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

Percentage Accurate: 99.8% → 99.8%

Time: 22.0s

Alternatives: 18

Speedup: 1.0×

• could not determine a ground truth

  1. x = -1.0437259775658254e+185
  2. y = 1.3933104988786059e+205
  3. z = 1.650551393592646e-254
  4. t = -1.7861746031288825e+296
  5. a = -2.3624898555359886e+296
  6. b = -3.464758063195252e-162
  7. c = 7.771992859020222e+22
  8. i = -1.312012248726626e-184

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

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ a (+ t (+ (* x (log y)) z))) (* (- 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 ((a + (t + ((x * log(y)) + z))) + ((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 = ((a + (t + ((x * log(y)) + z))) + ((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 ((a + (t + ((x * Math.log(y)) + z))) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $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. Final simplification 99.8%

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

Alternative 2: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+177}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= t_1 -5e+177)
     (+ (* y i) (+ a t_1))
     (if (<= t_1 2e+153)
       (+ (+ a (+ t (+ (* x (log y)) z))) (* y i))
       (+ (* y i) (+ t_1 (+ t a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if (t_1 <= -5e+177) {
		tmp = (y * i) + (a + t_1);
	} else if (t_1 <= 2e+153) {
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	} else {
		tmp = (y * i) + (t_1 + (t + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if (t_1 <= (-5d+177)) then
        tmp = (y * i) + (a + t_1)
    else if (t_1 <= 2d+153) then
        tmp = (a + (t + ((x * log(y)) + z))) + (y * i)
    else
        tmp = (y * i) + (t_1 + (t + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if (t_1 <= -5e+177) {
		tmp = (y * i) + (a + t_1);
	} else if (t_1 <= 2e+153) {
		tmp = (a + (t + ((x * Math.log(y)) + z))) + (y * i);
	} else {
		tmp = (y * i) + (t_1 + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if t_1 <= -5e+177:
		tmp = (y * i) + (a + t_1)
	elif t_1 <= 2e+153:
		tmp = (a + (t + ((x * math.log(y)) + z))) + (y * i)
	else:
		tmp = (y * i) + (t_1 + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (t_1 <= -5e+177)
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	elseif (t_1 <= 2e+153)
		tmp = Float64(Float64(a + Float64(t + Float64(Float64(x * log(y)) + z))) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (t_1 <= -5e+177)
		tmp = (y * i) + (a + t_1);
	elseif (t_1 <= 2e+153)
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	else
		tmp = (y * i) + (t_1 + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+177], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+153], N[(N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -5.0000000000000003e177

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 89.9%

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

      1. +-commutative 89.9%

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

      2. sub-neg 89.9%

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

      3. metadata-eval 89.9%

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

      4. +-commutative 89.9%

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

      5. fma-define 89.9%

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

      6. +-commutative 89.9%

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

      7. +-commutative 89.9%

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

   5. Applied egg-rr 89.9%

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

   6. Taylor expanded in t around 0 86.5%

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

   7. Taylor expanded in z around 0 80.0%

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

   if -5.0000000000000003e177 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 2e153

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 96.8%

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

      1. *-commutative 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in b around 0 92.7%

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

   if 2e153 < (*.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 x around 0 95.4%

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

   4. Taylor expanded in z around 0 94.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b - 0.5\right) \cdot \log c \leq -5 \cdot 10^{+177}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;\left(b - 0.5\right) \cdot \log c \leq 2 \cdot 10^{+153}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + z\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+63}:\\ \;\;\;\;\left(a + \left(t + t\_1\right)\right) + y \cdot i\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) z)))
   (if (<= x -1.7e+63)
     (+ (+ a (+ t t_1)) (* y i))
     (if (<= x 1.05e+54)
       (+ (* y i) (+ t (+ z (fma (log c) (+ b -0.5) a))))
       (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + z;
	double tmp;
	if (x <= -1.7e+63) {
		tmp = (a + (t + t_1)) + (y * i);
	} else if (x <= 1.05e+54) {
		tmp = (y * i) + (t + (z + fma(log(c), (b + -0.5), a)));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + z)
	tmp = 0.0
	if (x <= -1.7e+63)
		tmp = Float64(Float64(a + Float64(t + t_1)) + Float64(y * i));
	elseif (x <= 1.05e+54)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + fma(log(c), Float64(b + -0.5), a))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -1.7e+63], N[(N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+54], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6999999999999999e63

   1. Initial program 99.6%

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

   3. Taylor expanded in b around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in b around 0 90.3%

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

   if -1.6999999999999999e63 < x < 1.04999999999999993e54

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 98.7%

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

      1. +-commutative 98.7%

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

      2. associate-+r+ 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

      5. associate-+r+ 98.7%

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

      6. associate-+l+ 98.7%

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

      7. fma-define 98.7%

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

      8. +-commutative 98.7%

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

   5. Simplified 98.7%

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

   if 1.04999999999999993e54 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 90.3%

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

   7. Taylor expanded in t around 0 73.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+63}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $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. Taylor expanded in b around inf 97.5%

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

   1. *-commutative 97.5%

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

5. Simplified 97.5%

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

6. Final simplification 97.5%

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

Alternative 5: 47.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + b \cdot \log c\\ \mathbf{if}\;a \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \left(1 + i \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* b (log c)))))
   (if (<= a 2.4e-196)
     (+ z (* y i))
     (if (<= a 6.7e-115)
       t_1
       (if (<= a 1.55e-104)
         (* z (+ 1.0 (* i (/ y z))))
         (if (<= a 2.2e+30)
           (+ (* x (log y)) (* y i))
           (if (<= a 9.8e+67)
             t_1
             (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ z a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (b * log(c));
	double tmp;
	if (a <= 2.4e-196) {
		tmp = z + (y * i);
	} else if (a <= 6.7e-115) {
		tmp = t_1;
	} else if (a <= 1.55e-104) {
		tmp = z * (1.0 + (i * (y / z)));
	} else if (a <= 2.2e+30) {
		tmp = (x * log(y)) + (y * i);
	} else if (a <= 9.8e+67) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (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 = (y * i) + (b * log(c))
    if (a <= 2.4d-196) then
        tmp = z + (y * i)
    else if (a <= 6.7d-115) then
        tmp = t_1
    else if (a <= 1.55d-104) then
        tmp = z * (1.0d0 + (i * (y / z)))
    else if (a <= 2.2d+30) then
        tmp = (x * log(y)) + (y * i)
    else if (a <= 9.8d+67) then
        tmp = t_1
    else
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (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 = (y * i) + (b * Math.log(c));
	double tmp;
	if (a <= 2.4e-196) {
		tmp = z + (y * i);
	} else if (a <= 6.7e-115) {
		tmp = t_1;
	} else if (a <= 1.55e-104) {
		tmp = z * (1.0 + (i * (y / z)));
	} else if (a <= 2.2e+30) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if (a <= 9.8e+67) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (b * math.log(c))
	tmp = 0
	if a <= 2.4e-196:
		tmp = z + (y * i)
	elif a <= 6.7e-115:
		tmp = t_1
	elif a <= 1.55e-104:
		tmp = z * (1.0 + (i * (y / z)))
	elif a <= 2.2e+30:
		tmp = (x * math.log(y)) + (y * i)
	elif a <= 9.8e+67:
		tmp = t_1
	else:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(b * log(c)))
	tmp = 0.0
	if (a <= 2.4e-196)
		tmp = Float64(z + Float64(y * i));
	elseif (a <= 6.7e-115)
		tmp = t_1;
	elseif (a <= 1.55e-104)
		tmp = Float64(z * Float64(1.0 + Float64(i * Float64(y / z))));
	elseif (a <= 2.2e+30)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (a <= 9.8e+67)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (b * log(c));
	tmp = 0.0;
	if (a <= 2.4e-196)
		tmp = z + (y * i);
	elseif (a <= 6.7e-115)
		tmp = t_1;
	elseif (a <= 1.55e-104)
		tmp = z * (1.0 + (i * (y / z)));
	elseif (a <= 2.2e+30)
		tmp = (x * log(y)) + (y * i);
	elseif (a <= 9.8e+67)
		tmp = t_1;
	else
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	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[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 2.4e-196], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.7e-115], t$95$1, If[LessEqual[a, 1.55e-104], N[(z * N[(1.0 + N[(i * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+30], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.8e+67], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < 2.40000000000000021e-196

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 38.0%

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

   if 2.40000000000000021e-196 < a < 6.7000000000000002e-115 or 2.2e30 < a < 9.7999999999999998e67

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. sub-neg 85.1%

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

      3. metadata-eval 85.1%

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

      4. +-commutative 85.1%

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

      5. fma-define 85.1%

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

      6. +-commutative 85.1%

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

      7. +-commutative 85.1%

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

   5. Applied egg-rr 85.1%

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

   6. Taylor expanded in b around inf 54.6%

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

      1. *-commutative 54.6%

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

   8. Simplified 54.6%

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

   if 6.7000000000000002e-115 < a < 1.54999999999999988e-104

   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 1.7%

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

   4. Taylor expanded in z around inf 1.7%

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

      1. associate-/l* 1.7%

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

   6. Simplified 1.7%

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

   if 1.54999999999999988e-104 < a < 2.2e30

   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 42.9%

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

   if 9.7999999999999998e67 < a

   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 99.8%

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

      1. associate-/l* 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-/l* 99.7%

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

      5. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 74.0%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-115}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \left(1 + i \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+67}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+63}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq -7.1 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(1 + i \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ a (* (- b 0.5) (log c))))))
   (if (<= x -1.7e+63)
     (+ (* y i) (* x (+ (log y) (/ a x))))
     (if (<= x -7.1e-156)
       t_1
       (if (<= x -6e-261)
         (* z (+ 1.0 (* i (/ y z))))
         (if (<= x 2.7e+159) t_1 (+ (* y i) (* x (+ (log y) (/ z x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + ((b - 0.5) * log(c)));
	double tmp;
	if (x <= -1.7e+63) {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	} else if (x <= -7.1e-156) {
		tmp = t_1;
	} else if (x <= -6e-261) {
		tmp = z * (1.0 + (i * (y / z)));
	} else if (x <= 2.7e+159) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (x * (log(y) + (z / 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 = (y * i) + (a + ((b - 0.5d0) * log(c)))
    if (x <= (-1.7d+63)) then
        tmp = (y * i) + (x * (log(y) + (a / x)))
    else if (x <= (-7.1d-156)) then
        tmp = t_1
    else if (x <= (-6d-261)) then
        tmp = z * (1.0d0 + (i * (y / z)))
    else if (x <= 2.7d+159) then
        tmp = t_1
    else
        tmp = (y * i) + (x * (log(y) + (z / 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 = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	double tmp;
	if (x <= -1.7e+63) {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	} else if (x <= -7.1e-156) {
		tmp = t_1;
	} else if (x <= -6e-261) {
		tmp = z * (1.0 + (i * (y / z)));
	} else if (x <= 2.7e+159) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (x * (Math.log(y) + (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (a + ((b - 0.5) * math.log(c)))
	tmp = 0
	if x <= -1.7e+63:
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	elif x <= -7.1e-156:
		tmp = t_1
	elif x <= -6e-261:
		tmp = z * (1.0 + (i * (y / z)))
	elif x <= 2.7e+159:
		tmp = t_1
	else:
		tmp = (y * i) + (x * (math.log(y) + (z / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))))
	tmp = 0.0
	if (x <= -1.7e+63)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	elseif (x <= -7.1e-156)
		tmp = t_1;
	elseif (x <= -6e-261)
		tmp = Float64(z * Float64(1.0 + Float64(i * Float64(y / z))));
	elseif (x <= 2.7e+159)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (a + ((b - 0.5) * log(c)));
	tmp = 0.0;
	if (x <= -1.7e+63)
		tmp = (y * i) + (x * (log(y) + (a / x)));
	elseif (x <= -7.1e-156)
		tmp = t_1;
	elseif (x <= -6e-261)
		tmp = z * (1.0 + (i * (y / z)));
	elseif (x <= 2.7e+159)
		tmp = t_1;
	else
		tmp = (y * i) + (x * (log(y) + (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+63], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.1e-156], t$95$1, If[LessEqual[x, -6e-261], N[(z * N[(1.0 + N[(i * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+159], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6999999999999999e63

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. associate-/l* 99.5%

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

      4. +-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in a around inf 74.9%

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

   if -1.6999999999999999e63 < x < -7.1000000000000005e-156 or -6.0000000000000001e-261 < x < 2.70000000000000008e159

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 97.4%

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

      1. +-commutative 97.4%

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

      2. sub-neg 97.4%

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

      3. metadata-eval 97.4%

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

      4. +-commutative 97.4%

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

      5. fma-define 97.4%

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

      6. +-commutative 97.4%

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

      7. +-commutative 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in t around 0 82.8%

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

   7. Taylor expanded in z around 0 68.9%

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

   if -7.1000000000000005e-156 < x < -6.0000000000000001e-261

   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 57.3%

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

   4. Taylor expanded in z around inf 57.3%

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

      1. associate-/l* 57.4%

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

   6. Simplified 57.4%

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

   if 2.70000000000000008e159 < 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 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-/l* 99.8%

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

      4. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 78.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+63}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq -7.1 \cdot 10^{-156}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(1 + i \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+159}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+154} \lor \neg \left(b - 0.5 \leq 10^{+148}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -1e+154) (not (<= (- b 0.5) 1e+148)))
   (+ (* y i) (+ a (* (- b 0.5) (log c))))
   (+ (+ a (+ t (+ (* x (log y)) z))) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -1e+154) || !((b - 0.5) <= 1e+148)) {
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	} else {
		tmp = (a + (t + ((x * log(y)) + 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 (((b - 0.5d0) <= (-1d+154)) .or. (.not. ((b - 0.5d0) <= 1d+148))) then
        tmp = (y * i) + (a + ((b - 0.5d0) * log(c)))
    else
        tmp = (a + (t + ((x * log(y)) + 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 (((b - 0.5) <= -1e+154) || !((b - 0.5) <= 1e+148)) {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = (a + (t + ((x * Math.log(y)) + z))) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -1e+154) or not ((b - 0.5) <= 1e+148):
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	else:
		tmp = (a + (t + ((x * math.log(y)) + z))) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -1e+154) || !(Float64(b - 0.5) <= 1e+148))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	else
		tmp = Float64(Float64(a + Float64(t + Float64(Float64(x * log(y)) + 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 (((b - 0.5) <= -1e+154) || ~(((b - 0.5) <= 1e+148)))
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	else
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+154], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+148]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -1.00000000000000004e154 or 1e148 < (-.f64 b #s(literal 1/2 binary64))

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 92.7%

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

      1. +-commutative 92.7%

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

      2. sub-neg 92.7%

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

      3. metadata-eval 92.7%

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

      4. +-commutative 92.7%

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

      5. fma-define 92.7%

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

      6. +-commutative 92.7%

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

      7. +-commutative 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in t around 0 87.6%

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

   7. Taylor expanded in z around 0 84.3%

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

   if -1.00000000000000004e154 < (-.f64 b #s(literal 1/2 binary64)) < 1e148

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 96.8%

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

      1. *-commutative 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in b around 0 92.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+154} \lor \neg \left(b - 0.5 \leq 10^{+148}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-182}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \mathbf{elif}\;x \leq 0.78:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* x (+ (log y) (/ a x))))))
   (if (<= x -2e+88)
     t_1
     (if (<= x 2.55e-182)
       (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ z a)))))
       (if (<= x 0.78) (+ (* y i) (* b (log c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (x * (log(y) + (a / x)));
	double tmp;
	if (x <= -2e+88) {
		tmp = t_1;
	} else if (x <= 2.55e-182) {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	} else if (x <= 0.78) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (x * (log(y) + (a / x)))
    if (x <= (-2d+88)) then
        tmp = t_1
    else if (x <= 2.55d-182) then
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (z / a))))
    else if (x <= 0.78d0) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (x * (Math.log(y) + (a / x)));
	double tmp;
	if (x <= -2e+88) {
		tmp = t_1;
	} else if (x <= 2.55e-182) {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	} else if (x <= 0.78) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (x * (math.log(y) + (a / x)))
	tmp = 0
	if x <= -2e+88:
		tmp = t_1
	elif x <= 2.55e-182:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	elif x <= 0.78:
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))))
	tmp = 0.0
	if (x <= -2e+88)
		tmp = t_1;
	elseif (x <= 2.55e-182)
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	elseif (x <= 0.78)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (x * (log(y) + (a / x)));
	tmp = 0.0;
	if (x <= -2e+88)
		tmp = t_1;
	elseif (x <= 2.55e-182)
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	elseif (x <= 0.78)
		tmp = (y * i) + (b * log(c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+88], t$95$1, If[LessEqual[x, 2.55e-182], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.78], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.99999999999999992e88 or 0.78000000000000003 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. associate-/l* 99.6%

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

      4. +-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in a around inf 65.0%

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

   if -1.99999999999999992e88 < x < 2.55000000000000009e-182

   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 81.9%

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

      1. associate-/l* 81.9%

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

      2. sub-neg 81.9%

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

      3. metadata-eval 81.9%

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

      4. associate-/l* 81.9%

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

      5. +-commutative 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in z around inf 65.2%

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

   if 2.55000000000000009e-182 < x < 0.78000000000000003

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-define 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in b around inf 61.0%

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

      1. *-commutative 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+88}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-182}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \mathbf{elif}\;x \leq 0.78:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+154} \lor \neg \left(b - 0.5 \leq 10^{+148}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -1e+154) (not (<= (- b 0.5) 1e+148)))
   (+ (* y i) (+ a (* (- b 0.5) (log c))))
   (+ (* y i) (+ a (+ (* x (log y)) z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -1e+154) || !((b - 0.5) <= 1e+148)) {
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	} else {
		tmp = (y * i) + (a + ((x * log(y)) + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-1d+154)) .or. (.not. ((b - 0.5d0) <= 1d+148))) then
        tmp = (y * i) + (a + ((b - 0.5d0) * log(c)))
    else
        tmp = (y * i) + (a + ((x * log(y)) + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -1e+154) || !((b - 0.5) <= 1e+148)) {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = (y * i) + (a + ((x * Math.log(y)) + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -1e+154) or not ((b - 0.5) <= 1e+148):
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	else:
		tmp = (y * i) + (a + ((x * math.log(y)) + z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -1e+154) || !(Float64(b - 0.5) <= 1e+148))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -1e+154) || ~(((b - 0.5) <= 1e+148)))
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	else
		tmp = (y * i) + (a + ((x * log(y)) + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+154], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+148]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -1.00000000000000004e154 or 1e148 < (-.f64 b #s(literal 1/2 binary64))

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 92.7%

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

      1. +-commutative 92.7%

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

      2. sub-neg 92.7%

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

      3. metadata-eval 92.7%

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

      4. +-commutative 92.7%

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

      5. fma-define 92.7%

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

      6. +-commutative 92.7%

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

      7. +-commutative 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in t around 0 87.6%

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

   7. Taylor expanded in z around 0 84.3%

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

   if -1.00000000000000004e154 < (-.f64 b #s(literal 1/2 binary64)) < 1e148

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 96.8%

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

      1. *-commutative 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in b around 0 92.6%

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

   7. Taylor expanded in t around 0 77.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+154} \lor \neg \left(b - 0.5 \leq 10^{+148}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + z\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{+63}:\\ \;\;\;\;\left(a + \left(t + t\_1\right)\right) + y \cdot i\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+53}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) z)))
   (if (<= x -1.12e+63)
     (+ (+ a (+ t t_1)) (* y i))
     (if (<= x 2.7e+53)
       (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ z t))))
       (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + z;
	double tmp;
	if (x <= -1.12e+63) {
		tmp = (a + (t + t_1)) + (y * i);
	} else if (x <= 2.7e+53) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) + z
    if (x <= (-1.12d+63)) then
        tmp = (a + (t + t_1)) + (y * i)
    else if (x <= 2.7d+53) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (z + t)))
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * Math.log(y)) + z;
	double tmp;
	if (x <= -1.12e+63) {
		tmp = (a + (t + t_1)) + (y * i);
	} else if (x <= 2.7e+53) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (z + t)));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + z
	tmp = 0
	if x <= -1.12e+63:
		tmp = (a + (t + t_1)) + (y * i)
	elif x <= 2.7e+53:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (z + t)))
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + z)
	tmp = 0.0
	if (x <= -1.12e+63)
		tmp = Float64(Float64(a + Float64(t + t_1)) + Float64(y * i));
	elseif (x <= 2.7e+53)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + z;
	tmp = 0.0;
	if (x <= -1.12e+63)
		tmp = (a + (t + t_1)) + (y * i);
	elseif (x <= 2.7e+53)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -1.12e+63], N[(N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+53], 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[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.12000000000000006e63

   1. Initial program 99.6%

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

   3. Taylor expanded in b around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in b around 0 90.3%

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

   if -1.12000000000000006e63 < x < 2.70000000000000019e53

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 98.7%

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

   if 2.70000000000000019e53 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 90.3%

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

   7. Taylor expanded in t around 0 73.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+63}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+53}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + z\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+63}:\\ \;\;\;\;\left(a + \left(t + t\_1\right)\right) + y \cdot i\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) z)))
   (if (<= x -1.65e+63)
     (+ (+ a (+ t t_1)) (* y i))
     (if (<= x 1.15e+54)
       (+ (* y i) (+ (* (- b 0.5) (log c)) (+ z a)))
       (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + z;
	double tmp;
	if (x <= -1.65e+63) {
		tmp = (a + (t + t_1)) + (y * i);
	} else if (x <= 1.15e+54) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) + z
    if (x <= (-1.65d+63)) then
        tmp = (a + (t + t_1)) + (y * i)
    else if (x <= 1.15d+54) then
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (z + a))
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * Math.log(y)) + z;
	double tmp;
	if (x <= -1.65e+63) {
		tmp = (a + (t + t_1)) + (y * i);
	} else if (x <= 1.15e+54) {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (z + a));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + z
	tmp = 0
	if x <= -1.65e+63:
		tmp = (a + (t + t_1)) + (y * i)
	elif x <= 1.15e+54:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (z + a))
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + z)
	tmp = 0.0
	if (x <= -1.65e+63)
		tmp = Float64(Float64(a + Float64(t + t_1)) + Float64(y * i));
	elseif (x <= 1.15e+54)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(z + a)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + z;
	tmp = 0.0;
	if (x <= -1.65e+63)
		tmp = (a + (t + t_1)) + (y * i);
	elseif (x <= 1.15e+54)
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -1.65e+63], N[(N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+54], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6500000000000001e63

   1. Initial program 99.6%

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

   3. Taylor expanded in b around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in b around 0 90.3%

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

   if -1.6500000000000001e63 < x < 1.14999999999999997e54

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 98.7%

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

   4. Taylor expanded in t around 0 86.3%

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

   if 1.14999999999999997e54 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 90.3%

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

   7. Taylor expanded in t around 0 73.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+63}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.82 \cdot 10^{-152}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.82e-152)
   (+ z (* y i))
   (if (<= a 1.08e-26)
     (+ (* x (log y)) (* y i))
     (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ z a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.82e-152) {
		tmp = z + (y * i);
	} else if (a <= 1.08e-26) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.82d-152) then
        tmp = z + (y * i)
    else if (a <= 1.08d-26) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (z / a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.82e-152) {
		tmp = z + (y * i);
	} else if (a <= 1.08e-26) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.82e-152:
		tmp = z + (y * i)
	elif a <= 1.08e-26:
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.82e-152)
		tmp = Float64(z + Float64(y * i));
	elseif (a <= 1.08e-26)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.82e-152)
		tmp = z + (y * i);
	elseif (a <= 1.08e-26)
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.82e-152], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.08e-26], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.82000000000000009e-152

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 38.9%

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

   if 1.82000000000000009e-152 < a < 1.07999999999999996e-26

   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 49.7%

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

   if 1.07999999999999996e-26 < a

   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 99.8%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. associate-/l* 99.7%

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

      5. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 68.5%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.82 \cdot 10^{-152}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.8% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3.4e-9)
   (+ z (* y i))
   (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ z a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.4e-9) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 3.4d-9) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (z / a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.4e-9) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.4e-9:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.4e-9)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3.4e-9)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.4e-9], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.3999999999999998e-9

   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 38.3%

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

   if 3.3999999999999998e-9 < a

   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 99.8%

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

      1. associate-/l* 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-/l* 99.7%

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

      5. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 69.0%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.0% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.25 \cdot 10^{+96}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.25e+96) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.25e+96) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.25d+96) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.25e+96) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.25e+96:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.25e+96)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.25e+96)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.25e+96], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.2500000000000001e96

   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 37.9%

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

   if 1.2500000000000001e96 < a

   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 52.5%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.25 \cdot 10^{+96}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.8% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 6.2e+125) (* y i) a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.2e+125) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 6.2d+125) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.2e+125) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 6.2e+125:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 6.2e+125)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 6.2e+125)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 6.2e+125], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 6.2e125

   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. Step-by-step derivation

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 25.0%

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

      1. *-commutative 25.0%

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

   7. Simplified 25.0%

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

   if 6.2e125 < a

   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 55.0%

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

   4. Taylor expanded in a around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. associate-/l* 55.0%

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

      3. fma-define 55.0%

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(i, \frac{y}{a}, 1\right)} \]

   6. Simplified 55.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(i, \frac{y}{a}, 1\right)} \]

   7. Taylor expanded in i around 0 48.2%

      \[\leadsto a \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6.2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.9% accurate, 43.8× speedup

Math

\[\begin{array}{l} \\ a + y \cdot i \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a + 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. Taylor expanded in a around inf 37.0%

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

4. Final simplification 37.0%

   \[\leadsto a + y \cdot i \]
5. Add Preprocessing

Alternative 17: 16.1% accurate, 219.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

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

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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := t

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 x around 0 82.5%

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

4. Taylor expanded in t around inf 60.0%

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

5. Taylor expanded in t around inf 15.1%

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

6. Final simplification 15.1%

   \[\leadsto t \]
7. Add Preprocessing

Alternative 18: 16.3% accurate, 219.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in a around inf 37.0%

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

4. Taylor expanded in a around inf 33.6%

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

   1. +-commutative 33.6%

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

   2. associate-/l* 32.8%

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

   3. fma-define 32.8%

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(i, \frac{y}{a}, 1\right)} \]

6. Simplified 32.8%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(i, \frac{y}{a}, 1\right)} \]

7. Taylor expanded in i around 0 16.8%

   \[\leadsto a \cdot \color{blue}{1} \]

8. Final simplification 16.8%

   \[\leadsto a \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024074 
(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)))