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

Percentage Accurate: 99.8% → 99.8%

Time: 12.7s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \log y + \left(\log c \cdot \left(b + -0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 7e-50)
   (+ (* x (log y)) (+ (* (log c) (+ b -0.5)) (+ a (+ z t))))
   (+ (* y i) (+ (+ z a) (* b (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 7e-50) {
		tmp = (x * log(y)) + ((log(c) * (b + -0.5)) + (a + (z + t)));
	} else {
		tmp = (y * i) + ((z + a) + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 7d-50) then
        tmp = (x * log(y)) + ((log(c) * (b + (-0.5d0))) + (a + (z + t)))
    else
        tmp = (y * i) + ((z + a) + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 7e-50) {
		tmp = (x * Math.log(y)) + ((Math.log(c) * (b + -0.5)) + (a + (z + t)));
	} else {
		tmp = (y * i) + ((z + a) + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 7e-50:
		tmp = (x * math.log(y)) + ((math.log(c) * (b + -0.5)) + (a + (z + t)))
	else:
		tmp = (y * i) + ((z + a) + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 7e-50)
		tmp = Float64(Float64(x * log(y)) + Float64(Float64(log(c) * Float64(b + -0.5)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 7e-50)
		tmp = (x * log(y)) + ((log(c) * (b + -0.5)) + (a + (z + t)));
	else
		tmp = (y * i) + ((z + a) + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 7e-50], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.99999999999999993e-50

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. sum4-define N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. sum4-define N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 98.4%

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

   if 6.99999999999999993e-50 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 81.7%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 81.7%

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

   8. Simplified 81.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \log y + \left(\log c \cdot \left(b + -0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y + z\right) + y \cdot i\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+198}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (* x (log y)) z) (* y i))))
   (if (<= x -6.4e+193)
     t_1
     (if (<= x 6e+198)
       (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ z t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * log(y)) + z) + (y * i);
	double tmp;
	if (x <= -6.4e+193) {
		tmp = t_1;
	} else if (x <= 6e+198) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * log(y)) + z) + (y * i)
    if (x <= (-6.4d+193)) then
        tmp = t_1
    else if (x <= 6d+198) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (z + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * Math.log(y)) + z) + (y * i);
	double tmp;
	if (x <= -6.4e+193) {
		tmp = t_1;
	} else if (x <= 6e+198) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * math.log(y)) + z) + (y * i)
	tmp = 0
	if x <= -6.4e+193:
		tmp = t_1
	elif x <= 6e+198:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (z + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * log(y)) + z) + Float64(y * i))
	tmp = 0.0
	if (x <= -6.4e+193)
		tmp = t_1;
	elseif (x <= 6e+198)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(z + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * log(y)) + z) + (y * i);
	tmp = 0.0;
	if (x <= -6.4e+193)
		tmp = t_1;
	elseif (x <= 6e+198)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+193], t$95$1, If[LessEqual[x, 6e+198], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.40000000000000026e193 or 6.00000000000000037e198 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

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

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

      6. associate-+r+ N/A

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

      7. +-commutative N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

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

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

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

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

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

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

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

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

      16. /-lowering-/.f64 N/A

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

      17. /-lowering-/.f64 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 76.4%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

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

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

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

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

       4. log-lowering-log.f64 76.5%

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

   11. Simplified 76.5%

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

   if -6.40000000000000026e193 < x < 6.00000000000000037e198

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 94.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+193}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + y \cdot i\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+198}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y + z\right) + y \cdot i\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+199}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (* x (log y)) z) (* y i))))
   (if (<= x -5.8e+193)
     t_1
     (if (<= x 7e+199) (+ (* y i) (+ (* (- b 0.5) (log c)) (+ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * log(y)) + z) + (y * i);
	double tmp;
	if (x <= -5.8e+193) {
		tmp = t_1;
	} else if (x <= 7e+199) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * log(y)) + z) + (y * i)
    if (x <= (-5.8d+193)) then
        tmp = t_1
    else if (x <= 7d+199) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (z + a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * Math.log(y)) + z) + (y * i);
	double tmp;
	if (x <= -5.8e+193) {
		tmp = t_1;
	} else if (x <= 7e+199) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * math.log(y)) + z) + (y * i)
	tmp = 0
	if x <= -5.8e+193:
		tmp = t_1
	elif x <= 7e+199:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (z + a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * log(y)) + z) + Float64(y * i))
	tmp = 0.0
	if (x <= -5.8e+193)
		tmp = t_1;
	elseif (x <= 7e+199)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * log(y)) + z) + (y * i);
	tmp = 0.0;
	if (x <= -5.8e+193)
		tmp = t_1;
	elseif (x <= 7e+199)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+193], t$95$1, If[LessEqual[x, 7e+199], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.80000000000000026e193 or 6.99999999999999962e199 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

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

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

      6. associate-+r+ N/A

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

      7. +-commutative N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

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

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

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

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

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

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

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

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

      16. /-lowering-/.f64 N/A

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

      17. /-lowering-/.f64 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 76.4%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

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

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

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

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

       4. log-lowering-log.f64 76.5%

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

   11. Simplified 76.5%

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

   if -5.80000000000000026e193 < x < 6.99999999999999962e199

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 79.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+193}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + y \cdot i\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+199}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y + z\right) + y \cdot i\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+199}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (* x (log y)) z) (* y i))))
   (if (<= x -6.4e+193)
     t_1
     (if (<= x 1.55e+199) (+ (* y i) (+ (+ z a) (* b (log c)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * log(y)) + z) + (y * i);
	double tmp;
	if (x <= -6.4e+193) {
		tmp = t_1;
	} else if (x <= 1.55e+199) {
		tmp = (y * i) + ((z + a) + (b * log(c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * log(y)) + z) + (y * i)
    if (x <= (-6.4d+193)) then
        tmp = t_1
    else if (x <= 1.55d+199) then
        tmp = (y * i) + ((z + a) + (b * log(c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * Math.log(y)) + z) + (y * i);
	double tmp;
	if (x <= -6.4e+193) {
		tmp = t_1;
	} else if (x <= 1.55e+199) {
		tmp = (y * i) + ((z + a) + (b * Math.log(c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * math.log(y)) + z) + (y * i)
	tmp = 0
	if x <= -6.4e+193:
		tmp = t_1
	elif x <= 1.55e+199:
		tmp = (y * i) + ((z + a) + (b * math.log(c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * log(y)) + z) + Float64(y * i))
	tmp = 0.0
	if (x <= -6.4e+193)
		tmp = t_1;
	elseif (x <= 1.55e+199)
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(b * log(c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * log(y)) + z) + (y * i);
	tmp = 0.0;
	if (x <= -6.4e+193)
		tmp = t_1;
	elseif (x <= 1.55e+199)
		tmp = (y * i) + ((z + a) + (b * log(c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+193], t$95$1, If[LessEqual[x, 1.55e+199], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.40000000000000026e193 or 1.54999999999999993e199 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

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

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

      6. associate-+r+ N/A

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

      7. +-commutative N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

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

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

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

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

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

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

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

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

      16. /-lowering-/.f64 N/A

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

      17. /-lowering-/.f64 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 76.4%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

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

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

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

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

       4. log-lowering-log.f64 76.5%

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

   11. Simplified 76.5%

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

   if -6.40000000000000026e193 < x < 1.54999999999999993e199

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 79.6%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 78.1%

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

   8. Simplified 78.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+193}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + y \cdot i\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+199}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+136}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \log c \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ z (* (- b 0.5) (log c))))))
   (if (<= b -3.4e+83)
     t_1
     (if (<= b 1.05e+136) (+ (* y i) (+ (+ z a) (* (log c) -0.5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (z + ((b - 0.5) * log(c)));
	double tmp;
	if (b <= -3.4e+83) {
		tmp = t_1;
	} else if (b <= 1.05e+136) {
		tmp = (y * i) + ((z + a) + (log(c) * -0.5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (z + ((b - 0.5d0) * log(c)))
    if (b <= (-3.4d+83)) then
        tmp = t_1
    else if (b <= 1.05d+136) then
        tmp = (y * i) + ((z + a) + (log(c) * (-0.5d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (z + ((b - 0.5) * Math.log(c)));
	double tmp;
	if (b <= -3.4e+83) {
		tmp = t_1;
	} else if (b <= 1.05e+136) {
		tmp = (y * i) + ((z + a) + (Math.log(c) * -0.5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (z + ((b - 0.5) * math.log(c)))
	tmp = 0
	if b <= -3.4e+83:
		tmp = t_1
	elif b <= 1.05e+136:
		tmp = (y * i) + ((z + a) + (math.log(c) * -0.5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(z + Float64(Float64(b - 0.5) * log(c))))
	tmp = 0.0
	if (b <= -3.4e+83)
		tmp = t_1;
	elseif (b <= 1.05e+136)
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(log(c) * -0.5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (z + ((b - 0.5) * log(c)));
	tmp = 0.0;
	if (b <= -3.4e+83)
		tmp = t_1;
	elseif (b <= 1.05e+136)
		tmp = (y * i) + ((z + a) + (log(c) * -0.5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+83], t$95$1, If[LessEqual[b, 1.05e+136], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.3999999999999998e83 or 1.05e136 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 80.9%

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

   if -3.3999999999999998e83 < b < 1.05e136

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 65.1%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. log-lowering-log.f64 63.3%

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

   8. Simplified 63.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+83}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+136}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \log c \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+115}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.05e+115)
   (+ (* y i) (+ z a))
   (+ (* y i) (+ a (* (- b 0.5) (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.05e+115) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.05d+115)) then
        tmp = (y * i) + (z + a)
    else
        tmp = (y * i) + (a + ((b - 0.5d0) * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.05e+115) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.05e+115:
		tmp = (y * i) + (z + a)
	else:
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.05e+115)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.05e+115)
		tmp = (y * i) + (z + a);
	else
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.05e+115], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000002e115

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 76.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 76.3%

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

   8. Simplified 76.3%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

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

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 69.5%

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

   11. Simplified 69.5%

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

   if -1.05000000000000002e115 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 61.6%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+115}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 3.6e+52) (+ (* (log c) (+ b -0.5)) (+ z a)) (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 3.6e+52) {
		tmp = (log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 3.6d+52) then
        tmp = (log(c) * (b + (-0.5d0))) + (z + a)
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 3.6e+52) {
		tmp = (Math.log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 3.6e+52:
		tmp = (math.log(c) * (b + -0.5)) + (z + a)
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 3.6e+52)
		tmp = Float64(Float64(log(c) * Float64(b + -0.5)) + Float64(z + a));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 3.6e+52)
		tmp = (log(c) * (b + -0.5)) + (z + a);
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 3.6e+52], N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.6e52

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

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

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 58.7%

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

   8. Simplified 58.7%

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

   if 3.6e52 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 83.5%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

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

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 75.2%

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

   11. Simplified 75.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -5 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+238}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= b -5e+229) t_1 (if (<= b 1.22e+238) (+ (* y i) (+ z a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (b <= -5e+229) {
		tmp = t_1;
	} else if (b <= 1.22e+238) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if (b <= (-5d+229)) then
        tmp = t_1
    else if (b <= 1.22d+238) then
        tmp = (y * i) + (z + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (b <= -5e+229) {
		tmp = t_1;
	} else if (b <= 1.22e+238) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if b <= -5e+229:
		tmp = t_1
	elif b <= 1.22e+238:
		tmp = (y * i) + (z + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (b <= -5e+229)
		tmp = t_1;
	elseif (b <= 1.22e+238)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (b <= -5e+229)
		tmp = t_1;
	elseif (b <= 1.22e+238)
		tmp = (y * i) + (z + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+229], t$95$1, If[LessEqual[b, 1.22e+238], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.0000000000000005e229 or 1.2200000000000001e238 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 75.9%

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

   5. Simplified 75.9%

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

   if -5.0000000000000005e229 < b < 1.2200000000000001e238

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 69.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

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

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 59.3%

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

   11. Simplified 59.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+229}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+238}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+52}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.45e+52) (+ a (+ z (* b (log c)))) (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.45e+52) {
		tmp = a + (z + (b * log(c)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 1.45d+52) then
        tmp = a + (z + (b * log(c)))
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.45e+52) {
		tmp = a + (z + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.45e+52:
		tmp = a + (z + (b * math.log(c)))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.45e+52)
		tmp = Float64(a + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.45e+52)
		tmp = a + (z + (b * log(c)));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.45e+52], N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.45e52

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 65.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in y around 0

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

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

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

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

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

       3. *-commutative N/A

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

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

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

       5. log-lowering-log.f64 56.8%

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

   11. Simplified 56.8%

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

   if 1.45e52 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 83.5%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

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

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 75.2%

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

   11. Simplified 75.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+52}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+191}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x 8e+191) (+ (* y i) (+ z a)) (* x (log y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= 8e+191) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = x * log(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= 8d+191) then
        tmp = (y * i) + (z + a)
    else
        tmp = x * log(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= 8e+191) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = x * Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= 8e+191:
		tmp = (y * i) + (z + a)
	else:
		tmp = x * math.log(y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= 8e+191)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(x * log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= 8e+191)
		tmp = (y * i) + (z + a);
	else
		tmp = x * log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, 8e+191], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.00000000000000058e191

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 75.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 73.9%

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

   8. Simplified 73.9%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

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

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 58.2%

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

   11. Simplified 58.2%

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

   if 8.00000000000000058e191 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 55.0%

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

   5. Simplified 55.0%

      \[\leadsto \color{blue}{x \cdot \log y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+191}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 23.9% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+152}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-303}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2e+152) z (if (<= z -7e-303) (* y i) a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+152) {
		tmp = z;
	} else if (z <= -7e-303) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2d+152)) then
        tmp = z
    else if (z <= (-7d-303)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+152) {
		tmp = z;
	} else if (z <= -7e-303) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2e+152:
		tmp = z
	elif z <= -7e-303:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2e+152)
		tmp = z;
	elseif (z <= -7e-303)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2e+152)
		tmp = z;
	elseif (z <= -7e-303)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2e+152], z, If[LessEqual[z, -7e-303], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e152

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 61.3%

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

   if -2.0000000000000001e152 < z < -7e-303

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 36.0%

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

   5. Simplified 36.0%

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

   if -7e-303 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 15.7%

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

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+152}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-303}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.2% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.9 \cdot 10^{+103}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.9e+103) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.9e+103) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.9d+103) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.9e+103) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.9e+103:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.9e+103)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.9e+103)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.9e+103], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.8999999999999998e103

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 44.5%

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

   if 1.8999999999999998e103 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.7%

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

Alternative 14: 41.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+152}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.8e+152) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.8e+152) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3.8d+152)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.8e+152) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.8e+152:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.8e+152)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.8e+152)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.8e+152], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e152

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 61.3%

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

   if -3.8e152 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 42.9%

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

Alternative 15: 52.8% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around inf

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

5. Simplified 72.7%

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

6. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

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

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

   3. log-lowering-log.f64 71.4%

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

8. Simplified 71.4%

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

9. Taylor expanded in b around 0

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

    1. associate-+r+ N/A

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

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

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

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

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

    4. *-commutative N/A

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

    5. *-lowering-*.f64 55.5%

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

11. Simplified 55.5%

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

12. Final simplification 55.5%

    \[\leadsto y \cdot i + \left(z + a\right) \]
13. Add Preprocessing

Alternative 16: 20.8% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8 \cdot 10^{+108}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 8e+108) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 8e+108) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 8d+108) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 8e+108) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 8e+108:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 8e+108)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 8e+108)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 8e+108], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 8.0000000000000003e108

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 18.1%

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

   if 8.0000000000000003e108 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 41.1%

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

Alternative 17: 16.5% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around inf

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

5. Simplified 15.2%

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

Reproduce

herbie shell --seed 2024161 
(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)))