp = a + (z + ((y * i) + (-0.5 * math.log(c))))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if ((t_1 <= -5e+173) || !(t_1 <= 2e+43))
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	else
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(-0.5 * log(c)))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if ((t_1 <= -5e+173) || ~((t_1 <= 2e+43)))
		tmp = (y * i) + (a + t_1);
	else
		tmp = a + (z + ((y * i) + (-0.5 * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+173], N[Not[LessEqual[t$95$1, 2e+43]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b 1/2) (log.f64 c)) < -5.00000000000000034e173 or 2.00000000000000003e43 < (*.f64 (-.f64 b 1/2) (log.f64 c))

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 98.4%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in x around 0 71.2%

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

   if -5.00000000000000034e173 < (*.f64 (-.f64 b 1/2) (log.f64 c)) < 2.00000000000000003e43

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 80.5%

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

   3. Taylor expanded in b around 0 78.7%

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

   4. Taylor expanded in x around 0 64.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -5 \cdot 10^{+173} \lor \neg \left(\log c \cdot \left(b - 0.5\right) \leq 2 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. fma-def 99.9%

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

   4. sub-neg 99.9%

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

   5. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 5: 94.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+176} \lor \neg \left(x \leq 1.55 \cdot 10^{+187}\right):\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + x \cdot \log y\right)\right) + -0.5 \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.45e+176) (not (<= x 1.55e+187)))
   (+ (* y i) (+ (+ a (+ z (* x (log y)))) (* -0.5 (log c))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ z (+ t a))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.45e+176) || !(x <= 1.55e+187)) {
		tmp = (y * i) + ((a + (z + (x * log(y)))) + (-0.5 * log(c)));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + (t + a)));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.45d+176)) .or. (.not. (x <= 1.55d+187))) then
        tmp = (y * i) + ((a + (z + (x * log(y)))) + ((-0.5d0) * log(c)))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (z + (t + a)))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.45e+176) || !(x <= 1.55e+187)) {
		tmp = (y * i) + ((a + (z + (x * Math.log(y)))) + (-0.5 * Math.log(c)));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (z + (t + a)));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.45e+176) or not (x <= 1.55e+187):
		tmp = (y * i) + ((a + (z + (x * math.log(y)))) + (-0.5 * math.log(c)))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (z + (t + a)))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.45e+176) || !(x <= 1.55e+187))
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(z + Float64(x * log(y)))) + Float64(-0.5 * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(z + Float64(t + a))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.45e+176) || ~((x <= 1.55e+187)))
		tmp = (y * i) + ((a + (z + (x * log(y)))) + (-0.5 * log(c)));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + (t + a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.45e+176], N[Not[LessEqual[x, 1.55e+187]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45e176 or 1.55000000000000006e187 < 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. Taylor expanded in t around 0 92.2%

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

   3. Taylor expanded in b around 0 88.5%

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

   if -2.45e176 < x < 1.55000000000000006e187

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 96.3%

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

      1. associate-+r+ 96.3%

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

      2. +-commutative 96.3%

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

   4. Simplified 96.3%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+176} \lor \neg \left(x \leq 1.55 \cdot 10^{+187}\right):\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + x \cdot \log y\right)\right) + -0.5 \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \]

Alternative 6: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+170} \lor \neg \left(x \leq 1.8 \cdot 10^{+143}\right):\\ \;\;\;\;y \cdot i + \left(t_1 + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t_1 + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (or (<= x -1.9e+170) (not (<= x 1.8e+143)))
     (+ (* y i) (+ t_1 (+ a (* x (log y)))))
     (+ (* y i) (+ t_1 (+ z (+ t a)))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if ((x <= -1.9e+170) || !(x <= 1.8e+143)) {
		tmp = (y * i) + (t_1 + (a + (x * log(y))));
	} else {
		tmp = (y * i) + (t_1 + (z + (t + a)));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if ((x <= (-1.9d+170)) .or. (.not. (x <= 1.8d+143))) then
        tmp = (y * i) + (t_1 + (a + (x * log(y))))
    else
        tmp = (y * i) + (t_1 + (z + (t + a)))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if ((x <= -1.9e+170) || !(x <= 1.8e+143)) {
		tmp = (y * i) + (t_1 + (a + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (t_1 + (z + (t + a)));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if (x <= -1.9e+170) or not (x <= 1.8e+143):
		tmp = (y * i) + (t_1 + (a + (x * math.log(y))))
	else:
		tmp = (y * i) + (t_1 + (z + (t + a)))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if ((x <= -1.9e+170) || !(x <= 1.8e+143))
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(z + Float64(t + a))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if ((x <= -1.9e+170) || ~((x <= 1.8e+143)))
		tmp = (y * i) + (t_1 + (a + (x * log(y))));
	else
		tmp = (y * i) + (t_1 + (z + (t + a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.9e+170], N[Not[LessEqual[x, 1.8e+143]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e170 or 1.8e143 < 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. Taylor expanded in t around 0 92.5%

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

   3. Taylor expanded in z around 0 81.4%

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

   if -1.8999999999999999e170 < x < 1.8e143

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.3%

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

      1. associate-+r+ 97.3%

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

      2. +-commutative 97.3%

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

   4. Simplified 97.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+170} \lor \neg \left(x \leq 1.8 \cdot 10^{+143}\right):\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 8: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + (x * log(y)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in t around 0 86.8%

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

3. Final simplification 86.8%

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

Alternative 9: 90.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+196}:\\ \;\;\;\;t + \left(y \cdot i + t_1\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(a + \left(z + -0.5 \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.5e+196)
     (+ t (+ (* y i) t_1))
     (if (<= x 1.35e+209)
       (+ (* y i) (+ (* (log c) (- b 0.5)) (+ z (+ t a))))
       (+ t_1 (+ a (+ z (* -0.5 (log c)))))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.5e+196) {
		tmp = t + ((y * i) + t_1);
	} else if (x <= 1.35e+209) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + (t + a)));
	} else {
		tmp = t_1 + (a + (z + (-0.5 * log(c))));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.5d+196)) then
        tmp = t + ((y * i) + t_1)
    else if (x <= 1.35d+209) then
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (z + (t + a)))
    else
        tmp = t_1 + (a + (z + ((-0.5d0) * log(c))))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -1.5e+196) {
		tmp = t + ((y * i) + t_1);
	} else if (x <= 1.35e+209) {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (z + (t + a)));
	} else {
		tmp = t_1 + (a + (z + (-0.5 * Math.log(c))));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.5e+196:
		tmp = t + ((y * i) + t_1)
	elif x <= 1.35e+209:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (z + (t + a)))
	else:
		tmp = t_1 + (a + (z + (-0.5 * math.log(c))))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.5e+196)
		tmp = Float64(t + Float64(Float64(y * i) + t_1));
	elseif (x <= 1.35e+209)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(z + Float64(t + a))));
	else
		tmp = Float64(t_1 + Float64(a + Float64(z + Float64(-0.5 * log(c)))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.5e+196)
		tmp = t + ((y * i) + t_1);
	elseif (x <= 1.35e+209)
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + (t + a)));
	else
		tmp = t_1 + (a + (z + (-0.5 * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+196], N[(t + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+209], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(a + N[(z + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4999999999999999e196

   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. Step-by-step derivation

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 82.2%

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

   5. Taylor expanded in y around 0 82.2%

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

   if -1.4999999999999999e196 < x < 1.35e209

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.4%

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

      1. associate-+r+ 95.4%

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

      2. +-commutative 95.4%

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

   4. Simplified 95.4%

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

   if 1.35e209 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 91.3%

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

   3. Taylor expanded in b around 0 91.3%

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

   4. Taylor expanded in y around 0 86.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+196}:\\ \;\;\;\;t + \left(y \cdot i + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + \left(a + \left(z + -0.5 \cdot \log c\right)\right)\\ \end{array} \]

Alternative 10: 57.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot i + b \cdot \log c\\ t_2 := y \cdot i + \left(t + a\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -10:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* b (log c)))) (t_2 (+ (* y i) (+ t a))))
   (if (<= z -3.2e+164)
     (+ z (* y i))
     (if (<= z -5e+92)
       t_1
       (if (<= z -4.4e+72)
         t_2
         (if (<= z -10.0)
           t_1
           (if (<= z -1.8e-174)
             t_2
             (if (<= z 8.2e-241) t_1 (+ a (* y i))))))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (b * log(c));
	double t_2 = (y * i) + (t + a);
	double tmp;
	if (z <= -3.2e+164) {
		tmp = z + (y * i);
	} else if (z <= -5e+92) {
		tmp = t_1;
	} else if (z <= -4.4e+72) {
		tmp = t_2;
	} else if (z <= -10.0) {
		tmp = t_1;
	} else if (z <= -1.8e-174) {
		tmp = t_2;
	} else if (z <= 8.2e-241) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * i) + (b * log(c))
    t_2 = (y * i) + (t + a)
    if (z <= (-3.2d+164)) then
        tmp = z + (y * i)
    else if (z <= (-5d+92)) then
        tmp = t_1
    else if (z <= (-4.4d+72)) then
        tmp = t_2
    else if (z <= (-10.0d0)) then
        tmp = t_1
    else if (z <= (-1.8d-174)) then
        tmp = t_2
    else if (z <= 8.2d-241) then
        tmp = t_1
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (b * Math.log(c));
	double t_2 = (y * i) + (t + a);
	double tmp;
	if (z <= -3.2e+164) {
		tmp = z + (y * i);
	} else if (z <= -5e+92) {
		tmp = t_1;
	} else if (z <= -4.4e+72) {
		tmp = t_2;
	} else if (z <= -10.0) {
		tmp = t_1;
	} else if (z <= -1.8e-174) {
		tmp = t_2;
	} else if (z <= 8.2e-241) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (b * math.log(c))
	t_2 = (y * i) + (t + a)
	tmp = 0
	if z <= -3.2e+164:
		tmp = z + (y * i)
	elif z <= -5e+92:
		tmp = t_1
	elif z <= -4.4e+72:
		tmp = t_2
	elif z <= -10.0:
		tmp = t_1
	elif z <= -1.8e-174:
		tmp = t_2
	elif z <= 8.2e-241:
		tmp = t_1
	else:
		tmp = a + (y * i)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(b * log(c)))
	t_2 = Float64(Float64(y * i) + Float64(t + a))
	tmp = 0.0
	if (z <= -3.2e+164)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -5e+92)
		tmp = t_1;
	elseif (z <= -4.4e+72)
		tmp = t_2;
	elseif (z <= -10.0)
		tmp = t_1;
	elseif (z <= -1.8e-174)
		tmp = t_2;
	elseif (z <= 8.2e-241)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (b * log(c));
	t_2 = (y * i) + (t + a);
	tmp = 0.0;
	if (z <= -3.2e+164)
		tmp = z + (y * i);
	elseif (z <= -5e+92)
		tmp = t_1;
	elseif (z <= -4.4e+72)
		tmp = t_2;
	elseif (z <= -10.0)
		tmp = t_1;
	elseif (z <= -1.8e-174)
		tmp = t_2;
	elseif (z <= 8.2e-241)
		tmp = t_1;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+164], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e+92], t$95$1, If[LessEqual[z, -4.4e+72], t$95$2, If[LessEqual[z, -10.0], t$95$1, If[LessEqual[z, -1.8e-174], t$95$2, If[LessEqual[z, 8.2e-241], t$95$1, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999998e164

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 92.6%

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

   3. Taylor expanded in z around inf 77.4%

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

   if -3.1999999999999998e164 < z < -5.00000000000000022e92 or -4.4e72 < z < -10 or -1.79999999999999999e-174 < z < 8.1999999999999997e-241

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 84.0%

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

   3. Taylor expanded in b around inf 45.4%

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

   if -5.00000000000000022e92 < z < -4.4e72 or -10 < z < -1.79999999999999999e-174

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 75.4%

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

   5. Taylor expanded in t around 0 75.4%

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

   if 8.1999999999999997e-241 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 48.1%

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

   5. Taylor expanded in t around 0 35.4%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \mathbf{elif}\;z \leq -10:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-174}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-241}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 11: 90.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+196} \lor \neg \left(x \leq 2.2 \cdot 10^{+212}\right):\\ \;\;\;\;t + \left(y \cdot i + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.4e+196) (not (<= x 2.2e+212)))
   (+ t (+ (* y i) (* x (log y))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ z (+ t a))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.4e+196) || !(x <= 2.2e+212)) {
		tmp = t + ((y * i) + (x * log(y)));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + (t + a)));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.4d+196)) .or. (.not. (x <= 2.2d+212))) then
        tmp = t + ((y * i) + (x * log(y)))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (z + (t + a)))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.4e+196) || !(x <= 2.2e+212)) {
		tmp = t + ((y * i) + (x * Math.log(y)));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (z + (t + a)));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.4e+196) or not (x <= 2.2e+212):
		tmp = t + ((y * i) + (x * math.log(y)))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (z + (t + a)))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.4e+196) || !(x <= 2.2e+212))
		tmp = Float64(t + Float64(Float64(y * i) + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(z + Float64(t + a))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.4e+196) || ~((x <= 2.2e+212)))
		tmp = t + ((y * i) + (x * log(y)));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + (t + a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.4e+196], N[Not[LessEqual[x, 2.2e+212]], $MachinePrecision]], N[(t + N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4000000000000001e196 or 2.19999999999999995e212 < 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. Step-by-step derivation

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. fma-def 99.7%

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

      7. associate-+l+ 99.7%

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

      8. fma-def 99.7%

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

      9. +-commutative 99.7%

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

      10. associate-+l+ 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 84.9%

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

   5. Taylor expanded in y around 0 84.9%

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

   if -1.4000000000000001e196 < x < 2.19999999999999995e212

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.5%

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

      1. associate-+r+ 95.5%

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

      2. +-commutative 95.5%

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

   4. Simplified 95.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+196} \lor \neg \left(x \leq 2.2 \cdot 10^{+212}\right):\\ \;\;\;\;t + \left(y \cdot i + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + \left(t + a\right)\right)\right)\\ \end{array} \]

Alternative 12: 89.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+196} \lor \neg \left(x \leq 6.5 \cdot 10^{+212}\right):\\ \;\;\;\;t + \left(y \cdot i + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.5e+196) (not (<= x 6.5e+212)))
   (+ t (+ (* y i) (* x (log y))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a z)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.5e+196) || !(x <= 6.5e+212)) {
		tmp = t + ((y * i) + (x * log(y)));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + z));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.5d+196)) .or. (.not. (x <= 6.5d+212))) then
        tmp = t + ((y * i) + (x * log(y)))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + z))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.5e+196) || !(x <= 6.5e+212)) {
		tmp = t + ((y * i) + (x * Math.log(y)));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + z));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.5e+196) or not (x <= 6.5e+212):
		tmp = t + ((y * i) + (x * math.log(y)))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + z))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.5e+196) || !(x <= 6.5e+212))
		tmp = Float64(t + Float64(Float64(y * i) + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + z)));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.5e+196) || ~((x <= 6.5e+212)))
		tmp = t + ((y * i) + (x * log(y)));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.5e+196], N[Not[LessEqual[x, 6.5e+212]], $MachinePrecision]], N[(t + N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4999999999999999e196 or 6.49999999999999997e212 < 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. Step-by-step derivation

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. fma-def 99.7%

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

      7. associate-+l+ 99.7%

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

      8. fma-def 99.7%

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

      9. +-commutative 99.7%

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

      10. associate-+l+ 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 84.9%

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

   5. Taylor expanded in y around 0 84.9%

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

   if -1.4999999999999999e196 < x < 6.49999999999999997e212

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 85.5%

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

   3. Taylor expanded in x around 0 81.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+196} \lor \neg \left(x \leq 6.5 \cdot 10^{+212}\right):\\ \;\;\;\;t + \left(y \cdot i + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\right)\\ \end{array} \]

Alternative 13: 75.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+184} \lor \neg \left(b \leq 9.5 \cdot 10^{+123}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -7e+184) (not (<= b 9.5e+123)))
   (+ (* y i) (* b (log c)))
   (+ a (+ z (+ (* y i) (* -0.5 (log c)))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -7e+184) || !(b <= 9.5e+123)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = a + (z + ((y * i) + (-0.5 * log(c))));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-7d+184)) .or. (.not. (b <= 9.5d+123))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = a + (z + ((y * i) + ((-0.5d0) * log(c))))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -7e+184) || !(b <= 9.5e+123)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = a + (z + ((y * i) + (-0.5 * Math.log(c))));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -7e+184) or not (b <= 9.5e+123):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = a + (z + ((y * i) + (-0.5 * math.log(c))))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -7e+184) || !(b <= 9.5e+123))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(-0.5 * log(c)))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -7e+184) || ~((b <= 9.5e+123)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = a + (z + ((y * i) + (-0.5 * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -7e+184], N[Not[LessEqual[b, 9.5e+123]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.99999999999999956e184 or 9.4999999999999996e123 < b

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 98.9%

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

   3. Taylor expanded in b around inf 80.0%

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

   if -6.99999999999999956e184 < b < 9.4999999999999996e123

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 82.8%

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

   3. Taylor expanded in b around 0 79.3%

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

   4. Taylor expanded in x around 0 63.1%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+184} \lor \neg \left(b \leq 9.5 \cdot 10^{+123}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\\ \end{array} \]

Alternative 14: 61.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+131}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + \mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.6e+131) (+ z (* y i)) (+ t (fma y i a))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.6e+131) {
		tmp = z + (y * i);
	} else {
		tmp = t + fma(y, i, a);
	}
	return tmp;
}

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.6e+131)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(t + fma(y, i, a));
	end
	return tmp
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.6e+131], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * i + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e131

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.1%

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

   3. Taylor expanded in z around inf 66.3%

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

   if -1.6000000000000001e131 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 53.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+131}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + \mathsf{fma}\left(y, i, a\right)\\ \end{array} \]

Alternative 15: 39.0% accurate, 16.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := t + y \cdot i\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+102}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-173}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y i))))
   (if (<= z -1.6e+102)
     z
     (if (<= z -3.1e-53)
       t_1
       (if (<= z -5.5e-173) (+ t a) (if (<= z -7.5e-243) t_1 a))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * i);
	double tmp;
	if (z <= -1.6e+102) {
		tmp = z;
	} else if (z <= -3.1e-53) {
		tmp = t_1;
	} else if (z <= -5.5e-173) {
		tmp = t + a;
	} else if (z <= -7.5e-243) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * i)
    if (z <= (-1.6d+102)) then
        tmp = z
    else if (z <= (-3.1d-53)) then
        tmp = t_1
    else if (z <= (-5.5d-173)) then
        tmp = t + a
    else if (z <= (-7.5d-243)) then
        tmp = t_1
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * i);
	double tmp;
	if (z <= -1.6e+102) {
		tmp = z;
	} else if (z <= -3.1e-53) {
		tmp = t_1;
	} else if (z <= -5.5e-173) {
		tmp = t + a;
	} else if (z <= -7.5e-243) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * i)
	tmp = 0
	if z <= -1.6e+102:
		tmp = z
	elif z <= -3.1e-53:
		tmp = t_1
	elif z <= -5.5e-173:
		tmp = t + a
	elif z <= -7.5e-243:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * i))
	tmp = 0.0
	if (z <= -1.6e+102)
		tmp = z;
	elseif (z <= -3.1e-53)
		tmp = t_1;
	elseif (z <= -5.5e-173)
		tmp = Float64(t + a);
	elseif (z <= -7.5e-243)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * i);
	tmp = 0.0;
	if (z <= -1.6e+102)
		tmp = z;
	elseif (z <= -3.1e-53)
		tmp = t_1;
	elseif (z <= -5.5e-173)
		tmp = t + a;
	elseif (z <= -7.5e-243)
		tmp = t_1;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+102], z, If[LessEqual[z, -3.1e-53], t$95$1, If[LessEqual[z, -5.5e-173], N[(t + a), $MachinePrecision], If[LessEqual[z, -7.5e-243], t$95$1, a]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6e102

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 88.0%

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

   3. Taylor expanded in b around 0 77.9%

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

   4. Taylor expanded in z around inf 43.1%

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

   if -1.6e102 < z < -3.10000000000000015e-53 or -5.50000000000000022e-173 < z < -7.5e-243

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 43.0%

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

   if -3.10000000000000015e-53 < z < -5.50000000000000022e-173

   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. Step-by-step derivation

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 74.2%

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

   5. Taylor expanded in y around 0 43.5%

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

   if -7.5e-243 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 47.2%

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

   5. Taylor expanded in a around inf 14.3%

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

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+102}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-53}:\\ \;\;\;\;t + y \cdot i\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-173}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-243}:\\ \;\;\;\;t + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 38.9% accurate, 19.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+101}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-173}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-243}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6e+101)
   z
   (if (<= z -5e-54)
     (* y i)
     (if (<= z -5.5e-173) a (if (<= z -1.04e-243) (* y i) a)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6e+101) {
		tmp = z;
	} else if (z <= -5e-54) {
		tmp = y * i;
	} else if (z <= -5.5e-173) {
		tmp = a;
	} else if (z <= -1.04e-243) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-6d+101)) then
        tmp = z
    else if (z <= (-5d-54)) then
        tmp = y * i
    else if (z <= (-5.5d-173)) then
        tmp = a
    else if (z <= (-1.04d-243)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6e+101) {
		tmp = z;
	} else if (z <= -5e-54) {
		tmp = y * i;
	} else if (z <= -5.5e-173) {
		tmp = a;
	} else if (z <= -1.04e-243) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6e+101:
		tmp = z
	elif z <= -5e-54:
		tmp = y * i
	elif z <= -5.5e-173:
		tmp = a
	elif z <= -1.04e-243:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6e+101)
		tmp = z;
	elseif (z <= -5e-54)
		tmp = Float64(y * i);
	elseif (z <= -5.5e-173)
		tmp = a;
	elseif (z <= -1.04e-243)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -6e+101)
		tmp = z;
	elseif (z <= -5e-54)
		tmp = y * i;
	elseif (z <= -5.5e-173)
		tmp = a;
	elseif (z <= -1.04e-243)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6e+101], z, If[LessEqual[z, -5e-54], N[(y * i), $MachinePrecision], If[LessEqual[z, -5.5e-173], a, If[LessEqual[z, -1.04e-243], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999986e101

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 88.0%

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

   3. Taylor expanded in b around 0 77.9%

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

   4. Taylor expanded in z around inf 43.1%

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

   if -5.99999999999999986e101 < z < -5.00000000000000015e-54 or -5.50000000000000022e-173 < z < -1.0400000000000001e-243

   1. Initial program 99.9%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 30.5%

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

      1. *-commutative 30.5%

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

   6. Simplified 30.5%

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

   if -5.00000000000000015e-54 < z < -5.50000000000000022e-173 or -1.0400000000000001e-243 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 51.8%

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

   5. Taylor expanded in a around inf 17.7%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+101}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-173}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-243}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17: 38.9% accurate, 19.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+100}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-53}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-173}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-243}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -5.6e+100)
   z
   (if (<= z -3.6e-53)
     (* y i)
     (if (<= z -5.5e-173) (+ t a) (if (<= z -5e-243) (* y i) a)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.6e+100) {
		tmp = z;
	} else if (z <= -3.6e-53) {
		tmp = y * i;
	} else if (z <= -5.5e-173) {
		tmp = t + a;
	} else if (z <= -5e-243) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-5.6d+100)) then
        tmp = z
    else if (z <= (-3.6d-53)) then
        tmp = y * i
    else if (z <= (-5.5d-173)) then
        tmp = t + a
    else if (z <= (-5d-243)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.6e+100) {
		tmp = z;
	} else if (z <= -3.6e-53) {
		tmp = y * i;
	} else if (z <= -5.5e-173) {
		tmp = t + a;
	} else if (z <= -5e-243) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -5.6e+100:
		tmp = z
	elif z <= -3.6e-53:
		tmp = y * i
	elif z <= -5.5e-173:
		tmp = t + a
	elif z <= -5e-243:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -5.6e+100)
		tmp = z;
	elseif (z <= -3.6e-53)
		tmp = Float64(y * i);
	elseif (z <= -5.5e-173)
		tmp = Float64(t + a);
	elseif (z <= -5e-243)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -5.6e+100)
		tmp = z;
	elseif (z <= -3.6e-53)
		tmp = y * i;
	elseif (z <= -5.5e-173)
		tmp = t + a;
	elseif (z <= -5e-243)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -5.6e+100], z, If[LessEqual[z, -3.6e-53], N[(y * i), $MachinePrecision], If[LessEqual[z, -5.5e-173], N[(t + a), $MachinePrecision], If[LessEqual[z, -5e-243], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.5999999999999996e100

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 88.3%

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

   3. Taylor expanded in b around 0 78.4%

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

   4. Taylor expanded in z around inf 42.1%

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

   if -5.5999999999999996e100 < z < -3.5999999999999999e-53 or -5.50000000000000022e-173 < z < -5e-243

   1. Initial program 99.9%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 31.2%

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

      1. *-commutative 31.2%

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

   6. Simplified 31.2%

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

   if -3.5999999999999999e-53 < z < -5.50000000000000022e-173

   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. Step-by-step derivation

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 74.2%

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

   5. Taylor expanded in y around 0 43.5%

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

   if -5e-243 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 47.2%

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

   5. Taylor expanded in a around inf 14.3%

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

4. Final simplification 24.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+100}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-53}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-173}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-243}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 18: 61.2% accurate, 24.2× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.2e+131) (+ z (* y i)) (+ (* y i) (+ t a))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.2e+131) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + a);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3.2d+131)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (t + a)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.2e+131) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + a);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.2e+131:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (t + a)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.2e+131)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t + a));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.2e+131)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (t + a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.2e+131], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000002e131

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.1%

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

   3. Taylor expanded in z around inf 66.3%

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

   if -3.2000000000000002e131 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 53.6%

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

   5. Taylor expanded in t around 0 53.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \]

Alternative 19: 54.6% accurate, 31.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+180}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.9e+180) (+ z (* y i)) (+ t a)))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.9e+180) {
		tmp = z + (y * i);
	} else {
		tmp = t + a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.9d+180) then
        tmp = z + (y * i)
    else
        tmp = t + a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.9e+180) {
		tmp = z + (y * i);
	} else {
		tmp = t + a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.9e+180:
		tmp = z + (y * i)
	else:
		tmp = t + a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.9e+180)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(t + a);
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.9e+180)
		tmp = z + (y * i);
	else
		tmp = t + a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.9e+180], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(t + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.90000000000000007e180

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 86.6%

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

   3. Taylor expanded in z around inf 40.6%

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

   if 2.90000000000000007e180 < a

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. associate-+l+ 100.0%

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

      8. fma-def 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. fma-def 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 70.6%

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

   5. Taylor expanded in y around 0 65.9%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+180}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]

Alternative 20: 60.9% accurate, 31.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+130}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4.5e+130) (+ z (* y i)) (+ a (* y i))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.5e+130) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-4.5d+130)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.5e+130) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.5e+130:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.5e+130)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -4.5e+130)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.5e+130], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000039e130

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.1%

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

   3. Taylor expanded in z around inf 66.3%

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

   if -4.50000000000000039e130 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 53.6%

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

   5. Taylor expanded in t around 0 40.6%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+130}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 21: 39.0% accurate, 71.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (if (<= z -7.5e+132) z a))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7.5e+132) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-7.5d+132)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7.5e+132) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -7.5e+132:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -7.5e+132)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -7.5e+132)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -7.5e+132], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000017e132

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.1%

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

   3. Taylor expanded in b around 0 81.4%

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

   4. Taylor expanded in z around inf 46.2%

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

   if -7.50000000000000017e132 < z

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. fma-def 99.8%

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

      7. associate-+l+ 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 53.6%

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

   5. Taylor expanded in a around inf 18.8%

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

4. Final simplification 22.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 22: 23.5% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. fma-def 99.9%

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

   7. associate-+l+ 99.9%

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

   8. fma-def 99.9%

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

   9. +-commutative 99.9%

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

   10. associate-+l+ 99.9%

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

   11. fma-def 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in a around inf 51.7%

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

5. Taylor expanded in a around inf 17.0%

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

6. Final simplification 17.0%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023224 
(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)))