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

Percentage Accurate: 99.8% → 99.8%

Time: 13.0s

Alternatives: 23

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

Alternative 2: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ t_2 := y \cdot i + \left(z + t\_1\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 260:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot -0.5 + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))) (t_2 (+ (* y i) (+ z t_1))))
   (if (<= t_1 -2e+95)
     t_2
     (if (<= t_1 260.0)
       (+ (+ (* x (log y)) z) (+ t a))
       (if (<= t_1 5e+90) (+ (* y i) (+ (* (log c) -0.5) (+ z a))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double t_2 = (y * i) + (z + t_1);
	double tmp;
	if (t_1 <= -2e+95) {
		tmp = t_2;
	} else if (t_1 <= 260.0) {
		tmp = ((x * log(y)) + z) + (t + a);
	} else if (t_1 <= 5e+90) {
		tmp = (y * i) + ((log(c) * -0.5) + (z + a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    t_2 = (y * i) + (z + t_1)
    if (t_1 <= (-2d+95)) then
        tmp = t_2
    else if (t_1 <= 260.0d0) then
        tmp = ((x * log(y)) + z) + (t + a)
    else if (t_1 <= 5d+90) then
        tmp = (y * i) + ((log(c) * (-0.5d0)) + (z + a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * Math.log(c);
	double t_2 = (y * i) + (z + t_1);
	double tmp;
	if (t_1 <= -2e+95) {
		tmp = t_2;
	} else if (t_1 <= 260.0) {
		tmp = ((x * Math.log(y)) + z) + (t + a);
	} else if (t_1 <= 5e+90) {
		tmp = (y * i) + ((Math.log(c) * -0.5) + (z + a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	t_2 = (y * i) + (z + t_1)
	tmp = 0
	if t_1 <= -2e+95:
		tmp = t_2
	elif t_1 <= 260.0:
		tmp = ((x * math.log(y)) + z) + (t + a)
	elif t_1 <= 5e+90:
		tmp = (y * i) + ((math.log(c) * -0.5) + (z + a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	t_2 = Float64(Float64(y * i) + Float64(z + t_1))
	tmp = 0.0
	if (t_1 <= -2e+95)
		tmp = t_2;
	elseif (t_1 <= 260.0)
		tmp = Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a));
	elseif (t_1 <= 5e+90)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * -0.5) + Float64(z + a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	t_2 = (y * i) + (z + t_1);
	tmp = 0.0;
	if (t_1 <= -2e+95)
		tmp = t_2;
	elseif (t_1 <= 260.0)
		tmp = ((x * log(y)) + z) + (t + a);
	elseif (t_1 <= 5e+90)
		tmp = (y * i) + ((log(c) * -0.5) + (z + a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+95], t$95$2, If[LessEqual[t$95$1, 260.0], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+90], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -2.00000000000000004e95 or 5.0000000000000004e90 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 73.7%

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

   if -2.00000000000000004e95 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 260

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 83.8%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-commutative N/A

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

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

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

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

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

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

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

       8. +-lowering-+.f64 79.0%

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

   11. Simplified 79.0%

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

   if 260 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 5.0000000000000004e90

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 75.0%

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

   6. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b - 0.5\right) \cdot \log c \leq -2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;\left(b - 0.5\right) \cdot \log c \leq 260:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{elif}\;\left(b - 0.5\right) \cdot \log c \leq 5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot -0.5 + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;i \leq -126:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \log y + \left(\left(z + \left(t + a\right)\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= i -126.0)
     (+ (* y i) (+ t_1 (+ a (+ z t))))
     (if (<= i 2.2e-23)
       (+ (* x (log y)) (+ (+ z (+ t a)) (* (log c) (+ b -0.5))))
       (+ (* y i) (+ t_1 (+ z a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if (i <= -126.0) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else if (i <= 2.2e-23) {
		tmp = (x * log(y)) + ((z + (t + a)) + (log(c) * (b + -0.5)));
	} else {
		tmp = (y * i) + (t_1 + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if (i <= (-126.0d0)) then
        tmp = (y * i) + (t_1 + (a + (z + t)))
    else if (i <= 2.2d-23) then
        tmp = (x * log(y)) + ((z + (t + a)) + (log(c) * (b + (-0.5d0))))
    else
        tmp = (y * i) + (t_1 + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if (i <= -126.0) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else if (i <= 2.2e-23) {
		tmp = (x * Math.log(y)) + ((z + (t + a)) + (Math.log(c) * (b + -0.5)));
	} else {
		tmp = (y * i) + (t_1 + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if i <= -126.0:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	elif i <= 2.2e-23:
		tmp = (x * math.log(y)) + ((z + (t + a)) + (math.log(c) * (b + -0.5)))
	else:
		tmp = (y * i) + (t_1 + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (i <= -126.0)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	elseif (i <= 2.2e-23)
		tmp = Float64(Float64(x * log(y)) + Float64(Float64(z + Float64(t + a)) + Float64(log(c) * Float64(b + -0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (i <= -126.0)
		tmp = (y * i) + (t_1 + (a + (z + t)));
	elseif (i <= 2.2e-23)
		tmp = (x * log(y)) + ((z + (t + a)) + (log(c) * (b + -0.5)));
	else
		tmp = (y * i) + (t_1 + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -126.0], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.2e-23], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -126

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 90.4%

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

   5. Simplified 90.4%

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

   if -126 < i < 2.1999999999999999e-23

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 98.9%

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

   if 2.1999999999999999e-23 < i

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 75.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -126:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \log y + \left(\left(z + \left(t + a\right)\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \log y + \left(\left(z + \left(t + a\right)\right) + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+166}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.75e+152)
   (+ (* x (log y)) (+ (+ z (+ t a)) (* b (log c))))
   (if (<= x 7.2e+166)
     (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ z t))))
     (* x (+ (log y) (/ (+ z (* y i)) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.75e+152) {
		tmp = (x * log(y)) + ((z + (t + a)) + (b * log(c)));
	} else if (x <= 7.2e+166) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	} else {
		tmp = x * (log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-1.75d+152)) then
        tmp = (x * log(y)) + ((z + (t + a)) + (b * log(c)))
    else if (x <= 7.2d+166) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (z + t)))
    else
        tmp = x * (log(y) + ((z + (y * i)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.75e+152) {
		tmp = (x * Math.log(y)) + ((z + (t + a)) + (b * Math.log(c)));
	} else if (x <= 7.2e+166) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (z + t)));
	} else {
		tmp = x * (Math.log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.75e+152:
		tmp = (x * math.log(y)) + ((z + (t + a)) + (b * math.log(c)))
	elif x <= 7.2e+166:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (z + t)))
	else:
		tmp = x * (math.log(y) + ((z + (y * i)) / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.75e+152)
		tmp = Float64(Float64(x * log(y)) + Float64(Float64(z + Float64(t + a)) + Float64(b * log(c))));
	elseif (x <= 7.2e+166)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(x * Float64(log(y) + Float64(Float64(z + Float64(y * i)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -1.75e+152)
		tmp = (x * log(y)) + ((z + (t + a)) + (b * log(c)));
	elseif (x <= 7.2e+166)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	else
		tmp = x * (log(y) + ((z + (y * i)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.75e+152], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+166], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.74999999999999991e152

   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

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 91.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 91.4%

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

   8. Simplified 91.4%

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

   if -1.74999999999999991e152 < x < 7.1999999999999994e166

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 95.9%

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

   5. Simplified 95.9%

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

   if 7.1999999999999994e166 < 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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 65.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 65.8%

      \[\leadsto \left(\color{blue}{\frac{x \cdot \log y}{z}} + 1\right) \cdot z + y \cdot i \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)\right)} \]

       3. distribute-lft-out N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(-1 \cdot \left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right)\right)\right) \]

       5. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 88.7%

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

   11. Simplified 88.7%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \log y + \left(\left(z + \left(t + a\right)\right) + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+166}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -2 \cdot 10^{+162}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t\_1\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+167}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= x -2e+162)
     (+ (* y i) (+ (* x (log y)) t_1))
     (if (<= x 3.2e+167)
       (+ (* y i) (+ t_1 (+ a (+ z t))))
       (* x (+ (log y) (/ (+ z (* y i)) x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if (x <= -2e+162) {
		tmp = (y * i) + ((x * log(y)) + t_1);
	} else if (x <= 3.2e+167) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else {
		tmp = x * (log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if (x <= (-2d+162)) then
        tmp = (y * i) + ((x * log(y)) + t_1)
    else if (x <= 3.2d+167) then
        tmp = (y * i) + (t_1 + (a + (z + t)))
    else
        tmp = x * (log(y) + ((z + (y * i)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if (x <= -2e+162) {
		tmp = (y * i) + ((x * Math.log(y)) + t_1);
	} else if (x <= 3.2e+167) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else {
		tmp = x * (Math.log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if x <= -2e+162:
		tmp = (y * i) + ((x * math.log(y)) + t_1)
	elif x <= 3.2e+167:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	else:
		tmp = x * (math.log(y) + ((z + (y * i)) / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (x <= -2e+162)
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t_1));
	elseif (x <= 3.2e+167)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	else
		tmp = Float64(x * Float64(log(y) + Float64(Float64(z + Float64(y * i)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (x <= -2e+162)
		tmp = (y * i) + ((x * log(y)) + t_1);
	elseif (x <= 3.2e+167)
		tmp = (y * i) + (t_1 + (a + (z + t)));
	else
		tmp = x * (log(y) + ((z + (y * i)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+162], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+167], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9999999999999999e162

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 82.6%

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

   5. Simplified 82.6%

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

   if -1.9999999999999999e162 < x < 3.19999999999999981e167

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 95.5%

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

   5. Simplified 95.5%

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

   if 3.19999999999999981e167 < 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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 65.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 65.8%

      \[\leadsto \left(\color{blue}{\frac{x \cdot \log y}{z}} + 1\right) \cdot z + y \cdot i \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)\right)} \]

       3. distribute-lft-out N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(-1 \cdot \left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right)\right)\right) \]

       5. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 88.7%

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

   11. Simplified 88.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+162}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+167}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \log y + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+166}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -7.5e+155)
   (+ (* x (log y)) (+ z (* b (log c))))
   (if (<= x 7.2e+166)
     (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ z t))))
     (* x (+ (log y) (/ (+ z (* y i)) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -7.5e+155) {
		tmp = (x * log(y)) + (z + (b * log(c)));
	} else if (x <= 7.2e+166) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	} else {
		tmp = x * (log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-7.5d+155)) then
        tmp = (x * log(y)) + (z + (b * log(c)))
    else if (x <= 7.2d+166) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (z + t)))
    else
        tmp = x * (log(y) + ((z + (y * i)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -7.5e+155) {
		tmp = (x * Math.log(y)) + (z + (b * Math.log(c)));
	} else if (x <= 7.2e+166) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (z + t)));
	} else {
		tmp = x * (Math.log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -7.5e+155:
		tmp = (x * math.log(y)) + (z + (b * math.log(c)))
	elif x <= 7.2e+166:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (z + t)))
	else:
		tmp = x * (math.log(y) + ((z + (y * i)) / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -7.5e+155)
		tmp = Float64(Float64(x * log(y)) + Float64(z + Float64(b * log(c))));
	elseif (x <= 7.2e+166)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(x * Float64(log(y) + Float64(Float64(z + Float64(y * i)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -7.5e+155)
		tmp = (x * log(y)) + (z + (b * log(c)));
	elseif (x <= 7.2e+166)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	else
		tmp = x * (log(y) + ((z + (y * i)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -7.5e+155], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+166], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4999999999999999e155

   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

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 91.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in z around inf

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

   11. Simplified 80.3%

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

   if -7.4999999999999999e155 < x < 7.1999999999999994e166

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 95.9%

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

   5. Simplified 95.9%

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

   if 7.1999999999999994e166 < 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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 65.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 65.8%

      \[\leadsto \left(\color{blue}{\frac{x \cdot \log y}{z}} + 1\right) \cdot z + y \cdot i \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)\right)} \]

       3. distribute-lft-out N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(-1 \cdot \left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right)\right)\right) \]

       5. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 88.7%

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

   11. Simplified 88.7%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \log y + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+166}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+167}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -5.6e+159)
   (+ (+ (* x (log y)) z) (+ t a))
   (if (<= x 5e+167)
     (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ z t))))
     (* x (+ (log y) (/ (+ z (* y i)) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -5.6e+159) {
		tmp = ((x * log(y)) + z) + (t + a);
	} else if (x <= 5e+167) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	} else {
		tmp = x * (log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-5.6d+159)) then
        tmp = ((x * log(y)) + z) + (t + a)
    else if (x <= 5d+167) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (z + t)))
    else
        tmp = x * (log(y) + ((z + (y * i)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -5.6e+159) {
		tmp = ((x * Math.log(y)) + z) + (t + a);
	} else if (x <= 5e+167) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (z + t)));
	} else {
		tmp = x * (Math.log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -5.6e+159:
		tmp = ((x * math.log(y)) + z) + (t + a)
	elif x <= 5e+167:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (z + t)))
	else:
		tmp = x * (math.log(y) + ((z + (y * i)) / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -5.6e+159)
		tmp = Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a));
	elseif (x <= 5e+167)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(x * Float64(log(y) + Float64(Float64(z + Float64(y * i)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -5.6e+159)
		tmp = ((x * log(y)) + z) + (t + a);
	elseif (x <= 5e+167)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	else
		tmp = x * (log(y) + ((z + (y * i)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -5.6e+159], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+167], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.6000000000000002e159

   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

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 91.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-commutative N/A

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

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

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

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

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

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

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

       8. +-lowering-+.f64 76.8%

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

   11. Simplified 76.8%

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

   if -5.6000000000000002e159 < x < 4.9999999999999997e167

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 95.9%

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

   5. Simplified 95.9%

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

   if 4.9999999999999997e167 < 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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 65.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 65.8%

      \[\leadsto \left(\color{blue}{\frac{x \cdot \log y}{z}} + 1\right) \cdot z + y \cdot i \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)\right)} \]

       3. distribute-lft-out N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(-1 \cdot \left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right)\right)\right) \]

       5. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 88.7%

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

   11. Simplified 88.7%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+167}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{if}\;b - 0.5 \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b - 0.5 \leq 10^{+89}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ z (* (- b 0.5) (log c))))))
   (if (<= (- b 0.5) -2.5e+72)
     t_1
     (if (<= (- b 0.5) 1e+89) (+ (+ (* x (log y)) z) (+ t a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (z + ((b - 0.5) * log(c)));
	double tmp;
	if ((b - 0.5) <= -2.5e+72) {
		tmp = t_1;
	} else if ((b - 0.5) <= 1e+89) {
		tmp = ((x * log(y)) + z) + (t + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (z + ((b - 0.5d0) * log(c)))
    if ((b - 0.5d0) <= (-2.5d+72)) then
        tmp = t_1
    else if ((b - 0.5d0) <= 1d+89) then
        tmp = ((x * log(y)) + z) + (t + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (z + ((b - 0.5) * Math.log(c)));
	double tmp;
	if ((b - 0.5) <= -2.5e+72) {
		tmp = t_1;
	} else if ((b - 0.5) <= 1e+89) {
		tmp = ((x * Math.log(y)) + z) + (t + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (z + ((b - 0.5) * math.log(c)))
	tmp = 0
	if (b - 0.5) <= -2.5e+72:
		tmp = t_1
	elif (b - 0.5) <= 1e+89:
		tmp = ((x * math.log(y)) + z) + (t + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(z + Float64(Float64(b - 0.5) * log(c))))
	tmp = 0.0
	if (Float64(b - 0.5) <= -2.5e+72)
		tmp = t_1;
	elseif (Float64(b - 0.5) <= 1e+89)
		tmp = Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (z + ((b - 0.5) * log(c)));
	tmp = 0.0;
	if ((b - 0.5) <= -2.5e+72)
		tmp = t_1;
	elseif ((b - 0.5) <= 1e+89)
		tmp = ((x * log(y)) + z) + (t + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -2.5e+72], t$95$1, If[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+89], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -2.49999999999999996e72 or 9.99999999999999995e88 < (-.f64 b #s(literal 1/2 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 72.7%

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

   if -2.49999999999999996e72 < (-.f64 b #s(literal 1/2 binary64)) < 9.99999999999999995e88

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 83.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 79.7%

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

   8. Simplified 79.7%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-commutative N/A

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

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

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

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

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

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

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

       8. +-lowering-+.f64 77.9%

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

   11. Simplified 77.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;b - 0.5 \leq 10^{+89}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+152}:\\ \;\;\;\;\left(t\_1 + z\right) + \left(t + a\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+98}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+173}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -6.4e+152)
     (+ (+ t_1 z) (+ t a))
     (if (<= x -1.3e+98)
       (+ (* y i) (* b (log c)))
       (if (<= x 3.8e+173)
         (+ (* (log c) (+ b -0.5)) (+ z a))
         (+ t_1 (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -6.4e+152) {
		tmp = (t_1 + z) + (t + a);
	} else if (x <= -1.3e+98) {
		tmp = (y * i) + (b * log(c));
	} else if (x <= 3.8e+173) {
		tmp = (log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-6.4d+152)) then
        tmp = (t_1 + z) + (t + a)
    else if (x <= (-1.3d+98)) then
        tmp = (y * i) + (b * log(c))
    else if (x <= 3.8d+173) then
        tmp = (log(c) * (b + (-0.5d0))) + (z + a)
    else
        tmp = t_1 + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -6.4e+152) {
		tmp = (t_1 + z) + (t + a);
	} else if (x <= -1.3e+98) {
		tmp = (y * i) + (b * Math.log(c));
	} else if (x <= 3.8e+173) {
		tmp = (Math.log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -6.4e+152:
		tmp = (t_1 + z) + (t + a)
	elif x <= -1.3e+98:
		tmp = (y * i) + (b * math.log(c))
	elif x <= 3.8e+173:
		tmp = (math.log(c) * (b + -0.5)) + (z + a)
	else:
		tmp = t_1 + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -6.4e+152)
		tmp = Float64(Float64(t_1 + z) + Float64(t + a));
	elseif (x <= -1.3e+98)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	elseif (x <= 3.8e+173)
		tmp = Float64(Float64(log(c) * Float64(b + -0.5)) + Float64(z + a));
	else
		tmp = Float64(t_1 + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -6.4e+152)
		tmp = (t_1 + z) + (t + a);
	elseif (x <= -1.3e+98)
		tmp = (y * i) + (b * log(c));
	elseif (x <= 3.8e+173)
		tmp = (log(c) * (b + -0.5)) + (z + a);
	else
		tmp = t_1 + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+152], N[(N[(t$95$1 + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e+98], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+173], N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.40000000000000011e152

   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

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 91.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-commutative N/A

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

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

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

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

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

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

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

       8. +-lowering-+.f64 76.8%

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

   11. Simplified 76.8%

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

   if -6.40000000000000011e152 < x < -1.3e98

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 85.6%

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

   5. Simplified 85.6%

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

   if -1.3e98 < x < 3.80000000000000011e173

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 75.1%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 57.9%

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

   8. Simplified 57.9%

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

   if 3.80000000000000011e173 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 81.6%

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

   5. Simplified 81.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+152}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+98}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+173}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.5e+159)
   (+ (+ (* x (log y)) z) (+ t a))
   (if (<= x 1.9e+167)
     (+ (* y i) (+ (* (- b 0.5) (log c)) (+ z a)))
     (* x (+ (log y) (/ (+ z (* y i)) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.5e+159) {
		tmp = ((x * log(y)) + z) + (t + a);
	} else if (x <= 1.9e+167) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	} else {
		tmp = x * (log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-2.5d+159)) then
        tmp = ((x * log(y)) + z) + (t + a)
    else if (x <= 1.9d+167) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (z + a))
    else
        tmp = x * (log(y) + ((z + (y * i)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.5e+159) {
		tmp = ((x * Math.log(y)) + z) + (t + a);
	} else if (x <= 1.9e+167) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (z + a));
	} else {
		tmp = x * (Math.log(y) + ((z + (y * i)) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -2.5e+159:
		tmp = ((x * math.log(y)) + z) + (t + a)
	elif x <= 1.9e+167:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (z + a))
	else:
		tmp = x * (math.log(y) + ((z + (y * i)) / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.5e+159)
		tmp = Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a));
	elseif (x <= 1.9e+167)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(z + a)));
	else
		tmp = Float64(x * Float64(log(y) + Float64(Float64(z + Float64(y * i)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -2.5e+159)
		tmp = ((x * log(y)) + z) + (t + a);
	elseif (x <= 1.9e+167)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	else
		tmp = x * (log(y) + ((z + (y * i)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.5e+159], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+167], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.50000000000000002e159

   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

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 91.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-commutative N/A

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

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

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

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

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

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

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

       8. +-lowering-+.f64 76.8%

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

   11. Simplified 76.8%

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

   if -2.50000000000000002e159 < x < 1.89999999999999997e167

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 75.8%

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

   if 1.89999999999999997e167 < 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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 65.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 65.8%

      \[\leadsto \left(\color{blue}{\frac{x \cdot \log y}{z}} + 1\right) \cdot z + y \cdot i \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)\right)} \]

       3. distribute-lft-out N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(-1 \cdot \left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right)\right)\right) \]

       5. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 88.7%

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

   11. Simplified 88.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+167}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+179}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+114}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -9.5e+179)
   (+ (* y i) (* z (+ (/ a z) 1.0)))
   (if (<= z -7.8e+114)
     (+ (+ (* x (log y)) z) (+ t a))
     (+ (* y i) (+ a (* (- b 0.5) (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9.5e+179) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (z <= -7.8e+114) {
		tmp = ((x * log(y)) + z) + (t + a);
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-9.5d+179)) then
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    else if (z <= (-7.8d+114)) then
        tmp = ((x * log(y)) + z) + (t + a)
    else
        tmp = (y * i) + (a + ((b - 0.5d0) * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9.5e+179) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (z <= -7.8e+114) {
		tmp = ((x * Math.log(y)) + z) + (t + a);
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -9.5e+179:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	elif z <= -7.8e+114:
		tmp = ((x * math.log(y)) + z) + (t + a)
	else:
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -9.5e+179)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	elseif (z <= -7.8e+114)
		tmp = Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -9.5e+179)
		tmp = (y * i) + (z * ((a / z) + 1.0));
	elseif (z <= -7.8e+114)
		tmp = ((x * log(y)) + z) + (t + a);
	else
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -9.5e+179], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e+114], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5e179

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 70.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(a, z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 70.1%

      \[\leadsto \left(\color{blue}{\frac{a}{z}} + 1\right) \cdot z + y \cdot i \]

   if -9.5e179 < z < -7.8000000000000001e114

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. log-lowering-log.f64 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in b around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-commutative N/A

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

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

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

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

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

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

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

       8. +-lowering-+.f64 88.2%

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

   11. Simplified 88.2%

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

   if -7.8000000000000001e114 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 58.5%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+179}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+114}:\\ \;\;\;\;\left(x \cdot \log y + z\right) + \left(t + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+167}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (+ (log y) (/ (+ z (* y i)) x)))))
   (if (<= x -4.5e+97)
     t_1
     (if (<= x 6.5e+167) (+ (* (log c) (+ b -0.5)) (+ z a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (log(y) + ((z + (y * i)) / x));
	double tmp;
	if (x <= -4.5e+97) {
		tmp = t_1;
	} else if (x <= 6.5e+167) {
		tmp = (log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (log(y) + ((z + (y * i)) / x))
    if (x <= (-4.5d+97)) then
        tmp = t_1
    else if (x <= 6.5d+167) then
        tmp = (log(c) * (b + (-0.5d0))) + (z + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (Math.log(y) + ((z + (y * i)) / x));
	double tmp;
	if (x <= -4.5e+97) {
		tmp = t_1;
	} else if (x <= 6.5e+167) {
		tmp = (Math.log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * (math.log(y) + ((z + (y * i)) / x))
	tmp = 0
	if x <= -4.5e+97:
		tmp = t_1
	elif x <= 6.5e+167:
		tmp = (math.log(c) * (b + -0.5)) + (z + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * Float64(log(y) + Float64(Float64(z + Float64(y * i)) / x)))
	tmp = 0.0
	if (x <= -4.5e+97)
		tmp = t_1;
	elseif (x <= 6.5e+167)
		tmp = Float64(Float64(log(c) * Float64(b + -0.5)) + Float64(z + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * (log(y) + ((z + (y * i)) / x));
	tmp = 0.0;
	if (x <= -4.5e+97)
		tmp = t_1;
	elseif (x <= 6.5e+167)
		tmp = (log(c) * (b + -0.5)) + (z + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+97], t$95$1, If[LessEqual[x, 6.5e+167], N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999976e97 or 6.5e167 < 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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 67.5%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 54.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 54.8%

      \[\leadsto \left(\color{blue}{\frac{x \cdot \log y}{z}} + 1\right) \cdot z + y \cdot i \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \log y + -1 \cdot \frac{z + i \cdot y}{x}\right)\right)\right)} \]

       3. distribute-lft-out N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(-1 \cdot \left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto x \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\left(\log y + \frac{z + i \cdot y}{x}\right)\right)\right)\right)\right) \]

       5. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 76.4%

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

   11. Simplified 76.4%

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

   if -4.49999999999999976e97 < x < 6.5e167

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 74.9%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 57.7%

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

   8. Simplified 57.7%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+167}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z + y \cdot i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + y \cdot i\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+173}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (* y i))))
   (if (<= x -2.8e+147)
     t_1
     (if (<= x 1.55e+173) (+ (* (log c) (+ b -0.5)) (+ z a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + (y * i);
	double tmp;
	if (x <= -2.8e+147) {
		tmp = t_1;
	} else if (x <= 1.55e+173) {
		tmp = (log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) + (y * i)
    if (x <= (-2.8d+147)) then
        tmp = t_1
    else if (x <= 1.55d+173) then
        tmp = (log(c) * (b + (-0.5d0))) + (z + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * Math.log(y)) + (y * i);
	double tmp;
	if (x <= -2.8e+147) {
		tmp = t_1;
	} else if (x <= 1.55e+173) {
		tmp = (Math.log(c) * (b + -0.5)) + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + (y * i)
	tmp = 0
	if x <= -2.8e+147:
		tmp = t_1
	elif x <= 1.55e+173:
		tmp = (math.log(c) * (b + -0.5)) + (z + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + Float64(y * i))
	tmp = 0.0
	if (x <= -2.8e+147)
		tmp = t_1;
	elseif (x <= 1.55e+173)
		tmp = Float64(Float64(log(c) * Float64(b + -0.5)) + Float64(z + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + (y * i);
	tmp = 0.0;
	if (x <= -2.8e+147)
		tmp = t_1;
	elseif (x <= 1.55e+173)
		tmp = (log(c) * (b + -0.5)) + (z + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+147], t$95$1, If[LessEqual[x, 1.55e+173], N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e147 or 1.55e173 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 74.2%

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

   5. Simplified 74.2%

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

   if -2.8000000000000001e147 < x < 1.55e173

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 75.6%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-lowering-+.f64 57.0%

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

   8. Simplified 57.0%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+173}:\\ \;\;\;\;\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+40}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.06e+40)
   (+ (* y i) (* z (+ (/ a z) 1.0)))
   (if (<= z -1.12e-172) (+ (* x (log y)) a) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.06e+40) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (z <= -1.12e-172) {
		tmp = (x * log(y)) + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.06d+40)) then
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    else if (z <= (-1.12d-172)) then
        tmp = (x * log(y)) + a
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.06e+40) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (z <= -1.12e-172) {
		tmp = (x * Math.log(y)) + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.06e+40:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	elif z <= -1.12e-172:
		tmp = (x * math.log(y)) + a
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.06e+40)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	elseif (z <= -1.12e-172)
		tmp = Float64(Float64(x * log(y)) + a);
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.06e+40)
		tmp = (y * i) + (z * ((a / z) + 1.0));
	elseif (z <= -1.12e-172)
		tmp = (x * log(y)) + a;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.06e+40], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e-172], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05999999999999996e40

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 57.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(a, z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 57.4%

      \[\leadsto \left(\color{blue}{\frac{a}{z}} + 1\right) \cdot z + y \cdot i \]

   if -1.05999999999999996e40 < z < -1.11999999999999996e-172

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. cancel-sign-sub N/A

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

      4. log-rec N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-+r+ N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 84.4%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 41.5%

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

   if -1.11999999999999996e-172 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 41.4%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+40}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+38}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.95e+38)
   (+ (* y i) (* z (+ (/ a z) 1.0)))
   (if (<= z -8.5e+23) (* x (log y)) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.95e+38) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (z <= -8.5e+23) {
		tmp = x * log(y);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.95d+38)) then
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    else if (z <= (-8.5d+23)) then
        tmp = x * log(y)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.95e+38) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (z <= -8.5e+23) {
		tmp = x * Math.log(y);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.95e+38:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	elif z <= -8.5e+23:
		tmp = x * math.log(y)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.95e+38)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	elseif (z <= -8.5e+23)
		tmp = Float64(x * log(y));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.95e+38)
		tmp = (y * i) + (z * ((a / z) + 1.0));
	elseif (z <= -8.5e+23)
		tmp = x * log(y);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.95e+38], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e+23], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95000000000000012e38

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 57.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(a, z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 57.4%

      \[\leadsto \left(\color{blue}{\frac{a}{z}} + 1\right) \cdot z + y \cdot i \]

   if -1.95000000000000012e38 < z < -8.5000000000000001e23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. log-lowering-log.f64 39.8%

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

   5. Simplified 39.8%

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

   if -8.5000000000000001e23 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 39.3%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+38}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.8% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+48}:\\ \;\;\;\;t + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 6.2e-140)
   (+ t a)
   (if (<= y 5.2e-96) z (if (<= y 6.5e+48) (+ t a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 6.2e-140) {
		tmp = t + a;
	} else if (y <= 5.2e-96) {
		tmp = z;
	} else if (y <= 6.5e+48) {
		tmp = t + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 6.2d-140) then
        tmp = t + a
    else if (y <= 5.2d-96) then
        tmp = z
    else if (y <= 6.5d+48) then
        tmp = t + a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 6.2e-140) {
		tmp = t + a;
	} else if (y <= 5.2e-96) {
		tmp = z;
	} else if (y <= 6.5e+48) {
		tmp = t + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 6.2e-140:
		tmp = t + a
	elif y <= 5.2e-96:
		tmp = z
	elif y <= 6.5e+48:
		tmp = t + a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 6.2e-140)
		tmp = Float64(t + a);
	elseif (y <= 5.2e-96)
		tmp = z;
	elseif (y <= 6.5e+48)
		tmp = Float64(t + a);
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 6.2e-140)
		tmp = t + a;
	elseif (y <= 5.2e-96)
		tmp = z;
	elseif (y <= 6.5e+48)
		tmp = t + a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 6.2e-140], N[(t + a), $MachinePrecision], If[LessEqual[y, 5.2e-96], z, If[LessEqual[y, 6.5e+48], N[(t + a), $MachinePrecision], N[(y * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.1999999999999998e-140 or 5.2000000000000003e-96 < y < 6.49999999999999972e48

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

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

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

      6. /-lowering-/.f64 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

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

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

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

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      16. /-lowering-/.f64 75.0%

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

   8. Simplified 75.0%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 44.3%

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

   if 6.1999999999999998e-140 < y < 5.2000000000000003e-96

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 28.2%

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

   if 6.49999999999999972e48 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 46.9%

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

   5. Simplified 46.9%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+48}:\\ \;\;\;\;t + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.1% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+14}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.35e+14) (+ (* y i) (* z (+ (/ a z) 1.0))) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.35e+14) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.35d+14)) then
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.35e+14) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.35e+14:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.35e+14)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.35e+14)
		tmp = (y * i) + (z * ((a / z) + 1.0));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.35e+14], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.35e14

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft1-in N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

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

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\frac{\left(\log c \cdot \left(b + -0.5\right) + x \cdot \log y\right) + \left(a + t\right)}{z} + 1\right) \cdot z} + y \cdot i \]

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 55.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(a, z\right), 1\right), z\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   8. Simplified 55.0%

      \[\leadsto \left(\color{blue}{\frac{a}{z}} + 1\right) \cdot z + y \cdot i \]

   if -2.35e14 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 39.2%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+14}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.8% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.6 \cdot 10^{+47}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+98}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 7.6e+47) (+ z a) (if (<= y 3.6e+98) (+ a (* y i)) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 7.6e+47) {
		tmp = z + a;
	} else if (y <= 3.6e+98) {
		tmp = a + (y * i);
	} else {
		tmp = z + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 7.6d+47) then
        tmp = z + a
    else if (y <= 3.6d+98) then
        tmp = a + (y * i)
    else
        tmp = z + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 7.6e+47) {
		tmp = z + a;
	} else if (y <= 3.6e+98) {
		tmp = a + (y * i);
	} else {
		tmp = z + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 7.6e+47:
		tmp = z + a
	elif y <= 3.6e+98:
		tmp = a + (y * i)
	else:
		tmp = z + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 7.6e+47)
		tmp = Float64(z + a);
	elseif (y <= 3.6e+98)
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(z + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 7.6e+47)
		tmp = z + a;
	elseif (y <= 3.6e+98)
		tmp = a + (y * i);
	else
		tmp = z + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 7.6e+47], N[(z + a), $MachinePrecision], If[LessEqual[y, 3.6e+98], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.6000000000000007e47

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

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

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

      6. /-lowering-/.f64 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

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

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

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

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      16. /-lowering-/.f64 75.6%

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

   8. Simplified 75.6%

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

   9. Taylor expanded in z around inf

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

   11. Simplified 38.9%

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

   if 7.6000000000000007e47 < y < 3.59999999999999981e98

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 44.3%

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

   if 3.59999999999999981e98 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 54.7%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.6 \cdot 10^{+47}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+98}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.4% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-140}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 2.4e-140) a (if (<= y 4.7e+48) z (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 2.4e-140) {
		tmp = a;
	} else if (y <= 4.7e+48) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 2.4d-140) then
        tmp = a
    else if (y <= 4.7d+48) then
        tmp = z
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 2.4e-140) {
		tmp = a;
	} else if (y <= 4.7e+48) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 2.4e-140:
		tmp = a
	elif y <= 4.7e+48:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 2.4e-140)
		tmp = a;
	elseif (y <= 4.7e+48)
		tmp = z;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 2.4e-140)
		tmp = a;
	elseif (y <= 4.7e+48)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 2.4e-140], a, If[LessEqual[y, 4.7e+48], z, N[(y * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.39999999999999987e-140

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 25.9%

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

   if 2.39999999999999987e-140 < y < 4.70000000000000012e48

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 19.5%

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

   if 4.70000000000000012e48 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 46.9%

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

   5. Simplified 46.9%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-140}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.05e+48) (+ z a) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.05e+48) {
		tmp = z + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 1.05d+48) then
        tmp = z + a
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.05e+48) {
		tmp = z + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.05e+48:
		tmp = z + a
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.05e+48)
		tmp = Float64(z + a);
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.05e+48)
		tmp = z + a;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.05e+48], N[(z + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.0499999999999999e48

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

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

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

      6. /-lowering-/.f64 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), \left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right), \left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)}\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \left(\log y + \left(\frac{z}{x} + \color{blue}{\frac{t}{x}}\right)\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \left(\left(\log y + \frac{z}{x}\right) + \color{blue}{\frac{t}{x}}\right)\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\log y + \frac{z}{x}\right), \color{blue}{\left(\frac{t}{x}\right)}\right)\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\log y, \left(\frac{z}{x}\right)\right), \left(\frac{\color{blue}{t}}{x}\right)\right)\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \left(\frac{z}{x}\right)\right), \left(\frac{t}{x}\right)\right)\right)\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(z, x\right)\right), \left(\frac{t}{x}\right)\right)\right)\right)\right) \]

      16. /-lowering-/.f64 75.6%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(z, x\right)\right), \mathsf{/.f64}\left(t, \color{blue}{x}\right)\right)\right)\right)\right) \]

   8. Simplified 75.6%

      \[\leadsto \color{blue}{a + \left(\log c \cdot \left(b + -0.5\right) + x \cdot \left(\left(\log y + \frac{z}{x}\right) + \frac{t}{x}\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{z}\right) \]
   10. Step-by-step derivation

   11. Simplified 38.9%

       \[\leadsto a + \color{blue}{z} \]

   if 1.0499999999999999e48 < y

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 52.7%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.3% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{+49}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 8.8e+49) (+ 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 (y <= 8.8e+49) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 8.8d+49) then
        tmp = z + a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 8.8e+49) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 8.8e+49:
		tmp = z + a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 8.8e+49)
		tmp = Float64(z + a);
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 8.8e+49)
		tmp = z + a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 8.8e+49], N[(z + a), $MachinePrecision], N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.8000000000000003e49

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)}, a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right), a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\log y, \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right), a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right), a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{+.f64}\left(\left(\frac{t}{x}\right), \left(\frac{z}{x}\right)\right)\right)\right), a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, x\right), \left(\frac{z}{x}\right)\right)\right)\right), a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

      6. /-lowering-/.f64 78.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, x\right), \mathsf{/.f64}\left(z, x\right)\right)\right)\right), a\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(b, \frac{1}{2}\right), \mathsf{log.f64}\left(c\right)\right)\right), \mathsf{*.f64}\left(y, i\right)\right) \]

   5. Simplified 78.3%

      \[\leadsto \left(\left(\color{blue}{x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a + \left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right) + \log c \cdot \left(b - \frac{1}{2}\right)\right)} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right) + \log c \cdot \left(b - \frac{1}{2}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(\log c \cdot \left(b - \frac{1}{2}\right) + \color{blue}{x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\left(\log c \cdot \left(b - \frac{1}{2}\right)\right), \color{blue}{\left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\log c, \left(b - \frac{1}{2}\right)\right), \left(\color{blue}{x} \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)\right)\right) \]

      5. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b - \frac{1}{2}\right)\right), \left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), \left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \left(b + \frac{-1}{2}\right)\right), \left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \left(x \cdot \left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\log y + \left(\frac{t}{x} + \frac{z}{x}\right)\right)}\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \left(\log y + \left(\frac{z}{x} + \color{blue}{\frac{t}{x}}\right)\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \left(\left(\log y + \frac{z}{x}\right) + \color{blue}{\frac{t}{x}}\right)\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\log y + \frac{z}{x}\right), \color{blue}{\left(\frac{t}{x}\right)}\right)\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\log y, \left(\frac{z}{x}\right)\right), \left(\frac{\color{blue}{t}}{x}\right)\right)\right)\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \left(\frac{z}{x}\right)\right), \left(\frac{t}{x}\right)\right)\right)\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(z, x\right)\right), \left(\frac{t}{x}\right)\right)\right)\right)\right) \]

      16. /-lowering-/.f64 75.7%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(c\right), \mathsf{+.f64}\left(b, \frac{-1}{2}\right)\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{log.f64}\left(y\right), \mathsf{/.f64}\left(z, x\right)\right), \mathsf{/.f64}\left(t, \color{blue}{x}\right)\right)\right)\right)\right) \]

   8. Simplified 75.7%

      \[\leadsto \color{blue}{a + \left(\log c \cdot \left(b + -0.5\right) + x \cdot \left(\left(\log y + \frac{z}{x}\right) + \frac{t}{x}\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{z}\right) \]
   10. Step-by-step derivation

   11. Simplified 39.2%

       \[\leadsto a + \color{blue}{z} \]

   if 8.8000000000000003e49 < y

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{i \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 46.9%

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{y}\right) \]

   5. Simplified 46.9%

      \[\leadsto \color{blue}{i \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{+49}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.7% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -1.75e+48) 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 <= -1.75e+48) {
		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 <= (-1.75d+48)) 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 <= -1.75e+48) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.75e+48:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.75e+48)
		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 <= -1.75e+48)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.75e+48], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -1.7499999999999999e48

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   4. Step-by-step derivation

   5. Simplified 32.1%

      \[\leadsto \color{blue}{z} \]

   if -1.7499999999999999e48 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a} \]
   4. Step-by-step derivation

   5. Simplified 18.9%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 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 99.8%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a} \]
4. Step-by-step derivation

5. Simplified 16.9%

   \[\leadsto \color{blue}{a} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(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)))