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

Percentage Accurate: 99.8% → 99.8%

Time: 12.8s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 90.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ t_2 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+196}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+136}:\\ \;\;\;\;y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))) (t_2 (* (- b 0.5) (log c))))
   (if (<= t_2 -1e+196)
     (+ (* y i) (+ a t_1))
     (if (<= t_2 2e+136)
       (+ (* y i) (+ (+ (* x (log y)) z) (+ t a)))
       (+ (* 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 * log(c);
	double t_2 = (b - 0.5) * log(c);
	double tmp;
	if (t_2 <= -1e+196) {
		tmp = (y * i) + (a + t_1);
	} else if (t_2 <= 2e+136) {
		tmp = (y * i) + (((x * log(y)) + z) + (t + a));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = b * log(c)
    t_2 = (b - 0.5d0) * log(c)
    if (t_2 <= (-1d+196)) then
        tmp = (y * i) + (a + t_1)
    else if (t_2 <= 2d+136) then
        tmp = (y * i) + (((x * log(y)) + z) + (t + a))
    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 * Math.log(c);
	double t_2 = (b - 0.5) * Math.log(c);
	double tmp;
	if (t_2 <= -1e+196) {
		tmp = (y * i) + (a + t_1);
	} else if (t_2 <= 2e+136) {
		tmp = (y * i) + (((x * Math.log(y)) + z) + (t + a));
	} else {
		tmp = (y * i) + (t_1 + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	t_2 = (b - 0.5) * math.log(c)
	tmp = 0
	if t_2 <= -1e+196:
		tmp = (y * i) + (a + t_1)
	elif t_2 <= 2e+136:
		tmp = (y * i) + (((x * math.log(y)) + z) + (t + a))
	else:
		tmp = (y * i) + (t_1 + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	t_2 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (t_2 <= -1e+196)
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	elseif (t_2 <= 2e+136)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a)));
	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 * log(c);
	t_2 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (t_2 <= -1e+196)
		tmp = (y * i) + (a + t_1);
	elseif (t_2 <= 2e+136)
		tmp = (y * i) + (((x * log(y)) + z) + (t + a));
	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[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+196], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+136], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $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)) < -9.9999999999999995e195

   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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 92.2%

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

   if -9.9999999999999995e195 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 2.00000000000000012e136

   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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      6. log-lowering-log.f64 96.8%

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

   8. Simplified 96.8%

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

   if 2.00000000000000012e136 < (*.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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 69.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b - 0.5\right) \cdot \log c \leq -1 \cdot 10^{+196}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{elif}\;\left(b - 0.5\right) \cdot \log c \leq 2 \cdot 10^{+136}:\\ \;\;\;\;y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+70}:\\ \;\;\;\;y \cdot i + \left(\left(t\_1 + z\right) + \left(t + a\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+160}:\\ \;\;\;\;y \cdot i + \left(t\_2 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_2 + \left(t\_1 + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (* (- b 0.5) (log c))))
   (if (<= x -1.3e+70)
     (+ (* y i) (+ (+ t_1 z) (+ t a)))
     (if (<= x 1.2e+160)
       (+ (* y i) (+ t_2 (+ a (+ z t))))
       (+ (* y i) (+ t_2 (+ t_1 a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double t_2 = (b - 0.5) * log(c);
	double tmp;
	if (x <= -1.3e+70) {
		tmp = (y * i) + ((t_1 + z) + (t + a));
	} else if (x <= 1.2e+160) {
		tmp = (y * i) + (t_2 + (a + (z + t)));
	} else {
		tmp = (y * i) + (t_2 + (t_1 + 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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = (b - 0.5d0) * log(c)
    if (x <= (-1.3d+70)) then
        tmp = (y * i) + ((t_1 + z) + (t + a))
    else if (x <= 1.2d+160) then
        tmp = (y * i) + (t_2 + (a + (z + t)))
    else
        tmp = (y * i) + (t_2 + (t_1 + 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 = x * Math.log(y);
	double t_2 = (b - 0.5) * Math.log(c);
	double tmp;
	if (x <= -1.3e+70) {
		tmp = (y * i) + ((t_1 + z) + (t + a));
	} else if (x <= 1.2e+160) {
		tmp = (y * i) + (t_2 + (a + (z + t)));
	} else {
		tmp = (y * i) + (t_2 + (t_1 + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = (b - 0.5) * math.log(c)
	tmp = 0
	if x <= -1.3e+70:
		tmp = (y * i) + ((t_1 + z) + (t + a))
	elif x <= 1.2e+160:
		tmp = (y * i) + (t_2 + (a + (z + t)))
	else:
		tmp = (y * i) + (t_2 + (t_1 + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (x <= -1.3e+70)
		tmp = Float64(Float64(y * i) + Float64(Float64(t_1 + z) + Float64(t + a)));
	elseif (x <= 1.2e+160)
		tmp = Float64(Float64(y * i) + Float64(t_2 + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_2 + Float64(t_1 + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (x <= -1.3e+70)
		tmp = (y * i) + ((t_1 + z) + (t + a));
	elseif (x <= 1.2e+160)
		tmp = (y * i) + (t_2 + (a + (z + t)));
	else
		tmp = (y * i) + (t_2 + (t_1 + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+70], N[(N[(y * i), $MachinePrecision] + N[(N[(t$95$1 + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+160], N[(N[(y * i), $MachinePrecision] + N[(t$95$2 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$2 + N[(t$95$1 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e70

   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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      6. log-lowering-log.f64 96.3%

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

   8. Simplified 96.3%

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

   if -1.3e70 < x < 1.2000000000000001e160

   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 98.8%

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

   if 1.2000000000000001e160 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+70}:\\ \;\;\;\;y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+160}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(x \cdot \log y + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

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

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

   3. log-lowering-log.f64 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 5: 94.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+134}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ (+ (* x (log y)) z) (+ t a)))))
   (if (<= x -1.22e+70)
     t_1
     (if (<= x 1.1e+134)
       (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ z t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (((x * log(y)) + z) + (t + a));
	double tmp;
	if (x <= -1.22e+70) {
		tmp = t_1;
	} else if (x <= 1.1e+134) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (((x * log(y)) + z) + (t + a))
    if (x <= (-1.22d+70)) then
        tmp = t_1
    else if (x <= 1.1d+134) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (z + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (((x * Math.log(y)) + z) + (t + a));
	double tmp;
	if (x <= -1.22e+70) {
		tmp = t_1;
	} else if (x <= 1.1e+134) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (((x * math.log(y)) + z) + (t + a))
	tmp = 0
	if x <= -1.22e+70:
		tmp = t_1
	elif x <= 1.1e+134:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (z + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a)))
	tmp = 0.0
	if (x <= -1.22e+70)
		tmp = t_1;
	elseif (x <= 1.1e+134)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(z + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (((x * log(y)) + z) + (t + a));
	tmp = 0.0;
	if (x <= -1.22e+70)
		tmp = t_1;
	elseif (x <= 1.1e+134)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.22e+70], t$95$1, If[LessEqual[x, 1.1e+134], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.22e70 or 1.1e134 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      6. log-lowering-log.f64 94.9%

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

   8. Simplified 94.9%

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

   if -1.22e70 < x < 1.1e134

   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 98.7%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+70}:\\ \;\;\;\;y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+134}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ (+ (* x (log y)) z) (+ t a)))))
   (if (<= x -1.7e+70)
     t_1
     (if (<= x 1.55e+122) (+ (* y i) (+ (* (- b 0.5) (log c)) (+ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (((x * log(y)) + z) + (t + a));
	double tmp;
	if (x <= -1.7e+70) {
		tmp = t_1;
	} else if (x <= 1.55e+122) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (((x * log(y)) + z) + (t + a))
    if (x <= (-1.7d+70)) then
        tmp = t_1
    else if (x <= 1.55d+122) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (z + a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (((x * Math.log(y)) + z) + (t + a));
	double tmp;
	if (x <= -1.7e+70) {
		tmp = t_1;
	} else if (x <= 1.55e+122) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (((x * math.log(y)) + z) + (t + a))
	tmp = 0
	if x <= -1.7e+70:
		tmp = t_1
	elif x <= 1.55e+122:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (z + a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a)))
	tmp = 0.0
	if (x <= -1.7e+70)
		tmp = t_1;
	elseif (x <= 1.55e+122)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (((x * log(y)) + z) + (t + a));
	tmp = 0.0;
	if (x <= -1.7e+70)
		tmp = t_1;
	elseif (x <= 1.55e+122)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+70], t$95$1, If[LessEqual[x, 1.55e+122], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e70 or 1.54999999999999999e122 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      6. log-lowering-log.f64 94.9%

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

   8. Simplified 94.9%

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

   if -1.7e70 < x < 1.54999999999999999e122

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 79.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+70}:\\ \;\;\;\;y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+192}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(\frac{y}{x} + \frac{\log y}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.8e+158)
   (+ (* x (log y)) (* y i))
   (if (<= x 2.1e+192)
     (+ (* y i) (+ (* b (log c)) (+ z a)))
     (* x (* i (+ (/ y x) (/ (log y) i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.8e+158) {
		tmp = (x * log(y)) + (y * i);
	} else if (x <= 2.1e+192) {
		tmp = (y * i) + ((b * log(c)) + (z + a));
	} else {
		tmp = x * (i * ((y / x) + (log(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 (x <= (-1.8d+158)) then
        tmp = (x * log(y)) + (y * i)
    else if (x <= 2.1d+192) then
        tmp = (y * i) + ((b * log(c)) + (z + a))
    else
        tmp = x * (i * ((y / x) + (log(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 (x <= -1.8e+158) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if (x <= 2.1e+192) {
		tmp = (y * i) + ((b * Math.log(c)) + (z + a));
	} else {
		tmp = x * (i * ((y / x) + (Math.log(y) / i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.8e+158:
		tmp = (x * math.log(y)) + (y * i)
	elif x <= 2.1e+192:
		tmp = (y * i) + ((b * math.log(c)) + (z + a))
	else:
		tmp = x * (i * ((y / x) + (math.log(y) / i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.8e+158)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (x <= 2.1e+192)
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(z + a)));
	else
		tmp = Float64(x * Float64(i * Float64(Float64(y / x) + Float64(log(y) / i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -1.8e+158)
		tmp = (x * log(y)) + (y * i);
	elseif (x <= 2.1e+192)
		tmp = (y * i) + ((b * log(c)) + (z + a));
	else
		tmp = x * (i * ((y / x) + (log(y) / i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.8e+158], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+192], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(i * N[(N[(y / x), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999994e158

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 74.1%

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

   5. Simplified 74.1%

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

   if -1.79999999999999994e158 < x < 2.09999999999999995e192

   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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 75.4%

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

   if 2.09999999999999995e192 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 82.4%

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

   8. Simplified 82.4%

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

   9. Taylor expanded in i around inf

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

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

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

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

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

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

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

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

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

       5. log-lowering-log.f64 82.4%

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

   11. Simplified 82.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+192}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(\frac{y}{x} + \frac{\log y}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+173}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(\frac{y}{x} + \frac{\log y}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -8.2e+155)
   (+ (* x (log y)) (* y i))
   (if (<= x 4.8e+173)
     (+ (* y i) (+ z a))
     (* x (* i (+ (/ y x) (/ (log y) i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -8.2e+155) {
		tmp = (x * log(y)) + (y * i);
	} else if (x <= 4.8e+173) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = x * (i * ((y / x) + (log(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 (x <= (-8.2d+155)) then
        tmp = (x * log(y)) + (y * i)
    else if (x <= 4.8d+173) then
        tmp = (y * i) + (z + a)
    else
        tmp = x * (i * ((y / x) + (log(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 (x <= -8.2e+155) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if (x <= 4.8e+173) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = x * (i * ((y / x) + (Math.log(y) / i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -8.2e+155:
		tmp = (x * math.log(y)) + (y * i)
	elif x <= 4.8e+173:
		tmp = (y * i) + (z + a)
	else:
		tmp = x * (i * ((y / x) + (math.log(y) / i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -8.2e+155)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (x <= 4.8e+173)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(x * Float64(i * Float64(Float64(y / x) + Float64(log(y) / i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -8.2e+155)
		tmp = (x * log(y)) + (y * i);
	elseif (x <= 4.8e+173)
		tmp = (y * i) + (z + a);
	else
		tmp = x * (i * ((y / x) + (log(y) / i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -8.2e+155], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+173], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(x * N[(i * N[(N[(y / x), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.1999999999999996e155

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 74.1%

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

   5. Simplified 74.1%

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

   if -8.1999999999999996e155 < x < 4.7999999999999998e173

   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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 75.4%

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

   9. Taylor expanded in b around 0

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

       1. +-lowering-+.f64 61.5%

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

   11. Simplified 61.5%

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

   if 4.7999999999999998e173 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in i around inf

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

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

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

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

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

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

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

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

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

       5. log-lowering-log.f64 80.9%

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

   11. Simplified 80.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+173}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(\frac{y}{x} + \frac{\log y}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+173}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -8e+153)
   (+ (* x (log y)) (* y i))
   (if (<= x 7.5e+173) (+ (* y i) (+ z a)) (* x (+ (log y) (* i (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -8e+153) {
		tmp = (x * log(y)) + (y * i);
	} else if (x <= 7.5e+173) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = x * (log(y) + (i * (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-8d+153)) then
        tmp = (x * log(y)) + (y * i)
    else if (x <= 7.5d+173) then
        tmp = (y * i) + (z + a)
    else
        tmp = x * (log(y) + (i * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -8e+153) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if (x <= 7.5e+173) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = x * (Math.log(y) + (i * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -8e+153:
		tmp = (x * math.log(y)) + (y * i)
	elif x <= 7.5e+173:
		tmp = (y * i) + (z + a)
	else:
		tmp = x * (math.log(y) + (i * (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -8e+153)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (x <= 7.5e+173)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(x * Float64(log(y) + Float64(i * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -8e+153)
		tmp = (x * log(y)) + (y * i);
	elseif (x <= 7.5e+173)
		tmp = (y * i) + (z + a);
	else
		tmp = x * (log(y) + (i * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -8e+153], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+173], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(i * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8e153

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 74.1%

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

   5. Simplified 74.1%

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

   if -8e153 < x < 7.5e173

   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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 75.4%

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

   9. Taylor expanded in b around 0

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

       1. +-lowering-+.f64 61.5%

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

   11. Simplified 61.5%

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

   if 7.5e173 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 80.9%

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

   8. Simplified 80.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 80.9%

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

   10. Applied egg-rr 80.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+173}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + y \cdot i\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+173}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (* y i))))
   (if (<= x -3.3e+159) t_1 (if (<= x 4.5e+173) (+ (* y i) (+ z a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + (y * i);
	double tmp;
	if (x <= -3.3e+159) {
		tmp = t_1;
	} else if (x <= 4.5e+173) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) + (y * i)
    if (x <= (-3.3d+159)) then
        tmp = t_1
    else if (x <= 4.5d+173) then
        tmp = (y * i) + (z + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * Math.log(y)) + (y * i);
	double tmp;
	if (x <= -3.3e+159) {
		tmp = t_1;
	} else if (x <= 4.5e+173) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + (y * i)
	tmp = 0
	if x <= -3.3e+159:
		tmp = t_1
	elif x <= 4.5e+173:
		tmp = (y * i) + (z + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + Float64(y * i))
	tmp = 0.0
	if (x <= -3.3e+159)
		tmp = t_1;
	elseif (x <= 4.5e+173)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + (y * i);
	tmp = 0.0;
	if (x <= -3.3e+159)
		tmp = t_1;
	elseif (x <= 4.5e+173)
		tmp = (y * i) + (z + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+159], t$95$1, If[LessEqual[x, 4.5e+173], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2999999999999999e159 or 4.5000000000000002e173 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 77.5%

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

   5. Simplified 77.5%

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

   if -3.2999999999999999e159 < x < 4.5000000000000002e173

   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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 75.4%

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

   9. Taylor expanded in b around 0

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

       1. +-lowering-+.f64 61.5%

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

   11. Simplified 61.5%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+173}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+228}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -3.1e+192) t_1 (if (<= x 2.75e+228) (+ (* y i) (+ z a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -3.1e+192) {
		tmp = t_1;
	} else if (x <= 2.75e+228) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-3.1d+192)) then
        tmp = t_1
    else if (x <= 2.75d+228) then
        tmp = (y * i) + (z + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -3.1e+192) {
		tmp = t_1;
	} else if (x <= 2.75e+228) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -3.1e+192:
		tmp = t_1
	elif x <= 2.75e+228:
		tmp = (y * i) + (z + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.1e+192)
		tmp = t_1;
	elseif (x <= 2.75e+228)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -3.1e+192)
		tmp = t_1;
	elseif (x <= 2.75e+228)
		tmp = (y * i) + (z + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e+192], t$95$1, If[LessEqual[x, 2.75e+228], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999999e192 or 2.75000000000000004e228 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 69.0%

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

   5. Simplified 69.0%

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

   if -3.0999999999999999e192 < x < 2.75000000000000004e228

   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 b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 73.6%

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

   9. Taylor expanded in b around 0

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

       1. +-lowering-+.f64 60.7%

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

   11. Simplified 60.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+228}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 21.9% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.3e+111) z (if (<= z -5.6e+48) (* y i) a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.3e+111) {
		tmp = z;
	} else if (z <= -5.6e+48) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.3d+111)) then
        tmp = z
    else if (z <= (-5.6d+48)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.3e+111) {
		tmp = z;
	} else if (z <= -5.6e+48) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.3e+111:
		tmp = z
	elif z <= -5.6e+48:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.3e+111)
		tmp = z;
	elseif (z <= -5.6e+48)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.3e+111)
		tmp = z;
	elseif (z <= -5.6e+48)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.3e+111], z, If[LessEqual[z, -5.6e+48], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2999999999999999e111

   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 29.7%

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

   if -1.2999999999999999e111 < z < -5.60000000000000025e48

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 9.6%

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

   5. Simplified 9.6%

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

   if -5.60000000000000025e48 < 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 19.4%

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

4. Final simplification 20.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.2% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+207}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -7.5e+207) 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 <= -7.5e+207) {
		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 <= (-7.5d+207)) 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 <= -7.5e+207) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -7.5e+207:
		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 <= -7.5e+207)
		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 <= -7.5e+207)
		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, -7.5e+207], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999986e207

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 45.8%

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

   if -7.49999999999999986e207 < 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 38.7%

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

Alternative 14: 51.8% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

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

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

   3. log-lowering-log.f64 98.7%

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

5. Simplified 98.7%

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

6. Taylor expanded in z around inf

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

8. Simplified 63.5%

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

9. Taylor expanded in b around 0

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

    1. +-lowering-+.f64 51.5%

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

11. Simplified 51.5%

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

12. Final simplification 51.5%

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

Alternative 15: 21.7% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.55 \cdot 10^{+138}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 1.55e+138) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.55e+138) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.55d+138) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.55e+138) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.55e+138:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.55e+138)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.55e+138)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.55e+138], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 1.5499999999999999e138

   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 16.1%

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

   if 1.5499999999999999e138 < a

   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 a around inf

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

   5. Simplified 59.4%

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

Alternative 16: 16.1% 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 19.1%

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

Reproduce

herbie shell --seed 2024155 
(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)))