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

Percentage Accurate: 99.8% → 99.8%

Time: 17.0s

Alternatives: 20

Speedup: 1.0×

• could not determine a ground truth

  1. x = 5.105191254699662e-158
  2. y = 8.59256294854796e+193
  3. z = 6.021414582480887e+221
  4. t = -6.805403172819944e+47
  5. a = -5.935235657944822e+220
  6. b = -4.574387217702579e+186
  7. c = 8.210795066881564e+88
  8. i = 2.634216251038164e-254

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(y * i + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(z + N[(x * N[Log[y], $MachinePrecision] + N[(t + a), $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. 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. Final simplification 99.9%

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

Alternative 2: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := b \cdot \log c\\ t_3 := y \cdot i + \left(t\_1 + t\_2\right)\\ t_4 := a + \left(z + t\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+230}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+114}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + t\_4\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+160}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+243}:\\ \;\;\;\;y \cdot i + \left(t\_2 + t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y)))
        (t_2 (* b (log c)))
        (t_3 (+ (* y i) (+ t_1 t_2)))
        (t_4 (+ a (+ z t))))
   (if (<= x -1.45e+230)
     t_3
     (if (<= x 1.12e+114)
       (+ (* y i) (+ (* (log c) (- b 0.5)) t_4))
       (if (<= x 2.25e+160)
         t_3
         (if (<= x 1.8e+243)
           (+ (* y i) (+ t_2 t_4))
           (+ (* y i) (+ a t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double t_2 = b * log(c);
	double t_3 = (y * i) + (t_1 + t_2);
	double t_4 = a + (z + t);
	double tmp;
	if (x <= -1.45e+230) {
		tmp = t_3;
	} else if (x <= 1.12e+114) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + t_4);
	} else if (x <= 2.25e+160) {
		tmp = t_3;
	} else if (x <= 1.8e+243) {
		tmp = (y * i) + (t_2 + t_4);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = b * log(c)
    t_3 = (y * i) + (t_1 + t_2)
    t_4 = a + (z + t)
    if (x <= (-1.45d+230)) then
        tmp = t_3
    else if (x <= 1.12d+114) then
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + t_4)
    else if (x <= 2.25d+160) then
        tmp = t_3
    else if (x <= 1.8d+243) then
        tmp = (y * i) + (t_2 + t_4)
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double t_2 = b * Math.log(c);
	double t_3 = (y * i) + (t_1 + t_2);
	double t_4 = a + (z + t);
	double tmp;
	if (x <= -1.45e+230) {
		tmp = t_3;
	} else if (x <= 1.12e+114) {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + t_4);
	} else if (x <= 2.25e+160) {
		tmp = t_3;
	} else if (x <= 1.8e+243) {
		tmp = (y * i) + (t_2 + t_4);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = b * math.log(c)
	t_3 = (y * i) + (t_1 + t_2)
	t_4 = a + (z + t)
	tmp = 0
	if x <= -1.45e+230:
		tmp = t_3
	elif x <= 1.12e+114:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + t_4)
	elif x <= 2.25e+160:
		tmp = t_3
	elif x <= 1.8e+243:
		tmp = (y * i) + (t_2 + t_4)
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(b * log(c))
	t_3 = Float64(Float64(y * i) + Float64(t_1 + t_2))
	t_4 = Float64(a + Float64(z + t))
	tmp = 0.0
	if (x <= -1.45e+230)
		tmp = t_3;
	elseif (x <= 1.12e+114)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + t_4));
	elseif (x <= 2.25e+160)
		tmp = t_3;
	elseif (x <= 1.8e+243)
		tmp = Float64(Float64(y * i) + Float64(t_2 + t_4));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = b * log(c);
	t_3 = (y * i) + (t_1 + t_2);
	t_4 = a + (z + t);
	tmp = 0.0;
	if (x <= -1.45e+230)
		tmp = t_3;
	elseif (x <= 1.12e+114)
		tmp = (y * i) + ((log(c) * (b - 0.5)) + t_4);
	elseif (x <= 2.25e+160)
		tmp = t_3;
	elseif (x <= 1.8e+243)
		tmp = (y * i) + (t_2 + t_4);
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+230], t$95$3, If[LessEqual[x, 1.12e+114], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e+160], t$95$3, If[LessEqual[x, 1.8e+243], N[(N[(y * i), $MachinePrecision] + N[(t$95$2 + t$95$4), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.45e230 or 1.11999999999999999e114 < x < 2.2499999999999999e160

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 95.5%

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

   7. Taylor expanded in a around 0 95.7%

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

   if -1.45e230 < x < 1.11999999999999999e114

   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 97.5%

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

   if 2.2499999999999999e160 < x < 1.7999999999999998e243

   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 89.9%

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

   4. Taylor expanded in b around inf 89.9%

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

      1. *-commutative 99.8%

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

   6. Simplified 89.9%

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

   if 1.7999999999999998e243 < x

   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 b around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 90.7%

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

   7. Taylor expanded in b around 0 90.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+230}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+114}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+160}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+243}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+199}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + t\_2\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(t\_2 + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (* x (log y))))
   (if (<= x -1.2e+199)
     (+ (* y i) (+ (* b (log c)) (+ a t_2)))
     (if (<= x 2.9e+103)
       (fma y i (+ a (+ t (+ z t_1))))
       (+ a (+ t (+ z (+ t_2 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 = x * log(y);
	double tmp;
	if (x <= -1.2e+199) {
		tmp = (y * i) + ((b * log(c)) + (a + t_2));
	} else if (x <= 2.9e+103) {
		tmp = fma(y, i, (a + (t + (z + t_1))));
	} else {
		tmp = a + (t + (z + (t_2 + 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(x * log(y))
	tmp = 0.0
	if (x <= -1.2e+199)
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + t_2)));
	elseif (x <= 2.9e+103)
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + t_1))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_2 + t_1))));
	end
	return 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[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+199], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+103], N[(y * i + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(t$95$2 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.20000000000000007e199

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 94.8%

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

   if -1.20000000000000007e199 < x < 2.8999999999999998e103

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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 97.9%

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

   if 2.8999999999999998e103 < 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 90.5%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+199}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+200} \lor \neg \left(x \leq 3.9 \cdot 10^{+104}\right):\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.15e+200) (not (<= x 3.9e+104)))
   (+ (* y i) (+ (* b (log c)) (+ a (* x (log y)))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ 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 <= -1.15e+200) || !(x <= 3.9e+104)) {
		tmp = (y * i) + ((b * log(c)) + (a + (x * log(y))));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (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 <= (-1.15d+200)) .or. (.not. (x <= 3.9d+104))) then
        tmp = (y * i) + ((b * log(c)) + (a + (x * log(y))))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (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 <= -1.15e+200) || !(x <= 3.9e+104)) {
		tmp = (y * i) + ((b * Math.log(c)) + (a + (x * Math.log(y))));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.15e+200) or not (x <= 3.9e+104):
		tmp = (y * i) + ((b * math.log(c)) + (a + (x * math.log(y))))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.15e+200) || !(x <= 3.9e+104))
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + 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 <= -1.15e+200) || ~((x <= 3.9e+104)))
		tmp = (y * i) + ((b * log(c)) + (a + (x * log(y))));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.15e+200], N[Not[LessEqual[x, 3.9e+104]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15000000000000002e200 or 3.90000000000000017e104 < 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 b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 84.9%

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

   if -1.15000000000000002e200 < x < 3.90000000000000017e104

   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 97.9%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+200} \lor \neg \left(x \leq 3.9 \cdot 10^{+104}\right):\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+199} \lor \neg \left(x \leq 1.36 \cdot 10^{+105}\right):\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.3e+199) (not (<= x 1.36e+105)))
   (+ (* y i) (+ (* b (log c)) (+ a (* x (log y)))))
   (fma y i (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.3e+199) || !(x <= 1.36e+105)) {
		tmp = (y * i) + ((b * log(c)) + (a + (x * log(y))));
	} else {
		tmp = fma(y, i, (a + (t + (z + (log(c) * (b - 0.5))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.3e+199) || !(x <= 1.36e+105))
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(x * log(y)))));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.3e+199], N[Not[LessEqual[x, 1.36e+105]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e199 or 1.3599999999999999e105 < 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 b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 84.9%

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

   if -1.3000000000000001e199 < x < 1.3599999999999999e105

   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 97.9%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+199} \lor \neg \left(x \leq 1.36 \cdot 10^{+105}\right):\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -1.42 \cdot 10^{+230}:\\ \;\;\;\;y \cdot i + \left(t\_1 + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i + \left(t\_2 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \left(t\_1 + t\_2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (* (log c) (- b 0.5))))
   (if (<= x -1.42e+230)
     (+ (* y i) (+ t_1 (* b (log c))))
     (if (<= x 1.6e+113)
       (+ (* y i) (+ t_2 (+ a (+ z t))))
       (+ t (+ z (+ 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 = x * log(y);
	double t_2 = log(c) * (b - 0.5);
	double tmp;
	if (x <= -1.42e+230) {
		tmp = (y * i) + (t_1 + (b * log(c)));
	} else if (x <= 1.6e+113) {
		tmp = (y * i) + (t_2 + (a + (z + t)));
	} else {
		tmp = t + (z + (t_1 + 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 = x * log(y)
    t_2 = log(c) * (b - 0.5d0)
    if (x <= (-1.42d+230)) then
        tmp = (y * i) + (t_1 + (b * log(c)))
    else if (x <= 1.6d+113) then
        tmp = (y * i) + (t_2 + (a + (z + t)))
    else
        tmp = t + (z + (t_1 + 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 = x * Math.log(y);
	double t_2 = Math.log(c) * (b - 0.5);
	double tmp;
	if (x <= -1.42e+230) {
		tmp = (y * i) + (t_1 + (b * Math.log(c)));
	} else if (x <= 1.6e+113) {
		tmp = (y * i) + (t_2 + (a + (z + t)));
	} else {
		tmp = t + (z + (t_1 + t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = math.log(c) * (b - 0.5)
	tmp = 0
	if x <= -1.42e+230:
		tmp = (y * i) + (t_1 + (b * math.log(c)))
	elif x <= 1.6e+113:
		tmp = (y * i) + (t_2 + (a + (z + t)))
	else:
		tmp = t + (z + (t_1 + t_2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (x <= -1.42e+230)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(b * log(c))));
	elseif (x <= 1.6e+113)
		tmp = Float64(Float64(y * i) + Float64(t_2 + Float64(a + Float64(z + t))));
	else
		tmp = Float64(t + Float64(z + Float64(t_1 + t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (x <= -1.42e+230)
		tmp = (y * i) + (t_1 + (b * log(c)));
	elseif (x <= 1.6e+113)
		tmp = (y * i) + (t_2 + (a + (z + t)));
	else
		tmp = t + (z + (t_1 + t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.42e+230], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+113], N[(N[(y * i), $MachinePrecision] + N[(t$95$2 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.41999999999999991e230

   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 b around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 99.6%

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

   7. Taylor expanded in a around 0 99.6%

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

   if -1.41999999999999991e230 < x < 1.5999999999999999e113

   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 97.5%

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

   if 1.5999999999999999e113 < 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 89.8%

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

      1. associate-+r+ 89.8%

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

      2. associate-+r+ 89.8%

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

      3. +-commutative 89.8%

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

      4. +-commutative 89.8%

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

      5. +-commutative 89.8%

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

      6. sub-neg 89.8%

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

      7. metadata-eval 89.8%

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

      8. associate-+l+ 89.8%

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

      9. associate-+r+ 89.8%

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

      10. +-commutative 89.8%

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

      11. fma-define 89.8%

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

      12. associate-+l+ 89.8%

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

      13. associate-+r+ 89.8%

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

      14. +-commutative 89.8%

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

      15. fma-define 89.8%

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

      16. +-commutative 89.8%

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

      17. +-commutative 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in a around 0 83.0%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+230}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 8: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf 98.9%

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

   1. *-commutative 98.9%

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

5. Simplified 98.9%

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

6. Final simplification 98.9%

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

Alternative 9: 87.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+203} \lor \neg \left(x \leq 1.36 \cdot 10^{+105}\right) \land \left(x \leq 2.3 \cdot 10^{+194} \lor \neg \left(x \leq 1.35 \cdot 10^{+243}\right)\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.6e+203)
         (and (not (<= x 1.36e+105))
              (or (<= x 2.3e+194) (not (<= x 1.35e+243)))))
   (+ (* y i) (+ a (* x (log y))))
   (+ (* 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 <= -4.6e+203) || (!(x <= 1.36e+105) && ((x <= 2.3e+194) || !(x <= 1.35e+243)))) {
		tmp = (y * i) + (a + (x * log(y)));
	} 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 <= (-4.6d+203)) .or. (.not. (x <= 1.36d+105)) .and. (x <= 2.3d+194) .or. (.not. (x <= 1.35d+243))) then
        tmp = (y * i) + (a + (x * log(y)))
    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 <= -4.6e+203) || (!(x <= 1.36e+105) && ((x <= 2.3e+194) || !(x <= 1.35e+243)))) {
		tmp = (y * i) + (a + (x * Math.log(y)));
	} 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 <= -4.6e+203) or (not (x <= 1.36e+105) and ((x <= 2.3e+194) or not (x <= 1.35e+243))):
		tmp = (y * i) + (a + (x * math.log(y)))
	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 <= -4.6e+203) || (!(x <= 1.36e+105) && ((x <= 2.3e+194) || !(x <= 1.35e+243))))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	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 <= -4.6e+203) || (~((x <= 1.36e+105)) && ((x <= 2.3e+194) || ~((x <= 1.35e+243)))))
		tmp = (y * i) + (a + (x * log(y)));
	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, -4.6e+203], And[N[Not[LessEqual[x, 1.36e+105]], $MachinePrecision], Or[LessEqual[x, 2.3e+194], N[Not[LessEqual[x, 1.35e+243]], $MachinePrecision]]]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $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 2 regimes

2. if x < -4.5999999999999998e203 or 1.3599999999999999e105 < x < 2.30000000000000005e194 or 1.3500000000000001e243 < 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 b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 88.4%

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

   7. Taylor expanded in b around 0 83.8%

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

   if -4.5999999999999998e203 < x < 1.3599999999999999e105 or 2.30000000000000005e194 < x < 1.3500000000000001e243

   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 98.0%

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

   4. Taylor expanded in b around inf 96.8%

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

      1. *-commutative 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. Simplified 96.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+203} \lor \neg \left(x \leq 1.36 \cdot 10^{+105}\right) \land \left(x \leq 2.3 \cdot 10^{+194} \lor \neg \left(x \leq 1.35 \cdot 10^{+243}\right)\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(a + x \cdot \log y\right)\\ t_2 := a + \left(z + t\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+105}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + t\_2\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+195} \lor \neg \left(x \leq 1.55 \cdot 10^{+243}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ a (* x (log y))))) (t_2 (+ a (+ z t))))
   (if (<= x -1.7e+205)
     t_1
     (if (<= x 1.35e+105)
       (+ (* y i) (+ (* (log c) (- b 0.5)) t_2))
       (if (or (<= x 2.25e+195) (not (<= x 1.55e+243)))
         t_1
         (+ (* y i) (+ (* b (log c)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (x * log(y)));
	double t_2 = a + (z + t);
	double tmp;
	if (x <= -1.7e+205) {
		tmp = t_1;
	} else if (x <= 1.35e+105) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + t_2);
	} else if ((x <= 2.25e+195) || !(x <= 1.55e+243)) {
		tmp = t_1;
	} else {
		tmp = (y * i) + ((b * log(c)) + 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 = (y * i) + (a + (x * log(y)))
    t_2 = a + (z + t)
    if (x <= (-1.7d+205)) then
        tmp = t_1
    else if (x <= 1.35d+105) then
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + t_2)
    else if ((x <= 2.25d+195) .or. (.not. (x <= 1.55d+243))) then
        tmp = t_1
    else
        tmp = (y * i) + ((b * log(c)) + 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 = (y * i) + (a + (x * Math.log(y)));
	double t_2 = a + (z + t);
	double tmp;
	if (x <= -1.7e+205) {
		tmp = t_1;
	} else if (x <= 1.35e+105) {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + t_2);
	} else if ((x <= 2.25e+195) || !(x <= 1.55e+243)) {
		tmp = t_1;
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (a + (x * math.log(y)))
	t_2 = a + (z + t)
	tmp = 0
	if x <= -1.7e+205:
		tmp = t_1
	elif x <= 1.35e+105:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + t_2)
	elif (x <= 2.25e+195) or not (x <= 1.55e+243):
		tmp = t_1
	else:
		tmp = (y * i) + ((b * math.log(c)) + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))))
	t_2 = Float64(a + Float64(z + t))
	tmp = 0.0
	if (x <= -1.7e+205)
		tmp = t_1;
	elseif (x <= 1.35e+105)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + t_2));
	elseif ((x <= 2.25e+195) || !(x <= 1.55e+243))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (a + (x * log(y)));
	t_2 = a + (z + t);
	tmp = 0.0;
	if (x <= -1.7e+205)
		tmp = t_1;
	elseif (x <= 1.35e+105)
		tmp = (y * i) + ((log(c) * (b - 0.5)) + t_2);
	elseif ((x <= 2.25e+195) || ~((x <= 1.55e+243)))
		tmp = t_1;
	else
		tmp = (y * i) + ((b * log(c)) + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+205], t$95$1, If[LessEqual[x, 1.35e+105], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.25e+195], N[Not[LessEqual[x, 1.55e+243]], $MachinePrecision]], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e205 or 1.35000000000000008e105 < x < 2.25000000000000005e195 or 1.55e243 < 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 b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 88.4%

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

   7. Taylor expanded in b around 0 83.8%

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

   if -1.7e205 < x < 1.35000000000000008e105

   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 97.9%

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

   if 2.25000000000000005e195 < x < 1.55e243

   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 99.8%

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

   4. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+205}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+105}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+195} \lor \neg \left(x \leq 1.55 \cdot 10^{+243}\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+136}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+81}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + -0.5 \cdot \log c\right)\\ \mathbf{elif}\;z \leq -2000000 \lor \neg \left(z \leq 4.4 \cdot 10^{-290}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1e+136)
   (+ (* y i) (+ t (+ z (* (log c) (- b 0.5)))))
   (if (<= z -3.1e+81)
     (+ (* y i) (+ (+ a (+ z t)) (* -0.5 (log c))))
     (if (or (<= z -2000000.0) (not (<= z 4.4e-290)))
       (+ (* y i) (+ a (* b (log c))))
       (+ (* y i) (+ a (* x (log y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1e+136) {
		tmp = (y * i) + (t + (z + (log(c) * (b - 0.5))));
	} else if (z <= -3.1e+81) {
		tmp = (y * i) + ((a + (z + t)) + (-0.5 * log(c)));
	} else if ((z <= -2000000.0) || !(z <= 4.4e-290)) {
		tmp = (y * i) + (a + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (x * log(y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1d+136)) then
        tmp = (y * i) + (t + (z + (log(c) * (b - 0.5d0))))
    else if (z <= (-3.1d+81)) then
        tmp = (y * i) + ((a + (z + t)) + ((-0.5d0) * log(c)))
    else if ((z <= (-2000000.0d0)) .or. (.not. (z <= 4.4d-290))) then
        tmp = (y * i) + (a + (b * log(c)))
    else
        tmp = (y * i) + (a + (x * log(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1e+136) {
		tmp = (y * i) + (t + (z + (Math.log(c) * (b - 0.5))));
	} else if (z <= -3.1e+81) {
		tmp = (y * i) + ((a + (z + t)) + (-0.5 * Math.log(c)));
	} else if ((z <= -2000000.0) || !(z <= 4.4e-290)) {
		tmp = (y * i) + (a + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (x * Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1e+136:
		tmp = (y * i) + (t + (z + (math.log(c) * (b - 0.5))))
	elif z <= -3.1e+81:
		tmp = (y * i) + ((a + (z + t)) + (-0.5 * math.log(c)))
	elif (z <= -2000000.0) or not (z <= 4.4e-290):
		tmp = (y * i) + (a + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (x * math.log(y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1e+136)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	elseif (z <= -3.1e+81)
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(z + t)) + Float64(-0.5 * log(c))));
	elseif ((z <= -2000000.0) || !(z <= 4.4e-290))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1e+136)
		tmp = (y * i) + (t + (z + (log(c) * (b - 0.5))));
	elseif (z <= -3.1e+81)
		tmp = (y * i) + ((a + (z + t)) + (-0.5 * log(c)));
	elseif ((z <= -2000000.0) || ~((z <= 4.4e-290)))
		tmp = (y * i) + (a + (b * log(c)));
	else
		tmp = (y * i) + (a + (x * log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1e+136], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e+81], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2000000.0], N[Not[LessEqual[z, 4.4e-290]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000006e136

   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 91.7%

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

   4. Taylor expanded in a around 0 85.8%

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

   if -1.00000000000000006e136 < z < -3.1e81

   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 93.5%

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

   4. Taylor expanded in b around 0 87.8%

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

   if -3.1e81 < z < -2e6 or 4.4000000000000002e-290 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 99.5%

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

      1. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x around inf 69.3%

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

   7. Taylor expanded in x around 0 52.3%

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

   if -2e6 < z < 4.4000000000000002e-290

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 96.9%

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

      1. *-commutative 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in x around inf 83.8%

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

   7. Taylor expanded in b around 0 69.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+136}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+81}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + -0.5 \cdot \log c\right)\\ \mathbf{elif}\;z \leq -2000000 \lor \neg \left(z \leq 4.4 \cdot 10^{-290}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + y \cdot i\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+182}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -7200000:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* y i))))
   (if (<= z -7.2e+182)
     z
     (if (<= z -8.2e+160)
       t_1
       (if (<= z -2.7e+82)
         z
         (if (<= z -7200000.0) (+ (* y i) (* b (log c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (y * i);
	double tmp;
	if (z <= -7.2e+182) {
		tmp = z;
	} else if (z <= -8.2e+160) {
		tmp = t_1;
	} else if (z <= -2.7e+82) {
		tmp = z;
	} else if (z <= -7200000.0) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (y * i)
    if (z <= (-7.2d+182)) then
        tmp = z
    else if (z <= (-8.2d+160)) then
        tmp = t_1
    else if (z <= (-2.7d+82)) then
        tmp = z
    else if (z <= (-7200000.0d0)) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (y * i);
	double tmp;
	if (z <= -7.2e+182) {
		tmp = z;
	} else if (z <= -8.2e+160) {
		tmp = t_1;
	} else if (z <= -2.7e+82) {
		tmp = z;
	} else if (z <= -7200000.0) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (y * i)
	tmp = 0
	if z <= -7.2e+182:
		tmp = z
	elif z <= -8.2e+160:
		tmp = t_1
	elif z <= -2.7e+82:
		tmp = z
	elif z <= -7200000.0:
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(y * i))
	tmp = 0.0
	if (z <= -7.2e+182)
		tmp = z;
	elseif (z <= -8.2e+160)
		tmp = t_1;
	elseif (z <= -2.7e+82)
		tmp = z;
	elseif (z <= -7200000.0)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (y * i);
	tmp = 0.0;
	if (z <= -7.2e+182)
		tmp = z;
	elseif (z <= -8.2e+160)
		tmp = t_1;
	elseif (z <= -2.7e+82)
		tmp = z;
	elseif (z <= -7200000.0)
		tmp = (y * i) + (b * log(c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+182], z, If[LessEqual[z, -8.2e+160], t$95$1, If[LessEqual[z, -2.7e+82], z, If[LessEqual[z, -7200000.0], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e182 or -8.19999999999999996e160 < z < -2.6999999999999999e82

   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 94.8%

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

   4. Taylor expanded in z around inf 47.5%

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

   if -7.2e182 < z < -8.19999999999999996e160 or -7.2e6 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 98.6%

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

      1. *-commutative 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in x around inf 72.7%

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

   7. Taylor expanded in a around inf 44.6%

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

   if -2.6999999999999999e82 < z < -7.2e6

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 94.0%

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

   7. Taylor expanded in b around inf 38.1%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+182}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+160}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -7200000:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{+80} \lor \neg \left(y \leq 3.8 \cdot 10^{+127}\right) \land y \leq 9 \cdot 10^{+145}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y 1e+80) (and (not (<= y 3.8e+127)) (<= y 9e+145)))
   (+ a (+ t (+ z (* (log c) (- b 0.5)))))
   (+ (* y i) (+ a (* x (log y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= 1e+80) || (!(y <= 3.8e+127) && (y <= 9e+145))) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (a + (x * log(y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= 1d+80) .or. (.not. (y <= 3.8d+127)) .and. (y <= 9d+145)) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = (y * i) + (a + (x * log(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= 1e+80) || (!(y <= 3.8e+127) && (y <= 9e+145))) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (a + (x * Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= 1e+80) or (not (y <= 3.8e+127) and (y <= 9e+145)):
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = (y * i) + (a + (x * math.log(y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= 1e+80) || (!(y <= 3.8e+127) && (y <= 9e+145)))
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= 1e+80) || (~((y <= 3.8e+127)) && (y <= 9e+145)))
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	else
		tmp = (y * i) + (a + (x * log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, 1e+80], And[N[Not[LessEqual[y, 3.8e+127]], $MachinePrecision], LessEqual[y, 9e+145]]], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1e80 or 3.7999999999999998e127 < y < 8.9999999999999996e145

   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 83.5%

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

   4. Taylor expanded in y around 0 77.1%

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

   if 1e80 < y < 3.7999999999999998e127 or 8.9999999999999996e145 < y

   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 b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 84.0%

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

   7. Taylor expanded in b around 0 80.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{+80} \lor \neg \left(y \leq 3.8 \cdot 10^{+127}\right) \land y \leq 9 \cdot 10^{+145}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+120} \lor \neg \left(x \leq 1.75 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.8e+120) (not (<= x 1.75e+97)))
   (+ (* y i) (+ a (* x (log y))))
   (+ (* y i) (+ a (* b (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.8e+120) || !(x <= 1.75e+97)) {
		tmp = (y * i) + (a + (x * log(y)));
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-3.8d+120)) .or. (.not. (x <= 1.75d+97))) then
        tmp = (y * i) + (a + (x * log(y)))
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.8e+120) || !(x <= 1.75e+97)) {
		tmp = (y * i) + (a + (x * Math.log(y)));
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3.8e+120) or not (x <= 1.75e+97):
		tmp = (y * i) + (a + (x * math.log(y)))
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.8e+120) || !(x <= 1.75e+97))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3.8e+120) || ~((x <= 1.75e+97)))
		tmp = (y * i) + (a + (x * log(y)));
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.8e+120], N[Not[LessEqual[x, 1.75e+97]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998e120 or 1.75e97 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 81.0%

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

   7. Taylor expanded in b around 0 73.9%

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

   if -3.7999999999999998e120 < x < 1.75e97

   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 98.6%

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

      1. *-commutative 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in x around inf 62.3%

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

   7. Taylor expanded in x around 0 61.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+120} \lor \neg \left(x \leq 1.75 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+132}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-292}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -7e+132)
   (+ (* y i) (+ t (+ z (* (log c) (- b 0.5)))))
   (if (<= z 3.5e-292)
     (+ (* y i) (+ a (* x (log y))))
     (+ (* y i) (+ a (* b (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7e+132) {
		tmp = (y * i) + (t + (z + (log(c) * (b - 0.5))));
	} else if (z <= 3.5e-292) {
		tmp = (y * i) + (a + (x * log(y)));
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-7d+132)) then
        tmp = (y * i) + (t + (z + (log(c) * (b - 0.5d0))))
    else if (z <= 3.5d-292) then
        tmp = (y * i) + (a + (x * log(y)))
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7e+132) {
		tmp = (y * i) + (t + (z + (Math.log(c) * (b - 0.5))));
	} else if (z <= 3.5e-292) {
		tmp = (y * i) + (a + (x * Math.log(y)));
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -7e+132:
		tmp = (y * i) + (t + (z + (math.log(c) * (b - 0.5))))
	elif z <= 3.5e-292:
		tmp = (y * i) + (a + (x * math.log(y)))
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -7e+132)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	elseif (z <= 3.5e-292)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -7e+132)
		tmp = (y * i) + (t + (z + (log(c) * (b - 0.5))));
	elseif (z <= 3.5e-292)
		tmp = (y * i) + (a + (x * log(y)));
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -7e+132], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-292], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000041e132

   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 92.0%

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

   4. Taylor expanded in a around 0 86.4%

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

   if -7.00000000000000041e132 < z < 3.5e-292

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in x around inf 80.2%

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

   7. Taylor expanded in b around 0 66.5%

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

   if 3.5e-292 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 99.5%

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

      1. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x around inf 65.9%

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

   7. Taylor expanded in x around 0 49.6%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+132}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-292}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= t -2e-44) z (+ (* y i) (+ a (* b (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (t <= -2e-44) {
		tmp = z;
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (t <= (-2d-44)) then
        tmp = z
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (t <= -2e-44) {
		tmp = z;
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if t <= -2e-44:
		tmp = z
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (t <= -2e-44)
		tmp = z;
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (t <= -2e-44)
		tmp = z;
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[t, -2e-44], z, N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.99999999999999991e-44

   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 83.8%

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

   4. Taylor expanded in z around inf 21.1%

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

   if -1.99999999999999991e-44 < t

   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 98.8%

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

      1. *-commutative 98.8%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in x around inf 72.1%

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

   7. Taylor expanded in x around 0 57.4%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.3% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-11} \lor \neg \left(z \leq -4.2 \cdot 10^{-35}\right) \land z \leq -1.35 \cdot 10^{-148}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.3e+82)
   z
   (if (or (<= z -1.35e-11) (and (not (<= z -4.2e-35)) (<= z -1.35e-148)))
     (* y i)
     a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.3e+82) {
		tmp = z;
	} else if ((z <= -1.35e-11) || (!(z <= -4.2e-35) && (z <= -1.35e-148))) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.3d+82)) then
        tmp = z
    else if ((z <= (-1.35d-11)) .or. (.not. (z <= (-4.2d-35))) .and. (z <= (-1.35d-148))) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.3e+82) {
		tmp = z;
	} else if ((z <= -1.35e-11) || (!(z <= -4.2e-35) && (z <= -1.35e-148))) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.3e+82:
		tmp = z
	elif (z <= -1.35e-11) or (not (z <= -4.2e-35) and (z <= -1.35e-148)):
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.3e+82)
		tmp = z;
	elseif ((z <= -1.35e-11) || (!(z <= -4.2e-35) && (z <= -1.35e-148)))
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.3e+82)
		tmp = z;
	elseif ((z <= -1.35e-11) || (~((z <= -4.2e-35)) && (z <= -1.35e-148)))
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.3e+82], z, If[Or[LessEqual[z, -1.35e-11], And[N[Not[LessEqual[z, -4.2e-35]], $MachinePrecision], LessEqual[z, -1.35e-148]]], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999988e82

   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 91.9%

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

   4. Taylor expanded in z around inf 45.4%

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

   if -2.29999999999999988e82 < z < -1.35000000000000002e-11 or -4.2e-35 < z < -1.34999999999999994e-148

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 27.4%

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

      1. *-commutative 27.4%

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

   5. Simplified 27.4%

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

   if -1.35000000000000002e-11 < z < -4.2e-35 or -1.34999999999999994e-148 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 20.3%

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

4. Final simplification 27.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-11} \lor \neg \left(z \leq -4.2 \cdot 10^{-35}\right) \land z \leq -1.35 \cdot 10^{-148}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.5% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+182} \lor \neg \left(z \leq -9 \cdot 10^{+160}\right) \land z \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -7.2e+182) (and (not (<= z -9e+160)) (<= z -2.7e+82)))
   z
   (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -7.2e+182) || (!(z <= -9e+160) && (z <= -2.7e+82))) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-7.2d+182)) .or. (.not. (z <= (-9d+160))) .and. (z <= (-2.7d+82))) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -7.2e+182) || (!(z <= -9e+160) && (z <= -2.7e+82))) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -7.2e+182) or (not (z <= -9e+160) and (z <= -2.7e+82)):
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -7.2e+182) || (!(z <= -9e+160) && (z <= -2.7e+82)))
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -7.2e+182) || (~((z <= -9e+160)) && (z <= -2.7e+82)))
		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, -7.2e+182], And[N[Not[LessEqual[z, -9e+160]], $MachinePrecision], LessEqual[z, -2.7e+82]]], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e182 or -8.99999999999999959e160 < z < -2.6999999999999999e82

   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 94.8%

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

   4. Taylor expanded in z around inf 47.5%

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

   if -7.2e182 < z < -8.99999999999999959e160 or -2.6999999999999999e82 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 98.7%

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

   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 x around inf 74.5%

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

   7. Taylor expanded in a around inf 45.4%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+182} \lor \neg \left(z \leq -9 \cdot 10^{+160}\right) \land z \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 20.8% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -2.7e+82) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.7e+82) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.7d+82)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.7e+82) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.7e+82:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.7e+82)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.7e+82)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.7e+82], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e82

   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 91.9%

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

   4. Taylor expanded in z around inf 45.4%

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

   if -2.6999999999999999e82 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 20.5%

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

4. Final simplification 26.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 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 17.5%

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

4. Final simplification 17.5%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(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)))