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

Percentage Accurate: 84.9% → 99.8%

Time: 14.9s

Alternatives: 14

Speedup: 1.9×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))

C

double code(double x, double y, double z, double t) {
	return ((x * log(y)) + (z * log((1.0 - y)))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x * log(y)) + (z * log((1.0d0 - y)))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x * Math.log(y)) + (z * Math.log((1.0 - y)))) - t;
}

Python

def code(x, y, z, t):
	return ((x * math.log(y)) + (z * math.log((1.0 - y)))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * log(y)) + Float64(z * log(Float64(1.0 - y)))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x * log(y)) + (z * log((1.0 - y)))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Initial Program: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))

C

double code(double x, double y, double z, double t) {
	return ((x * log(y)) + (z * log((1.0 - y)))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x * log(y)) + (z * log((1.0d0 - y)))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x * Math.log(y)) + (z * Math.log((1.0 - y)))) - t;
}

Python

def code(x, y, z, t):
	return ((x * math.log(y)) + (z * math.log((1.0 - y)))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * log(y)) + Float64(z * log(Float64(1.0 - y)))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x * log(y)) + (z * log((1.0 - y)))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z, \mathsf{log1p}\left(-y\right), x \cdot \log y - t\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma z (log1p (- y)) (- (* x (log y)) t)))

C

double code(double x, double y, double z, double t) {
	return fma(z, log1p(-y), ((x * log(y)) - t));
}

Julia

function code(x, y, z, t)
	return fma(z, log1p(Float64(-y)), Float64(Float64(x * log(y)) - t))
end

Wolfram

code[x_, y_, z_, t_] := N[(z * N[Log[1 + (-y)], $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Step-by-step derivation

   1. +-commutative 83.6%

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

   2. associate--l+ 83.6%

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

   3. fma-define 83.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \log \left(1 - y\right), x \cdot \log y - t\right)} \]

   4. sub-neg 83.6%

      \[\leadsto \mathsf{fma}\left(z, \log \color{blue}{\left(1 + \left(-y\right)\right)}, x \cdot \log y - t\right) \]

   5. log1p-define 99.8%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{log1p}\left(-y\right)}, x \cdot \log y - t\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{log1p}\left(-y\right), x \cdot \log y - t\right)} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(z, \mathsf{log1p}\left(-y\right), x \cdot \log y - t\right) \]
6. Add Preprocessing

Alternative 2: 76.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \mathbf{elif}\;x \leq -3.25 \cdot 10^{-27} \lor \neg \left(x \leq 5.9 \cdot 10^{+147}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(z \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right) - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.1e+94)
     t_1
     (if (<= x -3.1e+65)
       (- (* z (- y)) t)
       (if (or (<= x -3.25e-27) (not (<= x 5.9e+147)))
         t_1
         (-
          (*
           y
           (- (* y (* z (- (* y (- (* y -0.25) 0.3333333333333333)) 0.5))) z))
          t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.1e+94) {
		tmp = t_1;
	} else if (x <= -3.1e+65) {
		tmp = (z * -y) - t;
	} else if ((x <= -3.25e-27) || !(x <= 5.9e+147)) {
		tmp = t_1;
	} else {
		tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.1d+94)) then
        tmp = t_1
    else if (x <= (-3.1d+65)) then
        tmp = (z * -y) - t
    else if ((x <= (-3.25d-27)) .or. (.not. (x <= 5.9d+147))) then
        tmp = t_1
    else
        tmp = (y * ((y * (z * ((y * ((y * (-0.25d0)) - 0.3333333333333333d0)) - 0.5d0))) - z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -1.1e+94) {
		tmp = t_1;
	} else if (x <= -3.1e+65) {
		tmp = (z * -y) - t;
	} else if ((x <= -3.25e-27) || !(x <= 5.9e+147)) {
		tmp = t_1;
	} else {
		tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.1e+94:
		tmp = t_1
	elif x <= -3.1e+65:
		tmp = (z * -y) - t
	elif (x <= -3.25e-27) or not (x <= 5.9e+147):
		tmp = t_1
	else:
		tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.1e+94)
		tmp = t_1;
	elseif (x <= -3.1e+65)
		tmp = Float64(Float64(z * Float64(-y)) - t);
	elseif ((x <= -3.25e-27) || !(x <= 5.9e+147))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(y * Float64(z * Float64(Float64(y * Float64(Float64(y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.1e+94)
		tmp = t_1;
	elseif (x <= -3.1e+65)
		tmp = (z * -y) - t;
	elseif ((x <= -3.25e-27) || ~((x <= 5.9e+147)))
		tmp = t_1;
	else
		tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+94], t$95$1, If[LessEqual[x, -3.1e+65], N[(N[(z * (-y)), $MachinePrecision] - t), $MachinePrecision], If[Or[LessEqual[x, -3.25e-27], N[Not[LessEqual[x, 5.9e+147]], $MachinePrecision]], t$95$1, N[(N[(y * N[(N[(y * N[(z * N[(N[(y * N[(N[(y * -0.25), $MachinePrecision] - 0.3333333333333333), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.10000000000000006e94 or -3.09999999999999991e65 < x < -3.25000000000000013e-27 or 5.9000000000000001e147 < x

   1. Initial program 97.0%

      \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.7%

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

   4. Taylor expanded in x around inf 85.6%

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

   if -1.10000000000000006e94 < x < -3.09999999999999991e65

   1. Initial program 71.7%

      \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.3%

      \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

   4. Taylor expanded in y around 0 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} - t \]

      2. neg-mul-1 100.0%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot z - t \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z - t} \]

   if -3.25000000000000013e-27 < x < 5.9000000000000001e147

   1. Initial program 76.8%

      \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 58.3%

      \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

   4. Taylor expanded in y around 0 81.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + y \cdot \left(-0.3333333333333333 \cdot z + -0.25 \cdot \left(y \cdot z\right)\right)\right)\right)} - t \]

   5. Taylor expanded in z around 0 81.1%

      \[\leadsto y \cdot \left(-1 \cdot z + \color{blue}{y \cdot \left(z \cdot \left(y \cdot \left(-0.25 \cdot y - 0.3333333333333333\right) - 0.5\right)\right)}\right) - t \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \mathbf{elif}\;x \leq -3.25 \cdot 10^{-27} \lor \neg \left(x \leq 5.9 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(z \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right) - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-78} \lor \neg \left(x \leq 880\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(z \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right) - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4e-78) (not (<= x 880.0)))
   (- (* x (log y)) t)
   (-
    (* y (- (* y (* z (- (* y (- (* y -0.25) 0.3333333333333333)) 0.5))) z))
    t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e-78) || !(x <= 880.0)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4d-78)) .or. (.not. (x <= 880.0d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = (y * ((y * (z * ((y * ((y * (-0.25d0)) - 0.3333333333333333d0)) - 0.5d0))) - z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e-78) || !(x <= 880.0)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4e-78) or not (x <= 880.0):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4e-78) || !(x <= 880.0))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(y * Float64(Float64(y * Float64(z * Float64(Float64(y * Float64(Float64(y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4e-78) || ~((x <= 880.0)))
		tmp = (x * log(y)) - t;
	else
		tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4e-78], N[Not[LessEqual[x, 880.0]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(N[(y * N[(z * N[(N[(y * N[(N[(y * -0.25), $MachinePrecision] - 0.3333333333333333), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4e-78 or 880 < x

   1. Initial program 93.0%

      \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.8%

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

   if -4e-78 < x < 880

   1. Initial program 72.9%

      \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 62.9%

      \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

   4. Taylor expanded in y around 0 89.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + y \cdot \left(-0.3333333333333333 \cdot z + -0.25 \cdot \left(y \cdot z\right)\right)\right)\right)} - t \]

   5. Taylor expanded in z around 0 89.6%

      \[\leadsto y \cdot \left(-1 \cdot z + \color{blue}{y \cdot \left(z \cdot \left(y \cdot \left(-0.25 \cdot y - 0.3333333333333333\right) - 0.5\right)\right)}\right) - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-78} \lor \neg \left(x \leq 880\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(z \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right) - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \log y + z \cdot \left(y \cdot \left(-1 + y \cdot -0.5\right)\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* x (log y)) (* z (* y (+ -1.0 (* y -0.5))))) t))

C

double code(double x, double y, double z, double t) {
	return ((x * log(y)) + (z * (y * (-1.0 + (y * -0.5))))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x * log(y)) + (z * (y * ((-1.0d0) + (y * (-0.5d0)))))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x * Math.log(y)) + (z * (y * (-1.0 + (y * -0.5))))) - t;
}

Python

def code(x, y, z, t):
	return ((x * math.log(y)) + (z * (y * (-1.0 + (y * -0.5))))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * log(y)) + Float64(z * Float64(y * Float64(-1.0 + Float64(y * -0.5))))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x * log(y)) + (z * (y * (-1.0 + (y * -0.5))))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[(y * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \left(x \cdot \log y + z \cdot \left(y \cdot \left(-1 + y \cdot -0.5\right)\right)\right) - t \]
5. Add Preprocessing

Alternative 5: 99.5% accurate, 1.8× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* x (log y)) (* y (- (* -0.5 (* z y)) z))) t))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \left(x \cdot \log y + y \cdot \left(-0.5 \cdot \left(z \cdot y\right) - z\right)\right) - t \]
5. Add Preprocessing

Alternative 6: 99.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \log y - z \cdot y\right) - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (- (* x (log y)) (* z y)) t))

C

double code(double x, double y, double z, double t) {
	return ((x * log(y)) - (z * y)) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x * log(y)) - (z * y)) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x * Math.log(y)) - (z * y)) - t;
}

Python

def code(x, y, z, t):
	return ((x * math.log(y)) - (z * y)) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * log(y)) - Float64(z * y)) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x * log(y)) - (z * y)) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.4%

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

   1. +-commutative 99.4%

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

   2. mul-1-neg 99.4%

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

   3. unsub-neg 99.4%

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

5. Simplified 99.4%

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

6. Final simplification 99.4%

   \[\leadsto \left(x \cdot \log y - z \cdot y\right) - t \]
7. Add Preprocessing

Alternative 7: 57.2% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(y \cdot \left(-1 + y \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (* z (* y (+ -1.0 (* y (- (* y (- (* y -0.25) 0.3333333333333333)) 0.5)))))
  t))

C

double code(double x, double y, double z, double t) {
	return (z * (y * (-1.0 + (y * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (z * (y * ((-1.0d0) + (y * ((y * ((y * (-0.25d0)) - 0.3333333333333333d0)) - 0.5d0))))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (z * (y * (-1.0 + (y * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))))) - t;
}

Python

def code(x, y, z, t):
	return (z * (y * (-1.0 + (y * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(z * Float64(y * Float64(-1.0 + Float64(y * Float64(Float64(y * Float64(Float64(y * -0.25) - 0.3333333333333333)) - 0.5))))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (z * (y * (-1.0 + (y * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(z * N[(y * N[(-1.0 + N[(y * N[(N[(y * N[(N[(y * -0.25), $MachinePrecision] - 0.3333333333333333), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 43.2%

   \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

4. Taylor expanded in y around 0 59.2%

   \[\leadsto z \cdot \color{blue}{\left(y \cdot \left(y \cdot \left(y \cdot \left(-0.25 \cdot y - 0.3333333333333333\right) - 0.5\right) - 1\right)\right)} - t \]

5. Final simplification 59.2%

   \[\leadsto z \cdot \left(y \cdot \left(-1 + y \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right)\right) - t \]
6. Add Preprocessing

Alternative 8: 57.2% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(y \cdot \left(z \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right) - z\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (* y (- (* y (* z (- (* y (- (* y -0.25) 0.3333333333333333)) 0.5))) z))
  t))

C

double code(double x, double y, double z, double t) {
	return (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y * ((y * (z * ((y * ((y * (-0.25d0)) - 0.3333333333333333d0)) - 0.5d0))) - z)) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
}

Python

def code(x, y, z, t):
	return (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(y * Float64(Float64(y * Float64(z * Float64(Float64(y * Float64(Float64(y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (y * ((y * (z * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5))) - z)) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * N[(N[(y * N[(z * N[(N[(y * N[(N[(y * -0.25), $MachinePrecision] - 0.3333333333333333), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 43.2%

   \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

4. Taylor expanded in y around 0 59.2%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + y \cdot \left(-0.3333333333333333 \cdot z + -0.25 \cdot \left(y \cdot z\right)\right)\right)\right)} - t \]

5. Taylor expanded in z around 0 59.2%

   \[\leadsto y \cdot \left(-1 \cdot z + \color{blue}{y \cdot \left(z \cdot \left(y \cdot \left(-0.25 \cdot y - 0.3333333333333333\right) - 0.5\right)\right)}\right) - t \]

6. Final simplification 59.2%

   \[\leadsto y \cdot \left(y \cdot \left(z \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right) - z\right) - t \]
7. Add Preprocessing

Alternative 9: 57.1% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(y \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (* z (* y (+ -1.0 (* y (- (* y -0.3333333333333333) 0.5))))) t))

C

double code(double x, double y, double z, double t) {
	return (z * (y * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (z * (y * ((-1.0d0) + (y * ((y * (-0.3333333333333333d0)) - 0.5d0))))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (z * (y * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
}

Python

def code(x, y, z, t):
	return (z * (y * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(z * Float64(y * Float64(-1.0 + Float64(y * Float64(Float64(y * -0.3333333333333333) - 0.5))))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (z * (y * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(z * N[(y * N[(-1.0 + N[(y * N[(N[(y * -0.3333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 43.2%

   \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

4. Taylor expanded in y around 0 59.1%

   \[\leadsto z \cdot \color{blue}{\left(y \cdot \left(y \cdot \left(-0.3333333333333333 \cdot y - 0.5\right) - 1\right)\right)} - t \]

5. Final simplification 59.1%

   \[\leadsto z \cdot \left(y \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t \]
6. Add Preprocessing

Alternative 10: 45.5% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+186} \lor \neg \left(z \leq 5.8 \cdot 10^{+190}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.5e+186) (not (<= z 5.8e+190))) (* z (- y)) (- t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e+186) || !(z <= 5.8e+190)) {
		tmp = z * -y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.5d+186)) .or. (.not. (z <= 5.8d+190))) then
        tmp = z * -y
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e+186) || !(z <= 5.8e+190)) {
		tmp = z * -y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.5e+186) or not (z <= 5.8e+190):
		tmp = z * -y
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.5e+186) || !(z <= 5.8e+190))
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.5e+186) || ~((z <= 5.8e+190)))
		tmp = z * -y;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.5e+186], N[Not[LessEqual[z, 5.8e+190]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], (-t)]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999987e186 or 5.79999999999999979e190 < z

   1. Initial program 45.4%

      \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 18.6%

      \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

   4. Taylor expanded in y around 0 72.3%

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

      1. associate-*r* 72.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} - t \]

      2. neg-mul-1 72.3%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot z - t \]

   6. Simplified 72.3%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z - t} \]

   7. Taylor expanded in y around inf 55.2%

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

      1. mul-1-neg 55.2%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. distribute-rgt-neg-in 55.2%

         \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   9. Simplified 55.2%

      \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   if -3.49999999999999987e186 < z < 5.79999999999999979e190

   1. Initial program 93.8%

      \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 49.2%

      \[\leadsto \color{blue}{-1 \cdot t} \]
   4. Step-by-step derivation

      1. neg-mul-1 49.2%

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

   5. Simplified 49.2%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+186} \lor \neg \left(z \leq 5.8 \cdot 10^{+190}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.0% accurate, 19.2× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* y (* z (+ -1.0 (* y -0.5)))) t))

C

double code(double x, double y, double z, double t) {
	return (y * (z * (-1.0 + (y * -0.5)))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (y * (z * (-1.0 + (y * -0.5)))) - t;
}

Python

def code(x, y, z, t):
	return (y * (z * (-1.0 + (y * -0.5)))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 43.2%

   \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

4. Taylor expanded in y around 0 59.2%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + y \cdot \left(-0.3333333333333333 \cdot z + -0.25 \cdot \left(y \cdot z\right)\right)\right)\right)} - t \]

5. Taylor expanded in y around 0 59.0%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + -0.5 \cdot \left(y \cdot z\right)\right)} - t \]
6. Step-by-step derivation

   1. associate-*r* 59.0%

      \[\leadsto y \cdot \left(-1 \cdot z + \color{blue}{\left(-0.5 \cdot y\right) \cdot z}\right) - t \]

   2. distribute-rgt-out 59.0%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(-1 + -0.5 \cdot y\right)\right)} - t \]

7. Simplified 59.0%

   \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-1 + -0.5 \cdot y\right)\right)} - t \]

8. Final simplification 59.0%

   \[\leadsto y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t \]
9. Add Preprocessing

Alternative 12: 57.0% accurate, 19.2× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(-0.5 \cdot \left(z \cdot y\right) - z\right) - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* y (- (* -0.5 (* z y)) z)) t))

C

double code(double x, double y, double z, double t) {
	return (y * ((-0.5 * (z * y)) - z)) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y * (((-0.5d0) * (z * y)) - z)) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (y * ((-0.5 * (z * y)) - z)) - t;
}

Python

def code(x, y, z, t):
	return (y * ((-0.5 * (z * y)) - z)) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(y * Float64(Float64(-0.5 * Float64(z * y)) - z)) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (y * ((-0.5 * (z * y)) - z)) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * N[(N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.7%

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

4. Taylor expanded in x around 0 59.0%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + -0.5 \cdot \left(y \cdot z\right)\right) - t} \]

5. Final simplification 59.0%

   \[\leadsto y \cdot \left(-0.5 \cdot \left(z \cdot y\right) - z\right) - t \]
6. Add Preprocessing

Alternative 13: 56.7% accurate, 35.2× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(-y\right) - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* z (- y)) t))

C

double code(double x, double y, double z, double t) {
	return (z * -y) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (z * -y) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (z * -y) - t;
}

Python

def code(x, y, z, t):
	return (z * -y) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(z * Float64(-y)) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (z * -y) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(z * (-y)), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 43.2%

   \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right) - t} \]

4. Taylor expanded in y around 0 58.7%

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

   1. associate-*r* 58.7%

      \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} - t \]

   2. neg-mul-1 58.7%

      \[\leadsto \color{blue}{\left(-y\right)} \cdot z - t \]

6. Simplified 58.7%

   \[\leadsto \color{blue}{\left(-y\right) \cdot z - t} \]

7. Final simplification 58.7%

   \[\leadsto z \cdot \left(-y\right) - t \]
8. Add Preprocessing

Alternative 14: 41.9% accurate, 105.5× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (- t))

C

double code(double x, double y, double z, double t) {
	return -t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = -t
end function

Java

public static double code(double x, double y, double z, double t) {
	return -t;
}

Python

def code(x, y, z, t):
	return -t

Julia

function code(x, y, z, t)
	return Float64(-t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = -t;
end

Wolfram

code[x_, y_, z_, t_] := (-t)

Derivation

1. Initial program 83.6%

   \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in t around inf 42.4%

   \[\leadsto \color{blue}{-1 \cdot t} \]
4. Step-by-step derivation

   1. neg-mul-1 42.4%

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

5. Simplified 42.4%

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

6. Final simplification 42.4%

   \[\leadsto -t \]
7. Add Preprocessing

Developer target: 99.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{0.3333333333333333}{1 \cdot \left(1 \cdot 1\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (*
   (- z)
   (+
    (+ (* 0.5 (* y y)) y)
    (* (/ 0.3333333333333333 (* 1.0 (* 1.0 1.0))) (* y (* y y)))))
  (- t (* x (log y)))))

C

double code(double x, double y, double z, double t) {
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * log(y)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (-z * (((0.5d0 * (y * y)) + y) + ((0.3333333333333333d0 / (1.0d0 * (1.0d0 * 1.0d0))) * (y * (y * y))))) - (t - (x * log(y)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * Math.log(y)));
}

Python

def code(x, y, z, t):
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * math.log(y)))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(-z) * Float64(Float64(Float64(0.5 * Float64(y * y)) + y) + Float64(Float64(0.3333333333333333 / Float64(1.0 * Float64(1.0 * 1.0))) * Float64(y * Float64(y * y))))) - Float64(t - Float64(x * log(y))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * log(y)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[((-z) * N[(N[(N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] + N[(N[(0.3333333333333333 / N[(1.0 * N[(1.0 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024074 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (- (* (- z) (+ (+ (* 0.5 (* y y)) y) (* (/ 0.3333333333333333 (* 1.0 (* 1.0 1.0))) (* y (* y y))))) (- t (* x (log y))))

  (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))