Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(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) - z) + log(t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(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) - z) + log(t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. sub-neg 99.9%

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

   3. sub-neg 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. +-commutative 99.9%

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

   7. unsub-neg 99.9%

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

   8. fma-udef 99.9%

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

   9. neg-sub0 99.9%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

   10. associate-+l- 99.9%

       \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

   11. neg-sub0 99.9%

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

   12. +-commutative 99.9%

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

   13. unsub-neg 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+21} \lor \neg \left(t_1 \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;t_1 - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (or (<= t_1 -4e+21) (not (<= t_1 5e-9)))
     (- t_1 z)
     (- (- (log t) z) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if ((t_1 <= -4e+21) || !(t_1 <= 5e-9)) {
		tmp = t_1 - z;
	} else {
		tmp = (log(t) - z) - y;
	}
	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)) - y
    if ((t_1 <= (-4d+21)) .or. (.not. (t_1 <= 5d-9))) then
        tmp = t_1 - z
    else
        tmp = (log(t) - z) - y
    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)) - y;
	double tmp;
	if ((t_1 <= -4e+21) || !(t_1 <= 5e-9)) {
		tmp = t_1 - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if (t_1 <= -4e+21) or not (t_1 <= 5e-9):
		tmp = t_1 - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if ((t_1 <= -4e+21) || !(t_1 <= 5e-9))
		tmp = Float64(t_1 - z);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if ((t_1 <= -4e+21) || ~((t_1 <= 5e-9)))
		tmp = t_1 - z;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+21], N[Not[LessEqual[t$95$1, 5e-9]], $MachinePrecision]], N[(t$95$1 - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -4e21 or 5.0000000000000001e-9 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.7%

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

   if -4e21 < (-.f64 (*.f64 x (log.f64 y)) y) < 5.0000000000000001e-9

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. sub-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-udef 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      10. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 98.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -4 \cdot 10^{+21} \lor \neg \left(x \cdot \log y - y \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 195:\\ \;\;\;\;\left(\log t + t_1\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 195.0) (- (+ (log t) t_1) z) (- (- t_1 y) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 195.0) {
		tmp = (log(t) + t_1) - z;
	} else {
		tmp = (t_1 - y) - z;
	}
	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 (y <= 195.0d0) then
        tmp = (log(t) + t_1) - z
    else
        tmp = (t_1 - y) - z
    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 (y <= 195.0) {
		tmp = (Math.log(t) + t_1) - z;
	} else {
		tmp = (t_1 - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 195.0:
		tmp = (math.log(t) + t_1) - z
	else:
		tmp = (t_1 - y) - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 195.0)
		tmp = Float64(Float64(log(t) + t_1) - z);
	else
		tmp = Float64(Float64(t_1 - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 195.0)
		tmp = (log(t) + t_1) - z;
	else
		tmp = (t_1 - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 195.0], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - z), $MachinePrecision], N[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 195

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.2%

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

   if 195 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.3%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 195:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = log(t) + (((x * log(y)) - y) - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 5: 68.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-225}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-79}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- y) z)))
   (if (<= x -4.3e+60)
     t_1
     (if (<= x -1e-210)
       t_2
       (if (<= x -1.12e-225)
         (log t)
         (if (<= x 1.75e-120)
           t_2
           (if (<= x 2.4e-79) (log t) (if (<= x 6.2e+164) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = -y - z;
	double tmp;
	if (x <= -4.3e+60) {
		tmp = t_1;
	} else if (x <= -1e-210) {
		tmp = t_2;
	} else if (x <= -1.12e-225) {
		tmp = log(t);
	} else if (x <= 1.75e-120) {
		tmp = t_2;
	} else if (x <= 2.4e-79) {
		tmp = log(t);
	} else if (x <= 6.2e+164) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = -y - z
    if (x <= (-4.3d+60)) then
        tmp = t_1
    else if (x <= (-1d-210)) then
        tmp = t_2
    else if (x <= (-1.12d-225)) then
        tmp = log(t)
    else if (x <= 1.75d-120) then
        tmp = t_2
    else if (x <= 2.4d-79) then
        tmp = log(t)
    else if (x <= 6.2d+164) then
        tmp = t_2
    else
        tmp = t_1
    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 t_2 = -y - z;
	double tmp;
	if (x <= -4.3e+60) {
		tmp = t_1;
	} else if (x <= -1e-210) {
		tmp = t_2;
	} else if (x <= -1.12e-225) {
		tmp = Math.log(t);
	} else if (x <= 1.75e-120) {
		tmp = t_2;
	} else if (x <= 2.4e-79) {
		tmp = Math.log(t);
	} else if (x <= 6.2e+164) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = -y - z
	tmp = 0
	if x <= -4.3e+60:
		tmp = t_1
	elif x <= -1e-210:
		tmp = t_2
	elif x <= -1.12e-225:
		tmp = math.log(t)
	elif x <= 1.75e-120:
		tmp = t_2
	elif x <= 2.4e-79:
		tmp = math.log(t)
	elif x <= 6.2e+164:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (x <= -4.3e+60)
		tmp = t_1;
	elseif (x <= -1e-210)
		tmp = t_2;
	elseif (x <= -1.12e-225)
		tmp = log(t);
	elseif (x <= 1.75e-120)
		tmp = t_2;
	elseif (x <= 2.4e-79)
		tmp = log(t);
	elseif (x <= 6.2e+164)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = -y - z;
	tmp = 0.0;
	if (x <= -4.3e+60)
		tmp = t_1;
	elseif (x <= -1e-210)
		tmp = t_2;
	elseif (x <= -1.12e-225)
		tmp = log(t);
	elseif (x <= 1.75e-120)
		tmp = t_2;
	elseif (x <= 2.4e-79)
		tmp = log(t);
	elseif (x <= 6.2e+164)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[x, -4.3e+60], t$95$1, If[LessEqual[x, -1e-210], t$95$2, If[LessEqual[x, -1.12e-225], N[Log[t], $MachinePrecision], If[LessEqual[x, 1.75e-120], t$95$2, If[LessEqual[x, 2.4e-79], N[Log[t], $MachinePrecision], If[LessEqual[x, 6.2e+164], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.29999999999999971e60 or 6.2000000000000003e164 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 66.9%

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

   if -4.29999999999999971e60 < x < -1e-210 or -1.12000000000000003e-225 < x < 1.75e-120 or 2.40000000000000006e-79 < x < 6.2000000000000003e164

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.0%

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

      1. add-sqr-sqrt 10.7%

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

      2. pow2 10.7%

         \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

   7. Applied egg-rr 10.7%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

   8. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{y \cdot {\left(\sqrt{-1}\right)}^{2}} - z \]
   9. Step-by-step derivation

      1. unpow2 0.0%

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

      2. rem-square-sqrt 74.6%

         \[\leadsto y \cdot \color{blue}{-1} - z \]

      3. *-commutative 74.6%

         \[\leadsto \color{blue}{-1 \cdot y} - z \]

      4. neg-mul-1 74.6%

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

   10. Simplified 74.6%

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

   if -1e-210 < x < -1.12000000000000003e-225 or 1.75e-120 < x < 2.40000000000000006e-79

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-udef 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      10. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in z around 0 93.1%

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

   7. Taylor expanded in y around 0 86.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-210}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-225}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-120}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-79}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+164}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+62} \lor \neg \left(x \leq 4.2 \cdot 10^{+167}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.65e+62) (not (<= x 4.2e+167)))
   (* x (log y))
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.65e+62) || !(x <= 4.2e+167)) {
		tmp = x * log(y);
	} else {
		tmp = (log(t) - z) - y;
	}
	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 <= (-1.65d+62)) .or. (.not. (x <= 4.2d+167))) then
        tmp = x * log(y)
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.65e+62) || !(x <= 4.2e+167)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.65e+62) or not (x <= 4.2e+167):
		tmp = x * math.log(y)
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.65e+62) || !(x <= 4.2e+167))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.65e+62) || ~((x <= 4.2e+167)))
		tmp = x * log(y);
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.65e+62], N[Not[LessEqual[x, 4.2e+167]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e62 or 4.1999999999999998e167 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 66.9%

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

   if -1.65e62 < x < 4.1999999999999998e167

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. unsub-neg 100.0%

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

      8. fma-udef 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      10. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      11. neg-sub0 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 94.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+62} \lor \neg \left(x \leq 4.2 \cdot 10^{+167}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10500000000 \lor \neg \left(z \leq 0.00085\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -10500000000.0) (not (<= z 0.00085)))
   (- (- y) z)
   (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -10500000000.0) || !(z <= 0.00085)) {
		tmp = -y - z;
	} else {
		tmp = log(t) - y;
	}
	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 <= (-10500000000.0d0)) .or. (.not. (z <= 0.00085d0))) then
        tmp = -y - z
    else
        tmp = log(t) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -10500000000.0) || !(z <= 0.00085)) {
		tmp = -y - z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -10500000000.0) or not (z <= 0.00085):
		tmp = -y - z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -10500000000.0) || !(z <= 0.00085))
		tmp = Float64(Float64(-y) - z);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -10500000000.0) || ~((z <= 0.00085)))
		tmp = -y - z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -10500000000.0], N[Not[LessEqual[z, 0.00085]], $MachinePrecision]], N[((-y) - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e10 or 8.49999999999999953e-4 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. add-sqr-sqrt 20.7%

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

      2. pow2 20.7%

         \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

   7. Applied egg-rr 20.7%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

   8. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{y \cdot {\left(\sqrt{-1}\right)}^{2}} - z \]
   9. Step-by-step derivation

      1. unpow2 0.0%

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

      2. rem-square-sqrt 82.3%

         \[\leadsto y \cdot \color{blue}{-1} - z \]

      3. *-commutative 82.3%

         \[\leadsto \color{blue}{-1 \cdot y} - z \]

      4. neg-mul-1 82.3%

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

   10. Simplified 82.3%

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

   if -1.05e10 < z < 8.49999999999999953e-4

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. +-commutative 99.8%

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

      7. unsub-neg 99.8%

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

      8. fma-udef 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      10. associate-+l- 99.8%

          \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      11. neg-sub0 99.8%

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

      12. +-commutative 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 63.2%

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

   6. Taylor expanded in z around 0 62.5%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10500000000 \lor \neg \left(z \leq 0.00085\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-235} \lor \neg \left(z \leq 5.5 \cdot 10^{-118}\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3e-235) (not (<= z 5.5e-118))) (- (- y) z) (log t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e-235) || !(z <= 5.5e-118)) {
		tmp = -y - z;
	} else {
		tmp = log(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 <= (-3d-235)) .or. (.not. (z <= 5.5d-118))) then
        tmp = -y - z
    else
        tmp = log(t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e-235) || !(z <= 5.5e-118)) {
		tmp = -y - z;
	} else {
		tmp = Math.log(t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3e-235) or not (z <= 5.5e-118):
		tmp = -y - z
	else:
		tmp = math.log(t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3e-235) || !(z <= 5.5e-118))
		tmp = Float64(Float64(-y) - z);
	else
		tmp = log(t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3e-235) || ~((z <= 5.5e-118)))
		tmp = -y - z;
	else
		tmp = log(t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3e-235], N[Not[LessEqual[z, 5.5e-118]], $MachinePrecision]], N[((-y) - z), $MachinePrecision], N[Log[t], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e-235 or 5.5000000000000003e-118 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 91.8%

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

      1. add-sqr-sqrt 20.6%

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

      2. pow2 20.6%

         \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

   7. Applied egg-rr 20.6%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

   8. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{y \cdot {\left(\sqrt{-1}\right)}^{2}} - z \]
   9. Step-by-step derivation

      1. unpow2 0.0%

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

      2. rem-square-sqrt 69.1%

         \[\leadsto y \cdot \color{blue}{-1} - z \]

      3. *-commutative 69.1%

         \[\leadsto \color{blue}{-1 \cdot y} - z \]

      4. neg-mul-1 69.1%

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

   10. Simplified 69.1%

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

   if -2.9999999999999999e-235 < z < 5.5000000000000003e-118

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. +-commutative 99.8%

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

      7. unsub-neg 99.8%

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

      8. fma-udef 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      10. associate-+l- 99.8%

          \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      11. neg-sub0 99.8%

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

      12. +-commutative 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 60.4%

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

   6. Taylor expanded in z around 0 60.4%

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

   7. Taylor expanded in y around 0 44.5%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-235} \lor \neg \left(z \leq 5.5 \cdot 10^{-118}\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 190:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 190.0) (- (log t) z) (- (- y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 190.0) {
		tmp = log(t) - z;
	} else {
		tmp = -y - z;
	}
	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 (y <= 190.0d0) then
        tmp = log(t) - z
    else
        tmp = -y - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 190.0) {
		tmp = Math.log(t) - z;
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 190.0:
		tmp = math.log(t) - z
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 190.0)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(Float64(-y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 190.0)
		tmp = log(t) - z;
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 190.0], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[((-y) - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 190

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.2%

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

   6. Taylor expanded in x around 0 72.2%

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

   if 190 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.3%

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

      1. add-sqr-sqrt 16.5%

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

      2. pow2 16.5%

         \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

   7. Applied egg-rr 16.5%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

   8. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{y \cdot {\left(\sqrt{-1}\right)}^{2}} - z \]
   9. Step-by-step derivation

      1. unpow2 0.0%

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

      2. rem-square-sqrt 72.3%

         \[\leadsto y \cdot \color{blue}{-1} - z \]

      3. *-commutative 72.3%

         \[\leadsto \color{blue}{-1 \cdot y} - z \]

      4. neg-mul-1 72.3%

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

   10. Simplified 72.3%

       \[\leadsto \color{blue}{\left(-y\right)} - z \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 190:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.2% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+83}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 7.5e+83) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.5e+83) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	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 (y <= 7.5d+83) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.5e+83) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7.5e+83:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.5e+83)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 7.5e+83)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.5e+83], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 7.49999999999999989e83

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 39.0%

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

      1. neg-mul-1 39.0%

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

   7. Simplified 39.0%

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

   if 7.49999999999999989e83 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.1%

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

      1. neg-mul-1 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+83}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.5% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 83.3%

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

   1. add-sqr-sqrt 19.3%

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

   2. pow2 19.3%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

7. Applied egg-rr 19.3%

   \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \log y - y}\right)}^{2}} - z \]

8. Taylor expanded in x around 0 0.0%

   \[\leadsto \color{blue}{y \cdot {\left(\sqrt{-1}\right)}^{2}} - z \]
9. Step-by-step derivation

   1. unpow2 0.0%

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

   2. rem-square-sqrt 56.5%

      \[\leadsto y \cdot \color{blue}{-1} - z \]

   3. *-commutative 56.5%

      \[\leadsto \color{blue}{-1 \cdot y} - z \]

   4. neg-mul-1 56.5%

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

10. Simplified 56.5%

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

11. Final simplification 56.5%

    \[\leadsto \left(-y\right) - z \]
12. Add Preprocessing

Alternative 12: 29.7% accurate, 104.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return -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 = -y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 28.9%

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

   1. neg-mul-1 28.9%

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

7. Simplified 28.9%

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

8. Final simplification 28.9%

   \[\leadsto -y \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))