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

Percentage Accurate: 99.8% → 99.8%

Time: 18.5s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

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
 (+ (+ (fma x (log y) z) (+ t a)) (+ (* y i) (* (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 (fma(x, log(y), z) + (t + a)) + ((y * i) + (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(fma(x, log(y), z) + Float64(t + a)) + Float64(Float64(y * i) + Float64(log(c) * Float64(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[(N[(x * N[Log[y], $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(N[(y * i), $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. 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. +-commutative 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. fma-def 99.9%

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

   7. +-commutative 99.9%

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

   8. sub-neg 99.9%

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

   9. 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%

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

Alternative 2: 93.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + x \cdot \log y\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+19}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(x, \log y, z + a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.45e+113)
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ t (* x (log y))))))
   (if (<= x 2.3e+19)
     (+ (* y i) (+ (+ t a) (+ z (* (log c) (+ b -0.5)))))
     (+ (* y i) (fma x (log y) (+ z a))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.45e+113) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (t + (x * log(y)))));
	} else if (x <= 2.3e+19) {
		tmp = (y * i) + ((t + a) + (z + (log(c) * (b + -0.5))));
	} else {
		tmp = (y * i) + fma(x, log(y), (z + a));
	}
	return tmp;
}

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.45e+113)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(t + Float64(x * log(y))))));
	elseif (x <= 2.3e+19)
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + Float64(z + Float64(log(c) * Float64(b + -0.5)))));
	else
		tmp = Float64(Float64(y * i) + fma(x, log(y), Float64(z + 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[x, -1.45e+113], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+19], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999992e113

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 88.1%

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

   if -1.44999999999999992e113 < x < 2.3e19

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.0%

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

      1. associate-+r+ 99.0%

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

      2. sub-neg 99.0%

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

      3. metadata-eval 99.0%

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

      4. +-commutative 99.0%

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

   4. Simplified 99.0%

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

   if 2.3e19 < 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%

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

      2. +-commutative 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. fma-def 99.7%

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

      7. +-commutative 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 95.9%

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

      1. *-commutative 95.9%

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

   6. Simplified 95.9%

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

   7. Taylor expanded in t around 0 86.8%

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

      1. associate-+r+ 86.8%

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

      2. +-commutative 86.8%

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

      3. fma-def 86.8%

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

   9. Simplified 86.8%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + x \cdot \log y\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+19}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(x, \log y, z + a\right)\\ \end{array} \]

Alternative 3: 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 4: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+85} \lor \neg \left(x \leq 2.3 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(x, \log y, z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \end{array} \]

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 -1.02e+85) (not (<= x 2.3e+19)))
   (+ (* y i) (fma x (log y) (+ z a)))
   (+ (* y i) (+ (+ t a) (+ z (* (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) {
	double tmp;
	if ((x <= -1.02e+85) || !(x <= 2.3e+19)) {
		tmp = (y * i) + fma(x, log(y), (z + a));
	} else {
		tmp = (y * i) + ((t + a) + (z + (log(c) * (b + -0.5))));
	}
	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 <= -1.02e+85) || !(x <= 2.3e+19))
		tmp = Float64(Float64(y * i) + fma(x, log(y), Float64(z + a)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + Float64(z + Float64(log(c) * Float64(b + -0.5)))));
	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[Or[LessEqual[x, -1.02e+85], N[Not[LessEqual[x, 2.3e+19]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e85 or 2.3e19 < x

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 91.2%

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

      1. *-commutative 91.2%

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

   6. Simplified 91.2%

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

   7. Taylor expanded in t around 0 83.6%

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

      1. associate-+r+ 83.6%

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

      2. +-commutative 83.6%

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

      3. fma-def 83.6%

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

   9. Simplified 83.6%

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

   if -1.02e85 < x < 2.3e19

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.6%

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

      1. associate-+r+ 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. +-commutative 99.6%

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

   4. Simplified 99.6%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+85} \lor \neg \left(x \leq 2.3 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(x, \log y, z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \]

Alternative 5: 90.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+229} \lor \neg \left(x \leq 9 \cdot 10^{+128}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \end{array} \]

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 -1.5e+229) (not (<= x 9e+128)))
   (+ (* y i) (+ a (+ t (* x (log y)))))
   (+ (* y i) (+ (+ t a) (+ z (* (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) {
	double tmp;
	if ((x <= -1.5e+229) || !(x <= 9e+128)) {
		tmp = (y * i) + (a + (t + (x * log(y))));
	} else {
		tmp = (y * i) + ((t + a) + (z + (log(c) * (b + -0.5))));
	}
	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+229)) .or. (.not. (x <= 9d+128))) then
        tmp = (y * i) + (a + (t + (x * log(y))))
    else
        tmp = (y * i) + ((t + a) + (z + (log(c) * (b + (-0.5d0)))))
    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+229) || !(x <= 9e+128)) {
		tmp = (y * i) + (a + (t + (x * Math.log(y))));
	} else {
		tmp = (y * i) + ((t + a) + (z + (Math.log(c) * (b + -0.5))));
	}
	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+229) or not (x <= 9e+128):
		tmp = (y * i) + (a + (t + (x * math.log(y))))
	else:
		tmp = (y * i) + ((t + a) + (z + (math.log(c) * (b + -0.5))))
	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+229) || !(x <= 9e+128))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + Float64(z + Float64(log(c) * Float64(b + -0.5)))));
	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+229) || ~((x <= 9e+128)))
		tmp = (y * i) + (a + (t + (x * log(y))));
	else
		tmp = (y * i) + ((t + a) + (z + (log(c) * (b + -0.5))));
	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+229], N[Not[LessEqual[x, 9e+128]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999999e229 or 9.0000000000000003e128 < 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. Step-by-step derivation

      1. associate-+l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 94.0%

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

      1. *-commutative 94.0%

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

   6. Simplified 94.0%

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

   7. Taylor expanded in z around 0 91.9%

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

   if -1.49999999999999999e229 < x < 9.0000000000000003e128

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.2%

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

      1. associate-+r+ 93.2%

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

      2. sub-neg 93.2%

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

      3. metadata-eval 93.2%

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

      4. +-commutative 93.2%

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

   4. Simplified 93.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+229} \lor \neg \left(x \leq 9 \cdot 10^{+128}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \]

Alternative 6: 74.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot i + \left(a + \left(t + x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-160}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+19}:\\ \;\;\;\;\left(t + a\right) + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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) (+ a (+ t (* x (log y)))))))
   (if (<= x -1.15e+113)
     t_1
     (if (<= x 2.1e-160)
       (+ (* y i) (+ z (+ t a)))
       (if (<= x 1.85e+19) (+ (+ t a) (+ z (* (log c) (- b 0.5)))) t_1)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (t + (x * log(y))));
	double tmp;
	if (x <= -1.15e+113) {
		tmp = t_1;
	} else if (x <= 2.1e-160) {
		tmp = (y * i) + (z + (t + a));
	} else if (x <= 1.85e+19) {
		tmp = (t + a) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (a + (t + (x * log(y))))
    if (x <= (-1.15d+113)) then
        tmp = t_1
    else if (x <= 2.1d-160) then
        tmp = (y * i) + (z + (t + a))
    else if (x <= 1.85d+19) then
        tmp = (t + a) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (t + (x * Math.log(y))));
	double tmp;
	if (x <= -1.15e+113) {
		tmp = t_1;
	} else if (x <= 2.1e-160) {
		tmp = (y * i) + (z + (t + a));
	} else if (x <= 1.85e+19) {
		tmp = (t + a) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (a + (t + (x * math.log(y))))
	tmp = 0
	if x <= -1.15e+113:
		tmp = t_1
	elif x <= 2.1e-160:
		tmp = (y * i) + (z + (t + a))
	elif x <= 1.85e+19:
		tmp = (t + a) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = t_1
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(x * log(y)))))
	tmp = 0.0
	if (x <= -1.15e+113)
		tmp = t_1;
	elseif (x <= 2.1e-160)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	elseif (x <= 1.85e+19)
		tmp = Float64(Float64(t + a) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (a + (t + (x * log(y))));
	tmp = 0.0;
	if (x <= -1.15e+113)
		tmp = t_1;
	elseif (x <= 2.1e-160)
		tmp = (y * i) + (z + (t + a));
	elseif (x <= 1.85e+19)
		tmp = (t + a) + (z + (log(c) * (b - 0.5)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+113], t$95$1, If[LessEqual[x, 2.1e-160], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+19], N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.14999999999999998e113 or 1.85e19 < x

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 90.5%

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

      1. *-commutative 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in z around 0 81.0%

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

   if -1.14999999999999998e113 < x < 2.1e-160

   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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 y around inf 89.4%

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

      1. *-commutative 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in x around 0 88.7%

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

      1. +-commutative 88.7%

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

      2. +-commutative 88.7%

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

      3. associate-+l+ 88.7%

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

      4. +-commutative 88.7%

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

   9. Simplified 88.7%

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

   if 2.1e-160 < x < 1.85e19

   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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 x around 0 98.4%

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

      1. associate-+r+ 98.4%

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

      2. +-commutative 98.4%

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

      3. sub-neg 98.4%

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

      4. metadata-eval 98.4%

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

      5. *-commutative 98.4%

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

      6. fma-udef 98.4%

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

      7. +-commutative 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in y around 0 80.7%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-160}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+19}:\\ \;\;\;\;\left(t + a\right) + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + x \cdot \log y\right)\right)\\ \end{array} \]

Alternative 7: 75.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot i + \left(a + \left(t + x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -1.36 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;\left(t + a\right) + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+19}:\\ \;\;\;\;\left(t + a\right) + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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) (+ a (+ t (* x (log y)))))))
   (if (<= x -1.36e+113)
     t_1
     (if (<= x 2.4e-160)
       (+ (+ t a) (+ z (+ (* y i) (* -0.5 (log c)))))
       (if (<= x 2e+19) (+ (+ t a) (+ z (* (log c) (- b 0.5)))) t_1)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (t + (x * log(y))));
	double tmp;
	if (x <= -1.36e+113) {
		tmp = t_1;
	} else if (x <= 2.4e-160) {
		tmp = (t + a) + (z + ((y * i) + (-0.5 * log(c))));
	} else if (x <= 2e+19) {
		tmp = (t + a) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (a + (t + (x * log(y))))
    if (x <= (-1.36d+113)) then
        tmp = t_1
    else if (x <= 2.4d-160) then
        tmp = (t + a) + (z + ((y * i) + ((-0.5d0) * log(c))))
    else if (x <= 2d+19) then
        tmp = (t + a) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (t + (x * Math.log(y))));
	double tmp;
	if (x <= -1.36e+113) {
		tmp = t_1;
	} else if (x <= 2.4e-160) {
		tmp = (t + a) + (z + ((y * i) + (-0.5 * Math.log(c))));
	} else if (x <= 2e+19) {
		tmp = (t + a) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (a + (t + (x * math.log(y))))
	tmp = 0
	if x <= -1.36e+113:
		tmp = t_1
	elif x <= 2.4e-160:
		tmp = (t + a) + (z + ((y * i) + (-0.5 * math.log(c))))
	elif x <= 2e+19:
		tmp = (t + a) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = t_1
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(x * log(y)))))
	tmp = 0.0
	if (x <= -1.36e+113)
		tmp = t_1;
	elseif (x <= 2.4e-160)
		tmp = Float64(Float64(t + a) + Float64(z + Float64(Float64(y * i) + Float64(-0.5 * log(c)))));
	elseif (x <= 2e+19)
		tmp = Float64(Float64(t + a) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (a + (t + (x * log(y))));
	tmp = 0.0;
	if (x <= -1.36e+113)
		tmp = t_1;
	elseif (x <= 2.4e-160)
		tmp = (t + a) + (z + ((y * i) + (-0.5 * log(c))));
	elseif (x <= 2e+19)
		tmp = (t + a) + (z + (log(c) * (b - 0.5)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.36e+113], t$95$1, If[LessEqual[x, 2.4e-160], N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[(y * i), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+19], N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35999999999999997e113 or 2e19 < x

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 90.5%

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

      1. *-commutative 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in z around 0 81.0%

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

   if -1.35999999999999997e113 < x < 2.39999999999999991e-160

   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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 x around 0 99.2%

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

      1. associate-+r+ 99.1%

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

      2. +-commutative 99.1%

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

      3. sub-neg 99.1%

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

      4. metadata-eval 99.1%

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

      5. *-commutative 99.1%

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

      6. fma-udef 99.1%

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

      7. +-commutative 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in b around 0 90.4%

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

   if 2.39999999999999991e-160 < x < 2e19

   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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 x around 0 98.4%

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

      1. associate-+r+ 98.4%

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

      2. +-commutative 98.4%

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

      3. sub-neg 98.4%

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

      4. metadata-eval 98.4%

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

      5. *-commutative 98.4%

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

      6. fma-udef 98.4%

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

      7. +-commutative 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in y around 0 80.7%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;\left(t + a\right) + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+19}:\\ \;\;\;\;\left(t + a\right) + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + x \cdot \log y\right)\right)\\ \end{array} \]

Alternative 8: 74.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1.26 \cdot 10^{+67} \lor \neg \left(i \leq 5.6 \cdot 10^{-73}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.26e+67) (not (<= i 5.6e-73)))
   (+ (* y i) (+ z (+ t a)))
   (+ a (+ z (* b (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 ((i <= -1.26e+67) || !(i <= 5.6e-73)) {
		tmp = (y * i) + (z + (t + a));
	} else {
		tmp = a + (z + (b * 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 ((i <= (-1.26d+67)) .or. (.not. (i <= 5.6d-73))) then
        tmp = (y * i) + (z + (t + a))
    else
        tmp = a + (z + (b * 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 ((i <= -1.26e+67) || !(i <= 5.6e-73)) {
		tmp = (y * i) + (z + (t + a));
	} else {
		tmp = a + (z + (b * 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 (i <= -1.26e+67) or not (i <= 5.6e-73):
		tmp = (y * i) + (z + (t + a))
	else:
		tmp = a + (z + (b * 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 ((i <= -1.26e+67) || !(i <= 5.6e-73))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	else
		tmp = Float64(a + Float64(z + Float64(b * 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 ((i <= -1.26e+67) || ~((i <= 5.6e-73)))
		tmp = (y * i) + (z + (t + a));
	else
		tmp = a + (z + (b * 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[i, -1.26e+67], N[Not[LessEqual[i, 5.6e-73]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.26e67 or 5.60000000000000023e-73 < i

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 y around inf 91.5%

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

      1. *-commutative 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in x around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. +-commutative 82.4%

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

      3. associate-+l+ 82.4%

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

      4. +-commutative 82.4%

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

   9. Simplified 82.4%

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

   if -1.26e67 < i < 5.60000000000000023e-73

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 77.5%

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

      1. associate-+r+ 77.5%

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

      2. +-commutative 77.5%

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

      3. sub-neg 77.5%

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

      4. metadata-eval 77.5%

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

      5. *-commutative 77.5%

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

      6. fma-udef 77.5%

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

      7. +-commutative 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in b around inf 71.5%

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

      1. *-commutative 71.5%

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

   9. Simplified 71.5%

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

   10. Taylor expanded in t around 0 55.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.26 \cdot 10^{+67} \lor \neg \left(i \leq 5.6 \cdot 10^{-73}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \end{array} \]

Alternative 9: 74.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3100000000:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 3100000000.0)
   (+ a (+ t (+ z (* x (log y)))))
   (+ (* y i) (+ 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 (y <= 3100000000.0) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = (y * i) + (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 (y <= 3100000000.0d0) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = (y * i) + (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 (y <= 3100000000.0) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (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 y <= 3100000000.0:
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + (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 (y <= 3100000000.0)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + 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 (y <= 3100000000.0)
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = (y * i) + (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[LessEqual[y, 3100000000.0], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.1e9

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 84.2%

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

      1. *-commutative 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in y around 0 80.5%

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

   if 3.1e9 < y

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 y around inf 88.2%

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

      1. *-commutative 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in x around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. +-commutative 78.6%

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

      3. associate-+l+ 78.6%

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

      4. +-commutative 78.6%

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

   9. Simplified 78.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3100000000:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]

Alternative 10: 74.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 4100000000:\\ \;\;\;\;a + \left(z + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 4100000000.0) (+ a (+ z (* x (log y)))) (+ (* y i) (+ 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 (y <= 4100000000.0) {
		tmp = a + (z + (x * log(y)));
	} else {
		tmp = (y * i) + (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 (y <= 4100000000.0d0) then
        tmp = a + (z + (x * log(y)))
    else
        tmp = (y * i) + (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 (y <= 4100000000.0) {
		tmp = a + (z + (x * Math.log(y)));
	} else {
		tmp = (y * i) + (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 y <= 4100000000.0:
		tmp = a + (z + (x * math.log(y)))
	else:
		tmp = (y * i) + (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 (y <= 4100000000.0)
		tmp = Float64(a + Float64(z + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + 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 (y <= 4100000000.0)
		tmp = a + (z + (x * log(y)));
	else
		tmp = (y * i) + (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[LessEqual[y, 4100000000.0], N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.1e9

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 84.2%

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

      1. *-commutative 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in y around 0 80.5%

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

   8. Taylor expanded in t around 0 65.6%

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

   if 4.1e9 < y

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 y around inf 88.2%

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

      1. *-commutative 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in x around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. +-commutative 78.6%

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

      3. associate-+l+ 78.6%

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

      4. +-commutative 78.6%

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

   9. Simplified 78.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4100000000:\\ \;\;\;\;a + \left(z + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]

Alternative 11: 72.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+231} \lor \neg \left(x \leq 2 \cdot 10^{+228}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.5e+231) (not (<= x 2e+228)))
   (* x (log y))
   (+ (* y i) (+ 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 <= -4.5e+231) || !(x <= 2e+228)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (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 <= (-4.5d+231)) .or. (.not. (x <= 2d+228))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (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 <= -4.5e+231) || !(x <= 2e+228)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (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 <= -4.5e+231) or not (x <= 2e+228):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (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 <= -4.5e+231) || !(x <= 2e+228))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + 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 <= -4.5e+231) || ~((x <= 2e+228)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (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, -4.5e+231], N[Not[LessEqual[x, 2e+228]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999991e231 or 1.9999999999999998e228 < x

   1. Initial program 99.5%

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

      1. associate-+l+ 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-+l+ 99.5%

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

      6. fma-def 99.5%

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

      7. +-commutative 99.5%

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

      8. sub-neg 99.5%

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

      9. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 94.1%

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

      1. *-commutative 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in y around 0 74.2%

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

   8. Taylor expanded in x around inf 70.3%

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

   if -4.49999999999999991e231 < x < 1.9999999999999998e228

   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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 y around inf 85.0%

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

      1. *-commutative 85.0%

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

   6. Simplified 85.0%

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

   7. Taylor expanded in x around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. +-commutative 77.0%

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

      3. associate-+l+ 77.0%

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

      4. +-commutative 77.0%

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

   9. Simplified 77.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+231} \lor \neg \left(x \leq 2 \cdot 10^{+228}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]

Alternative 12: 68.0% accurate, 24.3× speedup

Math

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

FPCore

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $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. +-commutative 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. fma-def 99.9%

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

   7. +-commutative 99.9%

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

   8. sub-neg 99.9%

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

   9. 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 y around inf 86.2%

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

   1. *-commutative 86.2%

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

6. Simplified 86.2%

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

7. Taylor expanded in x around 0 70.3%

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

   1. +-commutative 70.3%

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

   2. +-commutative 70.3%

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

   3. associate-+l+ 70.3%

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

   4. +-commutative 70.3%

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

9. Simplified 70.3%

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

10. Final simplification 70.3%

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

Alternative 13: 37.6% accurate, 30.7× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-231}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+181}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -1.1e-231) z (if (<= a 6.8e+181) (* y i) a)))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -1.1e-231) {
		tmp = z;
	} else if (a <= 6.8e+181) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-1.1d-231)) then
        tmp = z
    else if (a <= 6.8d+181) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -1.1e-231) {
		tmp = z;
	} else if (a <= 6.8e+181) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -1.1e-231:
		tmp = z
	elif a <= 6.8e+181:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -1.1e-231)
		tmp = z;
	elseif (a <= 6.8e+181)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -1.1e-231)
		tmp = z;
	elseif (a <= 6.8e+181)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -1.1e-231], z, If[LessEqual[a, 6.8e+181], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if a < -1.10000000000000005e-231

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.5%

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

      1. *-commutative 79.5%

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

   6. Simplified 79.5%

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

   7. Taylor expanded in y around 0 55.1%

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

   8. Taylor expanded in z around inf 13.1%

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

   if -1.10000000000000005e-231 < a < 6.80000000000000062e181

   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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 y around inf 93.0%

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

      1. *-commutative 93.0%

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

   6. Simplified 93.0%

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

   7. Taylor expanded in y around inf 33.5%

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

      1. *-commutative 33.5%

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

   9. Simplified 33.5%

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

   if 6.80000000000000062e181 < 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%

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

      2. +-commutative 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. fma-def 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. 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 85.8%

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

      1. *-commutative 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in y around 0 79.2%

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

   8. Taylor expanded in a around inf 74.2%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-231}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+181}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14: 51.5% accurate, 30.7× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+145}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -2.4e+145) (* y i) (if (<= i 1.4e+108) (+ z 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 (i <= -2.4e+145) {
		tmp = y * i;
	} else if (i <= 1.4e+108) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= (-2.4d+145)) then
        tmp = y * i
    else if (i <= 1.4d+108) then
        tmp = z + a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -2.4e+145) {
		tmp = y * i;
	} else if (i <= 1.4e+108) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -2.4e+145:
		tmp = y * i
	elif i <= 1.4e+108:
		tmp = z + a
	else:
		tmp = y * i
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -2.4e+145)
		tmp = Float64(y * i);
	elseif (i <= 1.4e+108)
		tmp = Float64(z + a);
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -2.4e+145)
		tmp = y * i;
	elseif (i <= 1.4e+108)
		tmp = z + a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -2.4e+145], N[(y * i), $MachinePrecision], If[LessEqual[i, 1.4e+108], N[(z + a), $MachinePrecision], N[(y * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -2.39999999999999992e145 or 1.3999999999999999e108 < i

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. 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 y around inf 91.7%

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

      1. *-commutative 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in y around inf 63.3%

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

      1. *-commutative 63.3%

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

   9. Simplified 63.3%

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

   if -2.39999999999999992e145 < i < 1.3999999999999999e108

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 83.6%

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

      1. *-commutative 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in y around 0 75.5%

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

   8. Taylor expanded in x around 0 56.6%

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

      1. +-commutative 56.6%

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

      2. associate-+l+ 56.6%

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

   10. Simplified 56.6%

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

   11. Taylor expanded in t around 0 42.4%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+145}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]

Alternative 15: 57.6% accurate, 31.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+151}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

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 -1.02e+151) (+ z a) (+ 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 <= -1.02e+151) {
		tmp = z + a;
	} 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 <= (-1.02d+151)) then
        tmp = z + a
    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 <= -1.02e+151) {
		tmp = z + a;
	} 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 <= -1.02e+151:
		tmp = z + a
	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 <= -1.02e+151)
		tmp = Float64(z + a);
	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 <= -1.02e+151)
		tmp = z + a;
	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, -1.02e+151], N[(z + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02000000000000002e151

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in y around 0 71.5%

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

   8. Taylor expanded in x around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. associate-+l+ 61.9%

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

   10. Simplified 61.9%

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

   11. Taylor expanded in t around 0 51.7%

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

   if -1.02000000000000002e151 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 47.6%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+151}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 16: 57.8% accurate, 31.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+151}:\\ \;\;\;\;t + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

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 -1.26e+151) (+ t (+ z a)) (+ 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 <= -1.26e+151) {
		tmp = t + (z + a);
	} 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 <= (-1.26d+151)) then
        tmp = t + (z + a)
    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 <= -1.26e+151) {
		tmp = t + (z + a);
	} 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 <= -1.26e+151:
		tmp = t + (z + a)
	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 <= -1.26e+151)
		tmp = Float64(t + Float64(z + a));
	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 <= -1.26e+151)
		tmp = t + (z + a);
	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, -1.26e+151], N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.26000000000000006e151

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in y around 0 71.5%

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

   8. Taylor expanded in x around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. associate-+l+ 61.9%

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

   10. Simplified 61.9%

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

   if -1.26000000000000006e151 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 47.6%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+151}:\\ \;\;\;\;t + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 17: 57.8% accurate, 31.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+151}:\\ \;\;\;\;z + \left(t + a\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

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 -1.35e+151) (+ z (+ t a)) (+ 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 <= -1.35e+151) {
		tmp = z + (t + a);
	} 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 <= (-1.35d+151)) then
        tmp = z + (t + a)
    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 <= -1.35e+151) {
		tmp = z + (t + a);
	} 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 <= -1.35e+151:
		tmp = z + (t + a)
	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 <= -1.35e+151)
		tmp = Float64(z + Float64(t + a));
	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 <= -1.35e+151)
		tmp = z + (t + a);
	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, -1.35e+151], N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e151

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in y around 0 71.5%

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

   8. Taylor expanded in x around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. associate-+l+ 61.9%

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

   10. Simplified 61.9%

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

   11. Taylor expanded in t around 0 61.9%

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

       1. +-commutative 61.9%

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

       2. +-commutative 61.9%

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

       3. associate-+l+ 61.9%

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

       4. +-commutative 61.9%

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

   13. Simplified 61.9%

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

   if -1.3500000000000001e151 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 47.6%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+151}:\\ \;\;\;\;z + \left(t + a\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 18: 38.0% accurate, 71.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+139}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (if (<= a 7.5e+139) z a))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.5e+139) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 7.5d+139) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.5e+139) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 7.5e+139:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 7.5e+139)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 7.5e+139)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 7.5e+139], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 7.49999999999999992e139

   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%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 85.8%

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

      1. *-commutative 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in y around 0 57.8%

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

   8. Taylor expanded in z around inf 19.7%

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

   if 7.49999999999999992e139 < 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%

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

      2. +-commutative 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. fma-def 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. 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 88.3%

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

      1. *-commutative 88.3%

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

   6. Simplified 88.3%

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

   7. Taylor expanded in y around 0 77.8%

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

   8. Taylor expanded in a around inf 66.9%

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

4. Final simplification 26.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+139}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 19: 22.9% 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%

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

   2. +-commutative 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. fma-def 99.9%

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

   7. +-commutative 99.9%

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

   8. sub-neg 99.9%

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

   9. 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 y around inf 86.2%

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

   1. *-commutative 86.2%

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

6. Simplified 86.2%

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

7. Taylor expanded in y around 0 60.8%

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

8. Taylor expanded in a around inf 19.0%

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

9. Final simplification 19.0%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023271 
(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)))