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

Percentage Accurate: 99.7% → 99.7%

Time: 17.5s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 91.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;i \leq -6.4:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + t\_1\right)\right)\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+39}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= i -6.4)
     (fma y i (+ a (+ t (+ z t_1))))
     (if (<= i 6e+39)
       (+ a (+ t (+ z (+ (* x (log y)) t_1))))
       (+ (* y i) (+ (* b (log c)) (+ a (+ z t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if (i <= -6.4) {
		tmp = fma(y, i, (a + (t + (z + t_1))));
	} else if (i <= 6e+39) {
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	} else {
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (i <= -6.4)
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + t_1))));
	elseif (i <= 6e+39)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.4], N[(y * i + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e+39], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.4000000000000004

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 93.8%

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

   if -6.4000000000000004 < i < 5.9999999999999999e39

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 97.5%

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

   if 5.9999999999999999e39 < i

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.1%

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

   4. Taylor expanded in b around inf 96.1%

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

      1. *-commutative 96.1%

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

   6. Simplified 96.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.4:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+39}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+158} \lor \neg \left(x \leq 3.25 \cdot 10^{+212}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5.4e+158) (not (<= x 3.25e+212)))
   (+ a (+ t (+ (* x (log y)) z)))
   (fma y i (+ a (+ t (+ z (* (- b 0.5) (log c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5.4e+158) || !(x <= 3.25e+212)) {
		tmp = a + (t + ((x * log(y)) + z));
	} else {
		tmp = fma(y, i, (a + (t + (z + ((b - 0.5) * log(c))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5.4e+158) || !(x <= 3.25e+212))
		tmp = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5.4e+158], N[Not[LessEqual[x, 3.25e+212]], $MachinePrecision]], N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999957e158 or 3.24999999999999999e212 < 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 y around 0 87.3%

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

   4. Taylor expanded in x around inf 81.3%

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

   if -5.39999999999999957e158 < x < 3.24999999999999999e212

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 95.5%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+158} \lor \neg \left(x \leq 3.25 \cdot 10^{+212}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((b * log(c)) + (a + (t + ((x * log(y)) + z))))
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) + ((b * Math.log(c)) + (a + (t + ((x * Math.log(y)) + z))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $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 98.7%

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

   1. *-commutative 85.4%

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

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%

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

Alternative 5: 82.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((b * log(c)) + (a + ((x * log(y)) + z)))
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) + ((b * Math.log(c)) + (a + ((x * Math.log(y)) + z)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $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 98.7%

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

   1. *-commutative 85.4%

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

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 t around 0 82.6%

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

7. Final simplification 82.6%

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

Alternative 6: 76.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b + -0.5\right)\\ t_2 := y \cdot i + \left(\left(a + \left(z + t\right)\right) + \log c \cdot -0.5\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + t\_1\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (+ b -0.5)))
        (t_2 (+ (* y i) (+ (+ a (+ z t)) (* (log c) -0.5)))))
   (if (<= b -2.8e+36)
     (+ (* y i) (+ (+ t a) t_1))
     (if (<= b 2.9e-162)
       t_2
       (if (<= b 2.1e-74)
         (+ a (+ t (+ (* x (log y)) z)))
         (if (<= b 2.4e-29) t_2 (+ 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 = log(c) * (b + -0.5);
	double t_2 = (y * i) + ((a + (z + t)) + (log(c) * -0.5));
	double tmp;
	if (b <= -2.8e+36) {
		tmp = (y * i) + ((t + a) + t_1);
	} else if (b <= 2.9e-162) {
		tmp = t_2;
	} else if (b <= 2.1e-74) {
		tmp = a + (t + ((x * log(y)) + z));
	} else if (b <= 2.4e-29) {
		tmp = t_2;
	} else {
		tmp = a + ((z + t) + 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) :: t_2
    real(8) :: tmp
    t_1 = log(c) * (b + (-0.5d0))
    t_2 = (y * i) + ((a + (z + t)) + (log(c) * (-0.5d0)))
    if (b <= (-2.8d+36)) then
        tmp = (y * i) + ((t + a) + t_1)
    else if (b <= 2.9d-162) then
        tmp = t_2
    else if (b <= 2.1d-74) then
        tmp = a + (t + ((x * log(y)) + z))
    else if (b <= 2.4d-29) then
        tmp = t_2
    else
        tmp = a + ((z + t) + 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 = Math.log(c) * (b + -0.5);
	double t_2 = (y * i) + ((a + (z + t)) + (Math.log(c) * -0.5));
	double tmp;
	if (b <= -2.8e+36) {
		tmp = (y * i) + ((t + a) + t_1);
	} else if (b <= 2.9e-162) {
		tmp = t_2;
	} else if (b <= 2.1e-74) {
		tmp = a + (t + ((x * Math.log(y)) + z));
	} else if (b <= 2.4e-29) {
		tmp = t_2;
	} else {
		tmp = a + ((z + t) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b + -0.5)
	t_2 = (y * i) + ((a + (z + t)) + (math.log(c) * -0.5))
	tmp = 0
	if b <= -2.8e+36:
		tmp = (y * i) + ((t + a) + t_1)
	elif b <= 2.9e-162:
		tmp = t_2
	elif b <= 2.1e-74:
		tmp = a + (t + ((x * math.log(y)) + z))
	elif b <= 2.4e-29:
		tmp = t_2
	else:
		tmp = a + ((z + t) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b + -0.5))
	t_2 = Float64(Float64(y * i) + Float64(Float64(a + Float64(z + t)) + Float64(log(c) * -0.5)))
	tmp = 0.0
	if (b <= -2.8e+36)
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + t_1));
	elseif (b <= 2.9e-162)
		tmp = t_2;
	elseif (b <= 2.1e-74)
		tmp = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)));
	elseif (b <= 2.4e-29)
		tmp = t_2;
	else
		tmp = Float64(a + Float64(Float64(z + t) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b + -0.5);
	t_2 = (y * i) + ((a + (z + t)) + (log(c) * -0.5));
	tmp = 0.0;
	if (b <= -2.8e+36)
		tmp = (y * i) + ((t + a) + t_1);
	elseif (b <= 2.9e-162)
		tmp = t_2;
	elseif (b <= 2.1e-74)
		tmp = a + (t + ((x * log(y)) + z));
	elseif (b <= 2.4e-29)
		tmp = t_2;
	else
		tmp = a + ((z + t) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+36], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e-162], t$95$2, If[LessEqual[b, 2.1e-74], N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-29], t$95$2, N[(a + N[(N[(z + t), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.8000000000000001e36

   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 0 92.5%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. associate-+r+ 83.4%

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

      2. sub-neg 83.4%

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

      3. metadata-eval 83.4%

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

   6. Simplified 83.4%

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

   if -2.8000000000000001e36 < b < 2.9000000000000001e-162 or 2.1e-74 < b < 2.39999999999999992e-29

   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 85.4%

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

   4. Taylor expanded in b around 0 84.6%

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

   if 2.9000000000000001e-162 < b < 2.1e-74

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.9%

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

   4. Taylor expanded in x around inf 88.9%

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

   if 2.39999999999999992e-29 < b

   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 92.2%

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

      1. add-cbrt-cube 38.6%

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

      2. pow3 38.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{\color{blue}{{\left(\left(b - 0.5\right) \cdot \log c\right)}^{3}}}\right) + y \cdot i \]

      3. sub-neg 38.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      4. metadata-eval 38.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\left(b + \color{blue}{-0.5}\right) \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 38.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\color{blue}{\left(\log c \cdot \left(b + -0.5\right)\right)}}^{3}}\right) + y \cdot i \]

   5. Applied egg-rr 38.6%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{\sqrt[3]{{\left(\log c \cdot \left(b + -0.5\right)\right)}^{3}}}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 83.6%

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

      1. associate-+r+ 83.6%

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

      2. sub-neg 83.6%

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

      3. metadata-eval 83.6%

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

      4. +-commutative 83.6%

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

   8. Simplified 83.6%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-162}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + \log c \cdot -0.5\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-29}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + \log c \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ t_2 := a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-123}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ (+ z t) (* (log c) (+ b -0.5)))))
        (t_2 (+ a (+ t (+ (* x (log y)) z)))))
   (if (<= x -9.2e+70)
     t_2
     (if (<= x -2.9e-6)
       t_1
       (if (<= x -8.8e-123) (+ a (* y i)) (if (<= x 2e+70) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + ((z + t) + (log(c) * (b + -0.5)));
	double t_2 = a + (t + ((x * log(y)) + z));
	double tmp;
	if (x <= -9.2e+70) {
		tmp = t_2;
	} else if (x <= -2.9e-6) {
		tmp = t_1;
	} else if (x <= -8.8e-123) {
		tmp = a + (y * i);
	} else if (x <= 2e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + ((z + t) + (log(c) * (b + (-0.5d0))))
    t_2 = a + (t + ((x * log(y)) + z))
    if (x <= (-9.2d+70)) then
        tmp = t_2
    else if (x <= (-2.9d-6)) then
        tmp = t_1
    else if (x <= (-8.8d-123)) then
        tmp = a + (y * i)
    else if (x <= 2d+70) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + ((z + t) + (Math.log(c) * (b + -0.5)));
	double t_2 = a + (t + ((x * Math.log(y)) + z));
	double tmp;
	if (x <= -9.2e+70) {
		tmp = t_2;
	} else if (x <= -2.9e-6) {
		tmp = t_1;
	} else if (x <= -8.8e-123) {
		tmp = a + (y * i);
	} else if (x <= 2e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + ((z + t) + (math.log(c) * (b + -0.5)))
	t_2 = a + (t + ((x * math.log(y)) + z))
	tmp = 0
	if x <= -9.2e+70:
		tmp = t_2
	elif x <= -2.9e-6:
		tmp = t_1
	elif x <= -8.8e-123:
		tmp = a + (y * i)
	elif x <= 2e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5))))
	t_2 = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)))
	tmp = 0.0
	if (x <= -9.2e+70)
		tmp = t_2;
	elseif (x <= -2.9e-6)
		tmp = t_1;
	elseif (x <= -8.8e-123)
		tmp = Float64(a + Float64(y * i));
	elseif (x <= 2e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + ((z + t) + (log(c) * (b + -0.5)));
	t_2 = a + (t + ((x * log(y)) + z));
	tmp = 0.0;
	if (x <= -9.2e+70)
		tmp = t_2;
	elseif (x <= -2.9e-6)
		tmp = t_1;
	elseif (x <= -8.8e-123)
		tmp = a + (y * i);
	elseif (x <= 2e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e+70], t$95$2, If[LessEqual[x, -2.9e-6], t$95$1, If[LessEqual[x, -8.8e-123], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+70], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.19999999999999975e70 or 2.00000000000000015e70 < 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 y around 0 79.8%

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

   4. Taylor expanded in x around inf 69.9%

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

   if -9.19999999999999975e70 < x < -2.9000000000000002e-6 or -8.80000000000000025e-123 < x < 2.00000000000000015e70

   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 99.4%

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

      1. add-cbrt-cube 68.0%

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

      2. pow3 68.0%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{\color{blue}{{\left(\left(b - 0.5\right) \cdot \log c\right)}^{3}}}\right) + y \cdot i \]

      3. sub-neg 68.0%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      4. metadata-eval 68.0%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\left(b + \color{blue}{-0.5}\right) \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 68.0%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\color{blue}{\left(\log c \cdot \left(b + -0.5\right)\right)}}^{3}}\right) + y \cdot i \]

   5. Applied egg-rr 68.0%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{\sqrt[3]{{\left(\log c \cdot \left(b + -0.5\right)\right)}^{3}}}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 86.1%

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

      1. associate-+r+ 86.1%

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

      2. sub-neg 86.1%

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

      3. metadata-eval 86.1%

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

      4. +-commutative 86.1%

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

   8. Simplified 86.1%

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

   if -2.9000000000000002e-6 < x < -8.80000000000000025e-123

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in a around inf 64.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+70}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-123}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+70}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ t_2 := a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-123}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \log c \cdot -0.5\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ (+ z t) (* (log c) (+ b -0.5)))))
        (t_2 (+ a (+ t (+ (* x (log y)) z)))))
   (if (<= x -3.3e+70)
     t_2
     (if (<= x -2.9e-6)
       t_1
       (if (<= x -8.8e-123)
         (+ (* y i) (+ a (+ t (* (log c) -0.5))))
         (if (<= x 6.2e+70) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + ((z + t) + (log(c) * (b + -0.5)));
	double t_2 = a + (t + ((x * log(y)) + z));
	double tmp;
	if (x <= -3.3e+70) {
		tmp = t_2;
	} else if (x <= -2.9e-6) {
		tmp = t_1;
	} else if (x <= -8.8e-123) {
		tmp = (y * i) + (a + (t + (log(c) * -0.5)));
	} else if (x <= 6.2e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + ((z + t) + (log(c) * (b + (-0.5d0))))
    t_2 = a + (t + ((x * log(y)) + z))
    if (x <= (-3.3d+70)) then
        tmp = t_2
    else if (x <= (-2.9d-6)) then
        tmp = t_1
    else if (x <= (-8.8d-123)) then
        tmp = (y * i) + (a + (t + (log(c) * (-0.5d0))))
    else if (x <= 6.2d+70) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + ((z + t) + (Math.log(c) * (b + -0.5)));
	double t_2 = a + (t + ((x * Math.log(y)) + z));
	double tmp;
	if (x <= -3.3e+70) {
		tmp = t_2;
	} else if (x <= -2.9e-6) {
		tmp = t_1;
	} else if (x <= -8.8e-123) {
		tmp = (y * i) + (a + (t + (Math.log(c) * -0.5)));
	} else if (x <= 6.2e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + ((z + t) + (math.log(c) * (b + -0.5)))
	t_2 = a + (t + ((x * math.log(y)) + z))
	tmp = 0
	if x <= -3.3e+70:
		tmp = t_2
	elif x <= -2.9e-6:
		tmp = t_1
	elif x <= -8.8e-123:
		tmp = (y * i) + (a + (t + (math.log(c) * -0.5)))
	elif x <= 6.2e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5))))
	t_2 = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)))
	tmp = 0.0
	if (x <= -3.3e+70)
		tmp = t_2;
	elseif (x <= -2.9e-6)
		tmp = t_1;
	elseif (x <= -8.8e-123)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(log(c) * -0.5))));
	elseif (x <= 6.2e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + ((z + t) + (log(c) * (b + -0.5)));
	t_2 = a + (t + ((x * log(y)) + z));
	tmp = 0.0;
	if (x <= -3.3e+70)
		tmp = t_2;
	elseif (x <= -2.9e-6)
		tmp = t_1;
	elseif (x <= -8.8e-123)
		tmp = (y * i) + (a + (t + (log(c) * -0.5)));
	elseif (x <= 6.2e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+70], t$95$2, If[LessEqual[x, -2.9e-6], t$95$1, If[LessEqual[x, -8.8e-123], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+70], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.30000000000000016e70 or 6.2000000000000006e70 < 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 y around 0 79.8%

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

   4. Taylor expanded in x around inf 69.9%

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

   if -3.30000000000000016e70 < x < -2.9000000000000002e-6 or -8.80000000000000025e-123 < x < 6.2000000000000006e70

   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 99.4%

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

      1. add-cbrt-cube 68.0%

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

      2. pow3 68.0%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{\color{blue}{{\left(\left(b - 0.5\right) \cdot \log c\right)}^{3}}}\right) + y \cdot i \]

      3. sub-neg 68.0%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      4. metadata-eval 68.0%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\left(b + \color{blue}{-0.5}\right) \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 68.0%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\color{blue}{\left(\log c \cdot \left(b + -0.5\right)\right)}}^{3}}\right) + y \cdot i \]

   5. Applied egg-rr 68.0%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{\sqrt[3]{{\left(\log c \cdot \left(b + -0.5\right)\right)}^{3}}}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 86.1%

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

      1. associate-+r+ 86.1%

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

      2. sub-neg 86.1%

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

      3. metadata-eval 86.1%

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

      4. +-commutative 86.1%

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

   8. Simplified 86.1%

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

   if -2.9000000000000002e-6 < x < -8.80000000000000025e-123

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in b around 0 89.0%

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

   5. Taylor expanded in z around 0 88.6%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+70}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-123}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \log c \cdot -0.5\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+70}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b + -0.5\right)\\ t_2 := y \cdot i + \left(\log c \cdot -0.5 + \left(z + a\right)\right)\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + t\_1\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-72}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (+ b -0.5)))
        (t_2 (+ (* y i) (+ (* (log c) -0.5) (+ z a)))))
   (if (<= b -3.5e+36)
     (+ (* y i) (+ (+ t a) t_1))
     (if (<= b 8.5e-162)
       t_2
       (if (<= b 2.6e-72)
         (+ a (+ t (+ (* x (log y)) z)))
         (if (<= b 2.4e-29) t_2 (+ 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 = log(c) * (b + -0.5);
	double t_2 = (y * i) + ((log(c) * -0.5) + (z + a));
	double tmp;
	if (b <= -3.5e+36) {
		tmp = (y * i) + ((t + a) + t_1);
	} else if (b <= 8.5e-162) {
		tmp = t_2;
	} else if (b <= 2.6e-72) {
		tmp = a + (t + ((x * log(y)) + z));
	} else if (b <= 2.4e-29) {
		tmp = t_2;
	} else {
		tmp = a + ((z + t) + 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) :: t_2
    real(8) :: tmp
    t_1 = log(c) * (b + (-0.5d0))
    t_2 = (y * i) + ((log(c) * (-0.5d0)) + (z + a))
    if (b <= (-3.5d+36)) then
        tmp = (y * i) + ((t + a) + t_1)
    else if (b <= 8.5d-162) then
        tmp = t_2
    else if (b <= 2.6d-72) then
        tmp = a + (t + ((x * log(y)) + z))
    else if (b <= 2.4d-29) then
        tmp = t_2
    else
        tmp = a + ((z + t) + 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 = Math.log(c) * (b + -0.5);
	double t_2 = (y * i) + ((Math.log(c) * -0.5) + (z + a));
	double tmp;
	if (b <= -3.5e+36) {
		tmp = (y * i) + ((t + a) + t_1);
	} else if (b <= 8.5e-162) {
		tmp = t_2;
	} else if (b <= 2.6e-72) {
		tmp = a + (t + ((x * Math.log(y)) + z));
	} else if (b <= 2.4e-29) {
		tmp = t_2;
	} else {
		tmp = a + ((z + t) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b + -0.5)
	t_2 = (y * i) + ((math.log(c) * -0.5) + (z + a))
	tmp = 0
	if b <= -3.5e+36:
		tmp = (y * i) + ((t + a) + t_1)
	elif b <= 8.5e-162:
		tmp = t_2
	elif b <= 2.6e-72:
		tmp = a + (t + ((x * math.log(y)) + z))
	elif b <= 2.4e-29:
		tmp = t_2
	else:
		tmp = a + ((z + t) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b + -0.5))
	t_2 = Float64(Float64(y * i) + Float64(Float64(log(c) * -0.5) + Float64(z + a)))
	tmp = 0.0
	if (b <= -3.5e+36)
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + t_1));
	elseif (b <= 8.5e-162)
		tmp = t_2;
	elseif (b <= 2.6e-72)
		tmp = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)));
	elseif (b <= 2.4e-29)
		tmp = t_2;
	else
		tmp = Float64(a + Float64(Float64(z + t) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b + -0.5);
	t_2 = (y * i) + ((log(c) * -0.5) + (z + a));
	tmp = 0.0;
	if (b <= -3.5e+36)
		tmp = (y * i) + ((t + a) + t_1);
	elseif (b <= 8.5e-162)
		tmp = t_2;
	elseif (b <= 2.6e-72)
		tmp = a + (t + ((x * log(y)) + z));
	elseif (b <= 2.4e-29)
		tmp = t_2;
	else
		tmp = a + ((z + t) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e+36], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-162], t$95$2, If[LessEqual[b, 2.6e-72], N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-29], t$95$2, N[(a + N[(N[(z + t), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.4999999999999998e36

   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 0 92.5%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. associate-+r+ 83.4%

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

      2. sub-neg 83.4%

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

      3. metadata-eval 83.4%

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

   6. Simplified 83.4%

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

   if -3.4999999999999998e36 < b < 8.49999999999999955e-162 or 2.59999999999999996e-72 < b < 2.39999999999999992e-29

   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 85.4%

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

   4. Taylor expanded in b around 0 84.6%

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

   5. Taylor expanded in t around 0 66.8%

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

      1. associate-+r+ 66.8%

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

   7. Simplified 66.8%

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

   if 8.49999999999999955e-162 < b < 2.59999999999999996e-72

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.9%

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

   4. Taylor expanded in x around inf 88.9%

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

   if 2.39999999999999992e-29 < b

   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 92.2%

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

      1. add-cbrt-cube 38.6%

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

      2. pow3 38.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{\color{blue}{{\left(\left(b - 0.5\right) \cdot \log c\right)}^{3}}}\right) + y \cdot i \]

      3. sub-neg 38.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      4. metadata-eval 38.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\left(b + \color{blue}{-0.5}\right) \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 38.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\color{blue}{\left(\log c \cdot \left(b + -0.5\right)\right)}}^{3}}\right) + y \cdot i \]

   5. Applied egg-rr 38.6%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{\sqrt[3]{{\left(\log c \cdot \left(b + -0.5\right)\right)}^{3}}}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 83.6%

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

      1. associate-+r+ 83.6%

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

      2. sub-neg 83.6%

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

      3. metadata-eval 83.6%

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

      4. +-commutative 83.6%

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

   8. Simplified 83.6%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot -0.5 + \left(z + a\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-72}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-29}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot -0.5 + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(x \cdot \log y + z\right)\right)\\ t_2 := y \cdot i + b \cdot \log c\\ \mathbf{if}\;b \leq -9 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-225}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ (* x (log y)) z)))) (t_2 (+ (* y i) (* b (log c)))))
   (if (<= b -9e+70)
     t_2
     (if (<= b -6.6e-289)
       t_1
       (if (<= b 2.8e-225) (+ a (* y i)) (if (<= b 1.6e+196) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + ((x * log(y)) + z));
	double t_2 = (y * i) + (b * log(c));
	double tmp;
	if (b <= -9e+70) {
		tmp = t_2;
	} else if (b <= -6.6e-289) {
		tmp = t_1;
	} else if (b <= 2.8e-225) {
		tmp = a + (y * i);
	} else if (b <= 1.6e+196) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (t + ((x * log(y)) + z))
    t_2 = (y * i) + (b * log(c))
    if (b <= (-9d+70)) then
        tmp = t_2
    else if (b <= (-6.6d-289)) then
        tmp = t_1
    else if (b <= 2.8d-225) then
        tmp = a + (y * i)
    else if (b <= 1.6d+196) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + ((x * Math.log(y)) + z));
	double t_2 = (y * i) + (b * Math.log(c));
	double tmp;
	if (b <= -9e+70) {
		tmp = t_2;
	} else if (b <= -6.6e-289) {
		tmp = t_1;
	} else if (b <= 2.8e-225) {
		tmp = a + (y * i);
	} else if (b <= 1.6e+196) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + ((x * math.log(y)) + z))
	t_2 = (y * i) + (b * math.log(c))
	tmp = 0
	if b <= -9e+70:
		tmp = t_2
	elif b <= -6.6e-289:
		tmp = t_1
	elif b <= 2.8e-225:
		tmp = a + (y * i)
	elif b <= 1.6e+196:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)))
	t_2 = Float64(Float64(y * i) + Float64(b * log(c)))
	tmp = 0.0
	if (b <= -9e+70)
		tmp = t_2;
	elseif (b <= -6.6e-289)
		tmp = t_1;
	elseif (b <= 2.8e-225)
		tmp = Float64(a + Float64(y * i));
	elseif (b <= 1.6e+196)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + ((x * log(y)) + z));
	t_2 = (y * i) + (b * log(c));
	tmp = 0.0;
	if (b <= -9e+70)
		tmp = t_2;
	elseif (b <= -6.6e-289)
		tmp = t_1;
	elseif (b <= 2.8e-225)
		tmp = a + (y * i);
	elseif (b <= 1.6e+196)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+70], t$95$2, If[LessEqual[b, -6.6e-289], t$95$1, If[LessEqual[b, 2.8e-225], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+196], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999999e70 or 1.59999999999999996e196 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 95.6%

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

   4. Taylor expanded in b around inf 74.0%

      \[\leadsto \color{blue}{b \cdot \log c} + y \cdot i \]
   5. Step-by-step derivation

      1. *-commutative 74.0%

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

   6. Simplified 74.0%

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

   if -8.9999999999999999e70 < b < -6.59999999999999994e-289 or 2.8e-225 < b < 1.59999999999999996e196

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 85.7%

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

   4. Taylor expanded in x around inf 79.7%

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

   if -6.59999999999999994e-289 < b < 2.8e-225

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.8%

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

   4. Taylor expanded in a around inf 67.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+70}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-289}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-225}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+196}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 90.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+159} \lor \neg \left(x \leq 2.3 \cdot 10^{+212}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -8e+159) (not (<= x 2.3e+212)))
   (+ a (+ t (+ (* x (log y)) z)))
   (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8e+159) || !(x <= 2.3e+212)) {
		tmp = a + (t + ((x * log(y)) + z));
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	}
	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+159)) .or. (.not. (x <= 2.3d+212))) then
        tmp = a + (t + ((x * log(y)) + z))
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (z + t)))
    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+159) || !(x <= 2.3e+212)) {
		tmp = a + (t + ((x * Math.log(y)) + z));
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -8e+159) or not (x <= 2.3e+212):
		tmp = a + (t + ((x * math.log(y)) + z))
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -8e+159) || !(x <= 2.3e+212))
		tmp = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -8e+159) || ~((x <= 2.3e+212)))
		tmp = a + (t + ((x * log(y)) + z));
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -8e+159], N[Not[LessEqual[x, 2.3e+212]], $MachinePrecision]], N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if x < -7.9999999999999994e159 or 2.2999999999999998e212 < 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 y around 0 87.3%

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

   4. Taylor expanded in x around inf 81.3%

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

   if -7.9999999999999994e159 < x < 2.2999999999999998e212

   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 95.5%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+159} \lor \neg \left(x \leq 2.3 \cdot 10^{+212}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+164} \lor \neg \left(x \leq 2.85 \cdot 10^{+212}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.1e+164) (not (<= x 2.85e+212)))
   (+ a (+ t (+ (* x (log y)) z)))
   (+ (* y i) (+ (* b (log c)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.1e+164) || !(x <= 2.85e+212)) {
		tmp = a + (t + ((x * log(y)) + z));
	} else {
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	}
	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 <= (-1.1d+164)) .or. (.not. (x <= 2.85d+212))) then
        tmp = a + (t + ((x * log(y)) + z))
    else
        tmp = (y * i) + ((b * log(c)) + (a + (z + t)))
    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 <= -1.1e+164) || !(x <= 2.85e+212)) {
		tmp = a + (t + ((x * Math.log(y)) + z));
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.1e+164) or not (x <= 2.85e+212):
		tmp = a + (t + ((x * math.log(y)) + z))
	else:
		tmp = (y * i) + ((b * math.log(c)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.1e+164) || !(x <= 2.85e+212))
		tmp = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.1e+164) || ~((x <= 2.85e+212)))
		tmp = a + (t + ((x * log(y)) + z));
	else
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.1e+164], N[Not[LessEqual[x, 2.85e+212]], $MachinePrecision]], N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.10000000000000003e164 or 2.8500000000000001e212 < 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 y around 0 87.3%

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

   4. Taylor expanded in x around inf 81.3%

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

   if -1.10000000000000003e164 < x < 2.8500000000000001e212

   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 95.5%

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

   4. Taylor expanded in b around inf 94.0%

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

      1. *-commutative 94.0%

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

   6. Simplified 94.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+164} \lor \neg \left(x \leq 2.85 \cdot 10^{+212}\right):\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+70}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot -0.5 + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 4.8e+40)
   (+ a (+ (+ z t) (* (log c) (+ b -0.5))))
   (if (<= y 8e+70)
     (+ a (+ t (+ (* x (log y)) z)))
     (+ (* y i) (+ (* (log c) -0.5) (+ z a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.8e+40) {
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	} else if (y <= 8e+70) {
		tmp = a + (t + ((x * log(y)) + z));
	} else {
		tmp = (y * i) + ((log(c) * -0.5) + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 4.8d+40) then
        tmp = a + ((z + t) + (log(c) * (b + (-0.5d0))))
    else if (y <= 8d+70) then
        tmp = a + (t + ((x * log(y)) + z))
    else
        tmp = (y * i) + ((log(c) * (-0.5d0)) + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.8e+40) {
		tmp = a + ((z + t) + (Math.log(c) * (b + -0.5)));
	} else if (y <= 8e+70) {
		tmp = a + (t + ((x * Math.log(y)) + z));
	} else {
		tmp = (y * i) + ((Math.log(c) * -0.5) + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 4.8e+40:
		tmp = a + ((z + t) + (math.log(c) * (b + -0.5)))
	elif y <= 8e+70:
		tmp = a + (t + ((x * math.log(y)) + z))
	else:
		tmp = (y * i) + ((math.log(c) * -0.5) + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 4.8e+40)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5))));
	elseif (y <= 8e+70)
		tmp = Float64(a + Float64(t + Float64(Float64(x * log(y)) + z)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * -0.5) + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 4.8e+40)
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	elseif (y <= 8e+70)
		tmp = a + (t + ((x * log(y)) + z));
	else
		tmp = (y * i) + ((log(c) * -0.5) + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 4.8e+40], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+70], N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 4.8e40

   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 0 88.2%

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

      1. add-cbrt-cube 58.3%

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

      2. pow3 58.3%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{\color{blue}{{\left(\left(b - 0.5\right) \cdot \log c\right)}^{3}}}\right) + y \cdot i \]

      3. sub-neg 58.3%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      4. metadata-eval 58.3%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\left(\left(b + \color{blue}{-0.5}\right) \cdot \log c\right)}^{3}}\right) + y \cdot i \]

      5. *-commutative 58.3%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \sqrt[3]{{\color{blue}{\left(\log c \cdot \left(b + -0.5\right)\right)}}^{3}}\right) + y \cdot i \]

   5. Applied egg-rr 58.3%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{\sqrt[3]{{\left(\log c \cdot \left(b + -0.5\right)\right)}^{3}}}\right) + y \cdot i \]

   6. Taylor expanded in y around 0 82.9%

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

      1. associate-+r+ 82.9%

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

      2. sub-neg 82.9%

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

      3. metadata-eval 82.9%

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

      4. +-commutative 82.9%

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

   8. Simplified 82.9%

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

   if 4.8e40 < y < 8.00000000000000058e70

   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 y around 0 99.6%

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

   4. Taylor expanded in x around inf 92.6%

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

   if 8.00000000000000058e70 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 88.7%

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

   4. Taylor expanded in b around 0 73.0%

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

   5. Taylor expanded in t around 0 64.9%

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

      1. associate-+r+ 64.9%

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

   7. Simplified 64.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+70}:\\ \;\;\;\;a + \left(t + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot -0.5 + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq 2 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-121}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y i))))
   (if (<= a 2e-143)
     t_1
     (if (<= a 2.5e-121)
       (+ (* y i) (* b (log c)))
       (if (<= a 6e+128) t_1 (+ a (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= 2e-143) {
		tmp = t_1;
	} else if (a <= 2.5e-121) {
		tmp = (y * i) + (b * log(c));
	} else if (a <= 6e+128) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z + (y * i)
    if (a <= 2d-143) then
        tmp = t_1
    else if (a <= 2.5d-121) then
        tmp = (y * i) + (b * log(c))
    else if (a <= 6d+128) then
        tmp = t_1
    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 t_1 = z + (y * i);
	double tmp;
	if (a <= 2e-143) {
		tmp = t_1;
	} else if (a <= 2.5e-121) {
		tmp = (y * i) + (b * Math.log(c));
	} else if (a <= 6e+128) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= 2e-143:
		tmp = t_1
	elif a <= 2.5e-121:
		tmp = (y * i) + (b * math.log(c))
	elif a <= 6e+128:
		tmp = t_1
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 2e-143)
		tmp = t_1;
	elseif (a <= 2.5e-121)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	elseif (a <= 6e+128)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= 2e-143)
		tmp = t_1;
	elseif (a <= 2.5e-121)
		tmp = (y * i) + (b * log(c));
	elseif (a <= 6e+128)
		tmp = t_1;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 2e-143], t$95$1, If[LessEqual[a, 2.5e-121], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+128], t$95$1, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.9999999999999999e-143 or 2.49999999999999995e-121 < a < 5.9999999999999997e128

   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 0 86.4%

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

   4. Taylor expanded in z around inf 35.3%

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

   if 1.9999999999999999e-143 < a < 2.49999999999999995e-121

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.2%

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

   4. Taylor expanded in b around inf 56.1%

      \[\leadsto \color{blue}{b \cdot \log c} + y \cdot i \]
   5. Step-by-step derivation

      1. *-commutative 56.1%

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

   6. Simplified 56.1%

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

   if 5.9999999999999997e128 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.9%

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

   4. Taylor expanded in a around inf 74.0%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-143}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-121}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+128}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.1% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+133} \lor \neg \left(z \leq -4 \cdot 10^{+99}\right) \land z \leq -1.95 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -4.8e+133) (and (not (<= z -4e+99)) (<= z -1.95e+76)))
   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 <= -4.8e+133) || (!(z <= -4e+99) && (z <= -1.95e+76))) {
		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 <= (-4.8d+133)) .or. (.not. (z <= (-4d+99))) .and. (z <= (-1.95d+76))) 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 <= -4.8e+133) || (!(z <= -4e+99) && (z <= -1.95e+76))) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -4.8e+133) or (not (z <= -4e+99) and (z <= -1.95e+76)):
		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 <= -4.8e+133) || (!(z <= -4e+99) && (z <= -1.95e+76)))
		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 <= -4.8e+133) || (~((z <= -4e+99)) && (z <= -1.95e+76)))
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -4.8e+133], And[N[Not[LessEqual[z, -4e+99]], $MachinePrecision], LessEqual[z, -1.95e+76]]], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7999999999999997e133 or -3.9999999999999999e99 < z < -1.94999999999999995e76

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.8%

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

   4. Taylor expanded in z around inf 39.7%

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

   if -4.7999999999999997e133 < z < -3.9999999999999999e99 or -1.94999999999999995e76 < z

   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 0 85.3%

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

   4. Taylor expanded in a around inf 38.6%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+133} \lor \neg \left(z \leq -4 \cdot 10^{+99}\right) \land z \leq -1.95 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.5% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-176}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-271}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+119}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -2.3e-176) z (if (<= a 4.7e-271) (* y i) (if (<= a 3.4e+119) 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 <= -2.3e-176) {
		tmp = z;
	} else if (a <= 4.7e-271) {
		tmp = y * i;
	} else if (a <= 3.4e+119) {
		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 <= (-2.3d-176)) then
        tmp = z
    else if (a <= 4.7d-271) then
        tmp = y * i
    else if (a <= 3.4d+119) 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 <= -2.3e-176) {
		tmp = z;
	} else if (a <= 4.7e-271) {
		tmp = y * i;
	} else if (a <= 3.4e+119) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -2.3e-176:
		tmp = z
	elif a <= 4.7e-271:
		tmp = y * i
	elif a <= 3.4e+119:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -2.3e-176)
		tmp = z;
	elseif (a <= 4.7e-271)
		tmp = Float64(y * i);
	elseif (a <= 3.4e+119)
		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 <= -2.3e-176)
		tmp = z;
	elseif (a <= 4.7e-271)
		tmp = y * i;
	elseif (a <= 3.4e+119)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -2.3e-176], z, If[LessEqual[a, 4.7e-271], N[(y * i), $MachinePrecision], If[LessEqual[a, 3.4e+119], z, a]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.3000000000000001e-176 or 4.70000000000000005e-271 < a < 3.40000000000000013e119

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 81.0%

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

   4. Taylor expanded in z around inf 17.7%

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

   if -2.3000000000000001e-176 < a < 4.70000000000000005e-271

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 20.6%

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

      1. *-commutative 20.6%

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

   5. Simplified 20.6%

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

   if 3.40000000000000013e119 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 60.6%

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

4. Final simplification 24.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-176}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-271}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+119}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.1% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{+125}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 4.2e+125) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.2e+125) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 4.2d+125) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.2e+125) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.2e+125:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.2e+125)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4.2e+125)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.2e+125], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.2000000000000001e125

   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 0 86.2%

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

   4. Taylor expanded in z around inf 34.8%

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

   if 4.2000000000000001e125 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.2%

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

   4. Taylor expanded in a around inf 72.1%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{+125}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.0% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.05 \cdot 10^{+119}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 2.05e+119) 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 <= 2.05e+119) {
		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 <= 2.05d+119) 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 <= 2.05e+119) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.05e+119:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.05e+119)
		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 <= 2.05e+119)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.05e+119], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 2.0499999999999999e119

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 81.2%

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

   4. Taylor expanded in z around inf 17.3%

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

   if 2.0499999999999999e119 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 60.6%

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

4. Final simplification 23.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.05 \cdot 10^{+119}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 16.2% 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 20.4%

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

4. Final simplification 20.4%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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)))