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

Percentage Accurate: 99.8% → 99.8%

Time: 12.1s

Alternatives: 10

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

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((b - 0.5) * log(c)) + (a + (((x * log(y)) + z) + t))) + (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 = (((b - 0.5d0) * log(c)) + (a + (((x * log(y)) + z) + t))) + (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 (((b - 0.5) * Math.log(c)) + (a + (((x * Math.log(y)) + z) + t))) + (y * i);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 92.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+109}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+138}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= t_1 -4e+109)
     (+ (* y i) (+ t_1 (+ a (+ z t))))
     (if (<= t_1 1e+138)
       (+ (* y i) (+ a (+ (+ (* x (log y)) z) t)))
       (+ (* y i) (+ t_1 (+ z 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 (t_1 <= -4e+109) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else if (t_1 <= 1e+138) {
		tmp = (y * i) + (a + (((x * log(y)) + z) + t));
	} else {
		tmp = (y * i) + (t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if (t_1 <= (-4d+109)) then
        tmp = (y * i) + (t_1 + (a + (z + t)))
    else if (t_1 <= 1d+138) then
        tmp = (y * i) + (a + (((x * log(y)) + z) + t))
    else
        tmp = (y * i) + (t_1 + (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 t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if (t_1 <= -4e+109) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else if (t_1 <= 1e+138) {
		tmp = (y * i) + (a + (((x * Math.log(y)) + z) + t));
	} else {
		tmp = (y * i) + (t_1 + (z + 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 t_1 <= -4e+109:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	elif t_1 <= 1e+138:
		tmp = (y * i) + (a + (((x * math.log(y)) + z) + t))
	else:
		tmp = (y * i) + (t_1 + (z + 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 (t_1 <= -4e+109)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	elseif (t_1 <= 1e+138)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(Float64(x * log(y)) + z) + t)));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(z + 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 (t_1 <= -4e+109)
		tmp = (y * i) + (t_1 + (a + (z + t)));
	elseif (t_1 <= 1e+138)
		tmp = (y * i) + (a + (((x * log(y)) + z) + t));
	else
		tmp = (y * i) + (t_1 + (z + 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[t$95$1, -4e+109], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+138], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -3.99999999999999993e109

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 92.2%

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

   if -3.99999999999999993e109 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 1e138

   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

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

      1. associate-*r* N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

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

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

   5. Simplified 76.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in b around 0

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

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

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

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

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

       3. +-commutative N/A

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

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

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

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

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

       6. log-lowering-log.f64 98.4%

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

   11. Simplified 98.4%

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

   if 1e138 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.7%

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

   3. Taylor expanded in 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 82.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b - 0.5\right) \cdot \log c \leq -4 \cdot 10^{+109}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;\left(b - 0.5\right) \cdot \log c \leq 10^{+138}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ t_2 := y \cdot i + \left(t\_1 + \left(z + a\right)\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+138}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))) (t_2 (+ (* y i) (+ t_1 (+ z a)))))
   (if (<= t_1 -4e+109)
     t_2
     (if (<= t_1 1e+138) (+ (* y i) (+ a (+ (+ (* x (log y)) z) t))) t_2))))

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 t_2 = (y * i) + (t_1 + (z + a));
	double tmp;
	if (t_1 <= -4e+109) {
		tmp = t_2;
	} else if (t_1 <= 1e+138) {
		tmp = (y * i) + (a + (((x * log(y)) + z) + t));
	} else {
		tmp = t_2;
	}
	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 = (b - 0.5d0) * log(c)
    t_2 = (y * i) + (t_1 + (z + a))
    if (t_1 <= (-4d+109)) then
        tmp = t_2
    else if (t_1 <= 1d+138) then
        tmp = (y * i) + (a + (((x * log(y)) + z) + t))
    else
        tmp = t_2
    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 t_2 = (y * i) + (t_1 + (z + a));
	double tmp;
	if (t_1 <= -4e+109) {
		tmp = t_2;
	} else if (t_1 <= 1e+138) {
		tmp = (y * i) + (a + (((x * Math.log(y)) + z) + t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	t_2 = (y * i) + (t_1 + (z + a))
	tmp = 0
	if t_1 <= -4e+109:
		tmp = t_2
	elif t_1 <= 1e+138:
		tmp = (y * i) + (a + (((x * math.log(y)) + z) + t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	t_2 = Float64(Float64(y * i) + Float64(t_1 + Float64(z + a)))
	tmp = 0.0
	if (t_1 <= -4e+109)
		tmp = t_2;
	elseif (t_1 <= 1e+138)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(Float64(x * log(y)) + z) + t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	t_2 = (y * i) + (t_1 + (z + a));
	tmp = 0.0;
	if (t_1 <= -4e+109)
		tmp = t_2;
	elseif (t_1 <= 1e+138)
		tmp = (y * i) + (a + (((x * log(y)) + z) + t));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+109], t$95$2, If[LessEqual[t$95$1, 1e+138], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -3.99999999999999993e109 or 1e138 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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 80.5%

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

   if -3.99999999999999993e109 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 1e138

   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

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

      1. associate-*r* N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

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

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

   5. Simplified 76.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in b around 0

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

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

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

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

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

       3. +-commutative N/A

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

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

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

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

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

       6. log-lowering-log.f64 98.4%

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

   11. Simplified 98.4%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b - 0.5\right) \cdot \log c \leq -4 \cdot 10^{+109}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{elif}\;\left(b - 0.5\right) \cdot \log c \leq 10^{+138}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(b - 0.5\right) \cdot \log c \leq 10^{+138}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + t\right) + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* (- b 0.5) (log c)) 1e+138)
   (+ (* y i) (+ a (+ (+ (* x (log y)) z) t)))
   (+ (* y i) (+ (+ z t) (* b (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) * log(c)) <= 1e+138) {
		tmp = (y * i) + (a + (((x * log(y)) + z) + t));
	} else {
		tmp = (y * i) + ((z + t) + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) * log(c)) <= 1d+138) then
        tmp = (y * i) + (a + (((x * log(y)) + z) + t))
    else
        tmp = (y * i) + ((z + t) + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) * Math.log(c)) <= 1e+138) {
		tmp = (y * i) + (a + (((x * Math.log(y)) + z) + t));
	} else {
		tmp = (y * i) + ((z + t) + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) * math.log(c)) <= 1e+138:
		tmp = (y * i) + (a + (((x * math.log(y)) + z) + t))
	else:
		tmp = (y * i) + ((z + t) + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(b - 0.5) * log(c)) <= 1e+138)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(Float64(x * log(y)) + z) + t)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(z + t) + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) * log(c)) <= 1e+138)
		tmp = (y * i) + (a + (((x * log(y)) + z) + t));
	else
		tmp = (y * i) + ((z + t) + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision], 1e+138], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(z + t), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 1e138

   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

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

      1. associate-*r* N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

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

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

   5. Simplified 76.6%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in b around 0

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

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

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

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

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

       3. +-commutative N/A

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

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

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

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

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

       6. log-lowering-log.f64 94.3%

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

   11. Simplified 94.3%

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

   if 1e138 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.7%

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

   3. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

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

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

   5. Simplified 75.6%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 75.6%

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

   8. Simplified 75.6%

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

   9. Taylor expanded in z around inf

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

   11. Simplified 85.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b - 0.5\right) \cdot \log c \leq 10^{+138}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + t\right) + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.7 \cdot 10^{-11}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{z}{y} + \left(i + \frac{a}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 5.7e-11)
   (+ (* (log c) (+ b -0.5)) (+ z a))
   (* y (+ (/ z y) (+ i (/ a y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.7e-11) {
		tmp = (log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = y * ((z / y) + (i + (a / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 5.7d-11) then
        tmp = (log(c) * (b + (-0.5d0))) + (z + a)
    else
        tmp = y * ((z / y) + (i + (a / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.7e-11) {
		tmp = (Math.log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = y * ((z / y) + (i + (a / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 5.7e-11:
		tmp = (math.log(c) * (b + -0.5)) + (z + a)
	else:
		tmp = y * ((z / y) + (i + (a / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 5.7e-11)
		tmp = Float64(Float64(log(c) * Float64(b + -0.5)) + Float64(z + a));
	else
		tmp = Float64(y * Float64(Float64(z / y) + Float64(i + Float64(a / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 5.7e-11)
		tmp = (log(c) * (b + -0.5)) + (z + a);
	else
		tmp = y * ((z / y) + (i + (a / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 5.7e-11], N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z / y), $MachinePrecision] + N[(i + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.6999999999999997e-11

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 62.5%

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

   6. Taylor expanded in 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. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-lowering-+.f64 61.5%

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

   8. Simplified 61.5%

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

   if 5.6999999999999997e-11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 73.5%

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

   6. Taylor expanded in y around inf

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

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

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

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

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

      6. +-commutative N/A

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

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

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

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

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

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

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

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

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

      17. /-lowering-/.f64 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in z around inf

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

       1. /-lowering-/.f64 66.1%

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

   11. Simplified 66.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.7 \cdot 10^{-11}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{z}{y} + \left(i + \frac{a}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.5% accurate, 18.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+74}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4e+74) (+ (* y i) (+ z t)) (+ 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 <= -4e+74) {
		tmp = (y * i) + (z + t);
	} 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 <= (-4d+74)) then
        tmp = (y * i) + (z + t)
    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 <= -4e+74) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4e+74:
		tmp = (y * i) + (z + t)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4e+74)
		tmp = Float64(Float64(y * i) + Float64(z + t));
	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 <= -4e+74)
		tmp = (y * i) + (z + t);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4e+74], N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999981e74

   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

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

      1. associate-*r* N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

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

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

   5. Simplified 71.8%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 71.8%

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

   8. Simplified 71.8%

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

   9. Taylor expanded in z around inf

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

   11. Simplified 78.5%

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

   12. Taylor expanded in b around 0

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

       1. +-lowering-+.f64 70.0%

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

   14. Simplified 70.0%

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

   if -3.99999999999999981e74 < 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 44.4%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+74}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.2e+71) (+ 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 <= -2.2e+71) {
		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 <= (-2.2d+71)) 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 <= -2.2e+71) {
		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 <= -2.2e+71:
		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 <= -2.2e+71)
		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 <= -2.2e+71)
		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, -2.2e+71], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.19999999999999995e71

   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 56.9%

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

   if -2.19999999999999995e71 < 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 44.2%

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

Alternative 8: 41.0% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+182}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.8e+182) 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 <= -2.8e+182) {
		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 <= (-2.8d+182)) 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 <= -2.8e+182) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.8e+182:
		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 <= -2.8e+182)
		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 <= -2.8e+182)
		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, -2.8e+182], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000006e182

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 46.3%

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

   if -2.80000000000000006e182 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 42.2%

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

Alternative 9: 20.8% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+70}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -2.05e+70) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.05e+70) {
		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 (z <= (-2.05d+70)) 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 (z <= -2.05e+70) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.05e+70:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.05e+70)
		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 (z <= -2.05e+70)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.05e+70], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.0500000000000001e70

   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 38.4%

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

   if -2.0500000000000001e70 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 23.4%

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

Alternative 10: 16.3% 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 20.6%

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

Reproduce

herbie shell --seed 2024138 
(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)))