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

Percentage Accurate: 99.9% → 99.8%

Time: 10.2s

Alternatives: 10

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: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(-2 \cdot y + \left(y + \log y \cdot x\right)\right) - z\right) + \log t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (+ (* -2.0 y) (+ y (* (log y) x))) z) (log t)))

C

double code(double x, double y, double z, double t) {
	return (((-2.0 * y) + (y + (log(y) * x))) - 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 = ((((-2.0d0) * y) + (y + (log(y) * x))) - z) + log(t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((-2.0 * y) + (y + (Math.log(y) * x))) - z) + Math.log(t);
}

Python

def code(x, y, z, t):
	return (((-2.0 * y) + (y + (math.log(y) * x))) - z) + math.log(t)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(-2.0 * y) + Float64(y + Float64(log(y) * x))) - z) + log(t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((-2.0 * y) + (y + (log(y) * x))) - z) + log(t);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(-2.0 * y), $MachinePrecision] + N[(y + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] + N[Log[t], $MachinePrecision]), $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. flip-- 44.3%

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

   2. pow2 44.3%

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

3. Applied egg-rr 44.3%

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

4. Taylor expanded in x around inf 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+29} \lor \neg \left(z \leq 7.4 \cdot 10^{+121}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log y \cdot x + \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05e+29) (not (<= z 7.4e+121)))
   (- (- z) y)
   (- (+ (* (log y) x) (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e+29) || !(z <= 7.4e+121)) {
		tmp = -z - y;
	} else {
		tmp = ((log(y) * x) + 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 <= (-1.05d+29)) .or. (.not. (z <= 7.4d+121))) then
        tmp = -z - y
    else
        tmp = ((log(y) * x) + 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 <= -1.05e+29) || !(z <= 7.4e+121)) {
		tmp = -z - y;
	} else {
		tmp = ((Math.log(y) * x) + Math.log(t)) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05e+29) or not (z <= 7.4e+121):
		tmp = -z - y
	else:
		tmp = ((math.log(y) * x) + math.log(t)) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e+29) || !(z <= 7.4e+121))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(Float64(Float64(log(y) * x) + log(t)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e+29) || ~((z <= 7.4e+121)))
		tmp = -z - y;
	else
		tmp = ((log(y) * x) + log(t)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e+29], N[Not[LessEqual[z, 7.4e+121]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e29 or 7.40000000000000025e121 < z

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in x around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. associate--r+ 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in z around inf 89.8%

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

      1. neg-mul-1 89.8%

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

   7. Simplified 89.8%

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

   if -1.0500000000000001e29 < z < 7.40000000000000025e121

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around 0 94.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+29} \lor \neg \left(z \leq 7.4 \cdot 10^{+121}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log y \cdot x + \log t\right) - y\\ \end{array} \]

Alternative 3: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+212} \lor \neg \left(x \leq 5 \cdot 10^{+142}\right):\\ \;\;\;\;\log y \cdot x + \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.1e+212) (not (<= x 5e+142)))
   (+ (* (log y) x) (log t))
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.1e+212) || !(x <= 5e+142)) {
		tmp = (log(y) * x) + log(t);
	} 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 <= (-1.1d+212)) .or. (.not. (x <= 5d+142))) then
        tmp = (log(y) * x) + log(t)
    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 <= -1.1e+212) || !(x <= 5e+142)) {
		tmp = (Math.log(y) * x) + Math.log(t);
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.1e+212) or not (x <= 5e+142):
		tmp = (math.log(y) * x) + math.log(t)
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.1e+212) || !(x <= 5e+142))
		tmp = Float64(Float64(log(y) * x) + log(t));
	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 <= -1.1e+212) || ~((x <= 5e+142)))
		tmp = (log(y) * x) + log(t);
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.1e+212], N[Not[LessEqual[x, 5e+142]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.09999999999999998e212 or 5.0000000000000001e142 < x

   1. Initial program 99.7%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around 0 90.4%

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

   3. Taylor expanded in y around 0 84.7%

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

   if -1.09999999999999998e212 < x < 5.0000000000000001e142

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in x around 0 89.0%

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

      1. +-commutative 89.0%

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

      2. associate--r+ 89.0%

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

   4. Simplified 89.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+212} \lor \neg \left(x \leq 5 \cdot 10^{+142}\right):\\ \;\;\;\;\log y \cdot x + \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[t], $MachinePrecision] + N[(N[(N[(N[Log[y], $MachinePrecision] * x), $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. Final simplification 99.9%

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

Alternative 5: 69.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17 \lor \neg \left(z \leq 1.15 \cdot 10^{-50}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -17.0) (not (<= z 1.15e-50))) (- (- z) y) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -17.0) || !(z <= 1.15e-50)) {
		tmp = -z - y;
	} 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 <= (-17.0d0)) .or. (.not. (z <= 1.15d-50))) then
        tmp = -z - y
    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 <= -17.0) || !(z <= 1.15e-50)) {
		tmp = -z - y;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -17.0) or not (z <= 1.15e-50):
		tmp = -z - y
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -17.0) || !(z <= 1.15e-50))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -17.0) || ~((z <= 1.15e-50)))
		tmp = -z - y;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -17.0], N[Not[LessEqual[z, 1.15e-50]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -17 or 1.1500000000000001e-50 < z

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in x around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. associate--r+ 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in z around inf 80.7%

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

      1. neg-mul-1 80.7%

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

   7. Simplified 80.7%

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

   if -17 < z < 1.1500000000000001e-50

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around 0 99.4%

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

   3. Taylor expanded in x around 0 64.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17 \lor \neg \left(z \leq 1.15 \cdot 10^{-50}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]

Alternative 6: 69.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{-19}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.2e-19) (- (log t) z) (- (- z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.2e-19) {
		tmp = log(t) - z;
	} else {
		tmp = -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 (y <= 7.2d-19) then
        tmp = log(t) - z
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.2e-19) {
		tmp = Math.log(t) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7.2e-19:
		tmp = math.log(t) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.2e-19)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 7.2e-19)
		tmp = log(t) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.2e-19], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.2000000000000002e-19

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around inf 63.4%

      \[\leadsto \color{blue}{-1 \cdot z} + \log t \]
   3. Step-by-step derivation

      1. neg-mul-1 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in z around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. +-commutative 63.4%

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

      3. sub-neg 63.4%

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

   7. Simplified 63.4%

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

   if 7.2000000000000002e-19 < y

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in x around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. associate--r+ 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in z around inf 82.7%

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

      1. neg-mul-1 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{-19}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 7: 70.6% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

2. Taylor expanded in x around 0 73.9%

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

   1. +-commutative 73.9%

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

   2. associate--r+ 73.9%

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

4. Simplified 73.9%

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

5. Final simplification 73.9%

   \[\leadsto \left(\log t - z\right) - y \]

Alternative 8: 47.4% accurate, 25.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 90000000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+112}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 90000000000.0)
   (- z)
   (if (<= y 4.8e+70) (- y) (if (<= y 6.2e+112) (- z) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 90000000000.0) {
		tmp = -z;
	} else if (y <= 4.8e+70) {
		tmp = -y;
	} else if (y <= 6.2e+112) {
		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 <= 90000000000.0d0) then
        tmp = -z
    else if (y <= 4.8d+70) then
        tmp = -y
    else if (y <= 6.2d+112) 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 <= 90000000000.0) {
		tmp = -z;
	} else if (y <= 4.8e+70) {
		tmp = -y;
	} else if (y <= 6.2e+112) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 90000000000.0:
		tmp = -z
	elif y <= 4.8e+70:
		tmp = -y
	elif y <= 6.2e+112:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 90000000000.0)
		tmp = Float64(-z);
	elseif (y <= 4.8e+70)
		tmp = Float64(-y);
	elseif (y <= 6.2e+112)
		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 <= 90000000000.0)
		tmp = -z;
	elseif (y <= 4.8e+70)
		tmp = -y;
	elseif (y <= 6.2e+112)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 90000000000.0], (-z), If[LessEqual[y, 4.8e+70], (-y), If[LessEqual[y, 6.2e+112], (-z), (-y)]]]

Derivation

1. Split input into 2 regimes

2. if y < 9e10 or 4.79999999999999974e70 < y < 6.19999999999999965e112

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in z around inf 64.0%

      \[\leadsto \color{blue}{-1 \cdot z} + \log t \]
   3. Step-by-step derivation

      1. neg-mul-1 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in z around inf 42.2%

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

      1. mul-1-neg 42.2%

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

   7. Simplified 42.2%

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

   if 9e10 < y < 4.79999999999999974e70 or 6.19999999999999965e112 < y

   1. Initial program 99.9%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

   2. Taylor expanded in x around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate--r+ 82.4%

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

   4. Simplified 82.4%

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

   5. Taylor expanded in y around inf 69.7%

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

      1. neg-mul-1 69.7%

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

   7. Simplified 69.7%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 90000000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+112}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9: 57.7% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

2. Taylor expanded in x around 0 73.9%

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

   1. +-commutative 73.9%

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

   2. associate--r+ 73.9%

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

4. Simplified 73.9%

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

5. Taylor expanded in z around inf 62.1%

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

   1. neg-mul-1 62.1%

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

7. Simplified 62.1%

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

8. Final simplification 62.1%

   \[\leadsto \left(-z\right) - y \]

Alternative 10: 29.9% 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. Taylor expanded in x around 0 73.9%

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

   1. +-commutative 73.9%

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

   2. associate--r+ 73.9%

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

4. Simplified 73.9%

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

5. Taylor expanded in y around inf 34.6%

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

   1. neg-mul-1 34.6%

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

7. Simplified 34.6%

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

8. Final simplification 34.6%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023221 
(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)))