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

Percentage Accurate: 99.8% → 99.8%

Time: 13.0s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ t (+ (* x (log y)) z)) 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 (((t + ((x * log(y)) + z)) + 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 = (((t + ((x * log(y)) + z)) + 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 (((t + ((x * Math.log(y)) + z)) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((t + ((x * math.log(y)) + z)) + 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(t + Float64(Float64(x * log(y)) + z)) + 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 = (((t + ((x * log(y)) + z)) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $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. Final simplification 99.9%

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

Alternative 2: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \log y + \left(\left(a + \left(z + t\right)\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 2.4e+14)
   (+ (* x (log y)) (+ (+ a (+ z t)) (* (log c) (+ b -0.5))))
   (+ (* y i) (+ (* (- b 0.5) (log c)) (+ 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 <= 2.4e+14) {
		tmp = (x * log(y)) + ((a + (z + t)) + (log(c) * (b + -0.5)));
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (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 <= 2.4d+14) then
        tmp = (x * log(y)) + ((a + (z + t)) + (log(c) * (b + (-0.5d0))))
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (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 <= 2.4e+14) {
		tmp = (x * Math.log(y)) + ((a + (z + t)) + (Math.log(c) * (b + -0.5)));
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 2.4e+14:
		tmp = (x * math.log(y)) + ((a + (z + t)) + (math.log(c) * (b + -0.5)))
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 2.4e+14)
		tmp = Float64(Float64(x * log(y)) + Float64(Float64(a + Float64(z + t)) + Float64(log(c) * Float64(b + -0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + 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 <= 2.4e+14)
		tmp = (x * log(y)) + ((a + (z + t)) + (log(c) * (b + -0.5)));
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 2.4e+14], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4e14

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. sum4-define N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. sum4-define N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 97.6%

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

   if 2.4e14 < 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 80.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \log y + \left(\left(a + \left(z + t\right)\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot i + \left(t\_1 + t\_2\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+204}:\\ \;\;\;\;y \cdot i + \left(t\_2 + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (* (- b 0.5) (log c))))
   (if (<= x -7.8e+180)
     (+ (* y i) (+ t_1 t_2))
     (if (<= x 5.8e+204) (+ (* y i) (+ t_2 (+ z a))) (+ t_1 (* y i))))))

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);
	double t_2 = (b - 0.5) * log(c);
	double tmp;
	if (x <= -7.8e+180) {
		tmp = (y * i) + (t_1 + t_2);
	} else if (x <= 5.8e+204) {
		tmp = (y * i) + (t_2 + (z + a));
	} else {
		tmp = t_1 + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = (b - 0.5d0) * log(c)
    if (x <= (-7.8d+180)) then
        tmp = (y * i) + (t_1 + t_2)
    else if (x <= 5.8d+204) then
        tmp = (y * i) + (t_2 + (z + a))
    else
        tmp = t_1 + (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 t_1 = x * Math.log(y);
	double t_2 = (b - 0.5) * Math.log(c);
	double tmp;
	if (x <= -7.8e+180) {
		tmp = (y * i) + (t_1 + t_2);
	} else if (x <= 5.8e+204) {
		tmp = (y * i) + (t_2 + (z + a));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = (b - 0.5) * math.log(c)
	tmp = 0
	if x <= -7.8e+180:
		tmp = (y * i) + (t_1 + t_2)
	elif x <= 5.8e+204:
		tmp = (y * i) + (t_2 + (z + a))
	else:
		tmp = t_1 + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (x <= -7.8e+180)
		tmp = Float64(Float64(y * i) + Float64(t_1 + t_2));
	elseif (x <= 5.8e+204)
		tmp = Float64(Float64(y * i) + Float64(t_2 + Float64(z + a)));
	else
		tmp = Float64(t_1 + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (x <= -7.8e+180)
		tmp = (y * i) + (t_1 + t_2);
	elseif (x <= 5.8e+204)
		tmp = (y * i) + (t_2 + (z + a));
	else
		tmp = t_1 + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+180], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+204], N[(N[(y * i), $MachinePrecision] + N[(t$95$2 + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.8000000000000002e180

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 80.2%

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

   5. Simplified 80.2%

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

   if -7.8000000000000002e180 < x < 5.80000000000000007e204

   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 73.4%

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

   if 5.80000000000000007e204 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 92.9%

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

   5. Simplified 92.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+204}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+103}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= z -3.2e+216)
     (+ (* y i) (+ z t_1))
     (if (<= z -4.7e+103)
       (+ a (+ (+ z t) (* (log c) (+ b -0.5))))
       (if (<= z -9e+69) (+ (* x (log y)) z) (+ (* y i) (+ t_1 (+ t a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if (z <= -3.2e+216) {
		tmp = (y * i) + (z + t_1);
	} else if (z <= -4.7e+103) {
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	} else if (z <= -9e+69) {
		tmp = (x * log(y)) + z;
	} else {
		tmp = (y * i) + (t_1 + (t + 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) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if (z <= (-3.2d+216)) then
        tmp = (y * i) + (z + t_1)
    else if (z <= (-4.7d+103)) then
        tmp = a + ((z + t) + (log(c) * (b + (-0.5d0))))
    else if (z <= (-9d+69)) then
        tmp = (x * log(y)) + z
    else
        tmp = (y * i) + (t_1 + (t + 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 t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if (z <= -3.2e+216) {
		tmp = (y * i) + (z + t_1);
	} else if (z <= -4.7e+103) {
		tmp = a + ((z + t) + (Math.log(c) * (b + -0.5)));
	} else if (z <= -9e+69) {
		tmp = (x * Math.log(y)) + z;
	} else {
		tmp = (y * i) + (t_1 + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if z <= -3.2e+216:
		tmp = (y * i) + (z + t_1)
	elif z <= -4.7e+103:
		tmp = a + ((z + t) + (math.log(c) * (b + -0.5)))
	elif z <= -9e+69:
		tmp = (x * math.log(y)) + z
	else:
		tmp = (y * i) + (t_1 + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (z <= -3.2e+216)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (z <= -4.7e+103)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5))));
	elseif (z <= -9e+69)
		tmp = Float64(Float64(x * log(y)) + z);
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (z <= -3.2e+216)
		tmp = (y * i) + (z + t_1);
	elseif (z <= -4.7e+103)
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	elseif (z <= -9e+69)
		tmp = (x * log(y)) + z;
	else
		tmp = (y * i) + (t_1 + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+216], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.7e+103], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e+69], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999997e216

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 84.3%

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

   if -3.1999999999999997e216 < z < -4.70000000000000033e103

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. sum4-define N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. sum4-define N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 95.8%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 91.3%

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

   8. Simplified 91.3%

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

   if -4.70000000000000033e103 < z < -8.9999999999999999e69

   1. Initial program 100.0%

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

   3. Taylor expanded in 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 100.0%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 35.1%

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

   if -8.9999999999999999e69 < 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 t around inf

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

   5. Simplified 72.3%

      \[\leadsto \left(\left(\color{blue}{t} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+103}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+215}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+103}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= z -8.5e+215)
     (+ (* y i) (+ z t_1))
     (if (<= z -4.7e+103)
       (+ a (+ (+ z t) (* (log c) (+ b -0.5))))
       (if (<= z -9e+69) (+ (* x (log y)) z) (+ (* y i) (+ 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 - 0.5) * log(c);
	double tmp;
	if (z <= -8.5e+215) {
		tmp = (y * i) + (z + t_1);
	} else if (z <= -4.7e+103) {
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	} else if (z <= -9e+69) {
		tmp = (x * log(y)) + z;
	} else {
		tmp = (y * i) + (a + 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 - 0.5d0) * log(c)
    if (z <= (-8.5d+215)) then
        tmp = (y * i) + (z + t_1)
    else if (z <= (-4.7d+103)) then
        tmp = a + ((z + t) + (log(c) * (b + (-0.5d0))))
    else if (z <= (-9d+69)) then
        tmp = (x * log(y)) + z
    else
        tmp = (y * i) + (a + 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 - 0.5) * Math.log(c);
	double tmp;
	if (z <= -8.5e+215) {
		tmp = (y * i) + (z + t_1);
	} else if (z <= -4.7e+103) {
		tmp = a + ((z + t) + (Math.log(c) * (b + -0.5)));
	} else if (z <= -9e+69) {
		tmp = (x * Math.log(y)) + z;
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if z <= -8.5e+215:
		tmp = (y * i) + (z + t_1)
	elif z <= -4.7e+103:
		tmp = a + ((z + t) + (math.log(c) * (b + -0.5)))
	elif z <= -9e+69:
		tmp = (x * math.log(y)) + z
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (z <= -8.5e+215)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (z <= -4.7e+103)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5))));
	elseif (z <= -9e+69)
		tmp = Float64(Float64(x * log(y)) + z);
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (z <= -8.5e+215)
		tmp = (y * i) + (z + t_1);
	elseif (z <= -4.7e+103)
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	elseif (z <= -9e+69)
		tmp = (x * log(y)) + z;
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+215], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.7e+103], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e+69], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.50000000000000064e215

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 84.3%

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

   if -8.50000000000000064e215 < z < -4.70000000000000033e103

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. sum4-define N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. sum4-define N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 95.8%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 91.3%

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

   8. Simplified 91.3%

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

   if -4.70000000000000033e103 < z < -8.9999999999999999e69

   1. Initial program 100.0%

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

   3. Taylor expanded in 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 100.0%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 35.1%

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

   if -8.9999999999999999e69 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.0%

      \[\leadsto \left(\color{blue}{a} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+215}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+103}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+219}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+103}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.85e+219)
   (+ z (* y i))
   (if (<= z -5.7e+103)
     (+ a (+ (+ z t) (* (log c) (+ b -0.5))))
     (if (<= z -9e+69)
       (+ (* x (log y)) z)
       (+ (* 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 <= -1.85e+219) {
		tmp = z + (y * i);
	} else if (z <= -5.7e+103) {
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	} else if (z <= -9e+69) {
		tmp = (x * log(y)) + z;
	} 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 <= (-1.85d+219)) then
        tmp = z + (y * i)
    else if (z <= (-5.7d+103)) then
        tmp = a + ((z + t) + (log(c) * (b + (-0.5d0))))
    else if (z <= (-9d+69)) then
        tmp = (x * log(y)) + z
    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 <= -1.85e+219) {
		tmp = z + (y * i);
	} else if (z <= -5.7e+103) {
		tmp = a + ((z + t) + (Math.log(c) * (b + -0.5)));
	} else if (z <= -9e+69) {
		tmp = (x * Math.log(y)) + z;
	} 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 <= -1.85e+219:
		tmp = z + (y * i)
	elif z <= -5.7e+103:
		tmp = a + ((z + t) + (math.log(c) * (b + -0.5)))
	elif z <= -9e+69:
		tmp = (x * math.log(y)) + z
	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 <= -1.85e+219)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -5.7e+103)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5))));
	elseif (z <= -9e+69)
		tmp = Float64(Float64(x * log(y)) + z);
	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 <= -1.85e+219)
		tmp = z + (y * i);
	elseif (z <= -5.7e+103)
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	elseif (z <= -9e+69)
		tmp = (x * log(y)) + z;
	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, -1.85e+219], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.7e+103], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e+69], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $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 4 regimes

2. if z < -1.85e219

   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 78.7%

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

   if -1.85e219 < z < -5.70000000000000033e103

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. sum4-define N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. sum4-define N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 95.8%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 91.3%

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

   8. Simplified 91.3%

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

   if -5.70000000000000033e103 < z < -8.9999999999999999e69

   1. Initial program 100.0%

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

   3. Taylor expanded in 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 100.0%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 35.1%

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

   if -8.9999999999999999e69 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 54.0%

      \[\leadsto \left(\color{blue}{a} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+219}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+103}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \log y + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + y \cdot i\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+205}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (* y i))))
   (if (<= x -8.6e+177)
     t_1
     (if (<= x 3.7e+205) (+ (* 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)) + (y * i);
	double tmp;
	if (x <= -8.6e+177) {
		tmp = t_1;
	} else if (x <= 3.7e+205) {
		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)) + (y * i)
    if (x <= (-8.6d+177)) then
        tmp = t_1
    else if (x <= 3.7d+205) 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)) + (y * i);
	double tmp;
	if (x <= -8.6e+177) {
		tmp = t_1;
	} else if (x <= 3.7e+205) {
		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)) + (y * i)
	tmp = 0
	if x <= -8.6e+177:
		tmp = t_1
	elif x <= 3.7e+205:
		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(x * log(y)) + Float64(y * i))
	tmp = 0.0
	if (x <= -8.6e+177)
		tmp = t_1;
	elseif (x <= 3.7e+205)
		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)) + (y * i);
	tmp = 0.0;
	if (x <= -8.6e+177)
		tmp = t_1;
	elseif (x <= 3.7e+205)
		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[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+177], t$95$1, If[LessEqual[x, 3.7e+205], 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 < -8.60000000000000074e177 or 3.69999999999999981e205 < 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

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

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

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

      2. log-lowering-log.f64 85.1%

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

   5. Simplified 85.1%

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

   if -8.60000000000000074e177 < x < 3.69999999999999981e205

   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 73.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+205}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 400:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 400.0)
   (+ a (+ (+ z t) (* (log c) (+ b -0.5))))
   (if (<= y 2.3e+14) (+ (* x (log y)) a) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 400.0) {
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	} else if (y <= 2.3e+14) {
		tmp = (x * log(y)) + a;
	} else {
		tmp = z + (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 (y <= 400.0d0) then
        tmp = a + ((z + t) + (log(c) * (b + (-0.5d0))))
    else if (y <= 2.3d+14) then
        tmp = (x * log(y)) + a
    else
        tmp = z + (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 (y <= 400.0) {
		tmp = a + ((z + t) + (Math.log(c) * (b + -0.5)));
	} else if (y <= 2.3e+14) {
		tmp = (x * Math.log(y)) + a;
	} else {
		tmp = z + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 400.0:
		tmp = a + ((z + t) + (math.log(c) * (b + -0.5)))
	elif y <= 2.3e+14:
		tmp = (x * math.log(y)) + a
	else:
		tmp = z + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 400.0)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5))));
	elseif (y <= 2.3e+14)
		tmp = Float64(Float64(x * log(y)) + a);
	else
		tmp = Float64(z + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 400.0)
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	elseif (y <= 2.3e+14)
		tmp = (x * log(y)) + a;
	else
		tmp = z + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 400.0], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+14], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 400

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. sum4-define N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. sum4-define N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 97.8%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 75.1%

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

   8. Simplified 75.1%

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

   if 400 < y < 2.3e14

   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 95.0%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 75.1%

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

   if 2.3e14 < 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

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

   5. Simplified 63.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 400:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 400:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 400.0)
   (+ (* (log c) (+ b -0.5)) (+ z a))
   (if (<= y 2.65e+14) (+ (* x (log y)) a) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 400.0) {
		tmp = (log(c) * (b + -0.5)) + (z + a);
	} else if (y <= 2.65e+14) {
		tmp = (x * log(y)) + a;
	} else {
		tmp = z + (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 (y <= 400.0d0) then
        tmp = (log(c) * (b + (-0.5d0))) + (z + a)
    else if (y <= 2.65d+14) then
        tmp = (x * log(y)) + a
    else
        tmp = z + (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 (y <= 400.0) {
		tmp = (Math.log(c) * (b + -0.5)) + (z + a);
	} else if (y <= 2.65e+14) {
		tmp = (x * Math.log(y)) + a;
	} else {
		tmp = z + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 400.0:
		tmp = (math.log(c) * (b + -0.5)) + (z + a)
	elif y <= 2.65e+14:
		tmp = (x * math.log(y)) + a
	else:
		tmp = z + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 400.0)
		tmp = Float64(Float64(log(c) * Float64(b + -0.5)) + Float64(z + a));
	elseif (y <= 2.65e+14)
		tmp = Float64(Float64(x * log(y)) + a);
	else
		tmp = Float64(z + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 400.0)
		tmp = (log(c) * (b + -0.5)) + (z + a);
	elseif (y <= 2.65e+14)
		tmp = (x * log(y)) + a;
	else
		tmp = z + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 400.0], N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+14], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 400

   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 58.0%

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

   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. +-commutative N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

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

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

      9. +-lowering-+.f64 55.9%

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

   8. Simplified 55.9%

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

   if 400 < y < 2.65e14

   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 95.0%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 75.1%

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

   if 2.65e14 < 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

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

   5. Simplified 63.8%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 400:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 400:\\ \;\;\;\;\left(z + a\right) + b \cdot \log c\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 400.0)
   (+ (+ z a) (* b (log c)))
   (if (<= y 4.1e+14) (+ (* x (log y)) a) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 400.0) {
		tmp = (z + a) + (b * log(c));
	} else if (y <= 4.1e+14) {
		tmp = (x * log(y)) + a;
	} else {
		tmp = z + (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 (y <= 400.0d0) then
        tmp = (z + a) + (b * log(c))
    else if (y <= 4.1d+14) then
        tmp = (x * log(y)) + a
    else
        tmp = z + (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 (y <= 400.0) {
		tmp = (z + a) + (b * Math.log(c));
	} else if (y <= 4.1e+14) {
		tmp = (x * Math.log(y)) + a;
	} else {
		tmp = z + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 400.0:
		tmp = (z + a) + (b * math.log(c))
	elif y <= 4.1e+14:
		tmp = (x * math.log(y)) + a
	else:
		tmp = z + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 400.0)
		tmp = Float64(Float64(z + a) + Float64(b * log(c)));
	elseif (y <= 4.1e+14)
		tmp = Float64(Float64(x * log(y)) + a);
	else
		tmp = Float64(z + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 400.0)
		tmp = (z + a) + (b * log(c));
	elseif (y <= 4.1e+14)
		tmp = (x * log(y)) + a;
	else
		tmp = z + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 400.0], N[(N[(z + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+14], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 400

   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 58.0%

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

   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. +-commutative N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

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

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

      9. +-lowering-+.f64 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

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

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

       3. log-lowering-log.f64 52.9%

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

   11. Simplified 52.9%

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

   if 400 < y < 4.1e14

   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 95.0%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 75.1%

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

   if 4.1e14 < 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

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

   5. Simplified 63.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 400:\\ \;\;\;\;\left(z + a\right) + b \cdot \log c\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{+117}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.04e+117)
   (+ z (* y i))
   (if (<= z -4.4e+68) (+ (* x (log y)) a) (+ 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 <= -1.04e+117) {
		tmp = z + (y * i);
	} else if (z <= -4.4e+68) {
		tmp = (x * log(y)) + a;
	} 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 <= (-1.04d+117)) then
        tmp = z + (y * i)
    else if (z <= (-4.4d+68)) then
        tmp = (x * log(y)) + a
    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 <= -1.04e+117) {
		tmp = z + (y * i);
	} else if (z <= -4.4e+68) {
		tmp = (x * Math.log(y)) + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.04e+117:
		tmp = z + (y * i)
	elif z <= -4.4e+68:
		tmp = (x * math.log(y)) + a
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.04e+117)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -4.4e+68)
		tmp = Float64(Float64(x * log(y)) + a);
	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 <= -1.04e+117)
		tmp = z + (y * i);
	elseif (z <= -4.4e+68)
		tmp = (x * log(y)) + a;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.04e+117], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e+68], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.03999999999999995e117

   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 58.1%

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

   if -1.03999999999999995e117 < z < -4.39999999999999974e68

   1. Initial program 100.0%

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

   3. Taylor expanded in 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 100.0%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 78.4%

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

   if -4.39999999999999974e68 < 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 40.4%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{+117}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.4% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+100}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 4.5e-68) z (if (<= a 1.5e+100) (* 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 (a <= 4.5e-68) {
		tmp = z;
	} else if (a <= 1.5e+100) {
		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 (a <= 4.5d-68) then
        tmp = z
    else if (a <= 1.5d+100) 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 (a <= 4.5e-68) {
		tmp = z;
	} else if (a <= 1.5e+100) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.5e-68:
		tmp = z
	elif a <= 1.5e+100:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.5e-68)
		tmp = z;
	elseif (a <= 1.5e+100)
		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 (a <= 4.5e-68)
		tmp = z;
	elseif (a <= 1.5e+100)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.5e-68], z, If[LessEqual[a, 1.5e+100], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if a < 4.49999999999999999e-68

   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 13.6%

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

   if 4.49999999999999999e-68 < a < 1.49999999999999993e100

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 26.5%

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

   5. Simplified 26.5%

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

   if 1.49999999999999993e100 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 45.8%

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

4. Final simplification 20.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+100}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.0% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+117}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.2e+117) (+ 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 (z <= -1.2e+117) {
		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 (z <= (-1.2d+117)) 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 (z <= -1.2e+117) {
		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 z <= -1.2e+117:
		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 (z <= -1.2e+117)
		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 (z <= -1.2e+117)
		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[z, -1.2e+117], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1999999999999999e117

   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 58.1%

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

   if -1.1999999999999999e117 < 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 41.1%

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

Alternative 14: 41.4% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -8.5e+140) 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 <= -8.5e+140) {
		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 <= (-8.5d+140)) 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 <= -8.5e+140) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -8.5e+140:
		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 <= -8.5e+140)
		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 <= -8.5e+140)
		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, -8.5e+140], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999996e140

   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 44.7%

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

   if -8.4999999999999996e140 < 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 40.5%

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

Alternative 15: 20.6% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.22 \cdot 10^{+56}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 1.22e+56) 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 <= 1.22e+56) {
		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 <= 1.22d+56) 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 <= 1.22e+56) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.22e+56:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.22e+56)
		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 <= 1.22e+56)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.22e+56], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 1.22e56

   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 15.0%

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

   if 1.22e56 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 41.7%

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

Alternative 16: 16.7% 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 15.5%

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

Reproduce

herbie shell --seed 2024158 
(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)))