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

Percentage Accurate: 99.9% → 99.9%

Time: 10.2s

Alternatives: 11

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, 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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -3.2 \cdot 10^{+216}:\\ \;\;\;\;t\_2 + \log t\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+48}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log t + \left(t\_1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -3.2e+216)
     (+ t_2 (log t))
     (if (<= t_2 -1e+48) (- (log t) (+ y z)) (+ (log t) (- t_1 z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -3.2e+216) {
		tmp = t_2 + log(t);
	} else if (t_2 <= -1e+48) {
		tmp = log(t) - (y + z);
	} else {
		tmp = log(t) + (t_1 - 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) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-3.2d+216)) then
        tmp = t_2 + log(t)
    else if (t_2 <= (-1d+48)) then
        tmp = log(t) - (y + z)
    else
        tmp = log(t) + (t_1 - 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 t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -3.2e+216) {
		tmp = t_2 + Math.log(t);
	} else if (t_2 <= -1e+48) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = Math.log(t) + (t_1 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -3.2e+216:
		tmp = t_2 + math.log(t)
	elif t_2 <= -1e+48:
		tmp = math.log(t) - (y + z)
	else:
		tmp = math.log(t) + (t_1 - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -3.2e+216)
		tmp = Float64(t_2 + log(t));
	elseif (t_2 <= -1e+48)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(log(t) + Float64(t_1 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -3.2e+216)
		tmp = t_2 + log(t);
	elseif (t_2 <= -1e+48)
		tmp = log(t) - (y + z);
	else
		tmp = log(t) + (t_1 - z);
	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[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -3.2e+216], N[(t$95$2 + N[Log[t], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e+48], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] + N[(t$95$1 - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -3.1999999999999997e216

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 90.3%

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

   if -3.1999999999999997e216 < (-.f64 (*.f64 x (log.f64 y)) y) < -1.00000000000000004e48

   1. Initial program 100.0%

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

      1. add-cbrt-cube 99.9%

         \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

      2. pow3 99.9%

         \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   5. Taylor expanded in x around 0 87.8%

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

   if -1.00000000000000004e48 < (-.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. Add Preprocessing

   3. Taylor expanded in y around 0 95.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -3.2 \cdot 10^{+216}:\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \mathbf{elif}\;x \cdot \log y - y \leq -1 \cdot 10^{+48}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log t + \left(x \cdot \log y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+96} \lor \neg \left(x \leq 2.1 \cdot 10^{+28}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.2e+96) (not (<= x 2.1e+28)))
   (+ (- (* x (log y)) y) (log t))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.2e+96) || !(x <= 2.1e+28)) {
		tmp = ((x * log(y)) - y) + log(t);
	} else {
		tmp = log(t) - (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 ((x <= (-8.2d+96)) .or. (.not. (x <= 2.1d+28))) then
        tmp = ((x * log(y)) - y) + log(t)
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.2e+96) || !(x <= 2.1e+28)) {
		tmp = ((x * Math.log(y)) - y) + Math.log(t);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.2e+96) or not (x <= 2.1e+28):
		tmp = ((x * math.log(y)) - y) + math.log(t)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.2e+96) || !(x <= 2.1e+28))
		tmp = Float64(Float64(Float64(x * log(y)) - y) + log(t));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.2e+96) || ~((x <= 2.1e+28)))
		tmp = ((x * log(y)) - y) + log(t);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.2e+96], N[Not[LessEqual[x, 2.1e+28]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.19999999999999996e96 or 2.09999999999999989e28 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 87.2%

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

   if -8.19999999999999996e96 < x < 2.09999999999999989e28

   1. Initial program 100.0%

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

      1. add-cbrt-cube 100.0%

         \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

      2. pow3 100.0%

         \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   5. Taylor expanded in x around 0 95.3%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+96} \lor \neg \left(x \leq 2.1 \cdot 10^{+28}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+159} \lor \neg \left(x \leq 9.2 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot \log y + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e+159) (not (<= x 9.2e+123)))
   (+ (* x (log y)) (log t))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+159) || !(x <= 9.2e+123)) {
		tmp = (x * log(y)) + log(t);
	} else {
		tmp = log(t) - (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 ((x <= (-7.2d+159)) .or. (.not. (x <= 9.2d+123))) then
        tmp = (x * log(y)) + log(t)
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+159) || !(x <= 9.2e+123)) {
		tmp = (x * Math.log(y)) + Math.log(t);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e+159) or not (x <= 9.2e+123):
		tmp = (x * math.log(y)) + math.log(t)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e+159) || !(x <= 9.2e+123))
		tmp = Float64(Float64(x * log(y)) + log(t));
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e+159) || ~((x <= 9.2e+123)))
		tmp = (x * log(y)) + log(t);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e+159], N[Not[LessEqual[x, 9.2e+123]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.20000000000000073e159 or 9.19999999999999962e123 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 78.4%

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

   if -7.20000000000000073e159 < x < 9.19999999999999962e123

   1. Initial program 100.0%

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

      1. add-cbrt-cube 99.9%

         \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

      2. pow3 100.0%

         \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   5. Taylor expanded in x around 0 90.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+159} \lor \neg \left(x \leq 9.2 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot \log y + \log t\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+232}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(t \cdot {y}^{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 5.8e+232) (- (log t) (+ y z)) (log (* t (pow y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5.8e+232) {
		tmp = log(t) - (y + z);
	} else {
		tmp = log((t * pow(y, x)));
	}
	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 <= 5.8d+232) then
        tmp = log(t) - (y + z)
    else
        tmp = log((t * (y ** x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5.8e+232) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = Math.log((t * Math.pow(y, x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 5.8e+232:
		tmp = math.log(t) - (y + z)
	else:
		tmp = math.log((t * math.pow(y, x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 5.8e+232)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = log(Float64(t * (y ^ x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 5.8e+232)
		tmp = log(t) - (y + z);
	else
		tmp = log((t * (y ^ x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 5.8e+232], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[Log[N[(t * N[Power[y, x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.80000000000000047e232

   1. Initial program 99.9%

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

      1. add-cbrt-cube 99.8%

         \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

      2. pow3 99.8%

         \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   5. Taylor expanded in x around 0 77.1%

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

   if 5.80000000000000047e232 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 99.6%

      \[\leadsto \color{blue}{x \cdot \log y} + \log t \]
   4. Step-by-step derivation

      1. *-un-lft-identity 99.6%

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

      2. +-commutative 99.6%

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

      3. add-log-exp 25.8%

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

      4. sum-log 25.8%

         \[\leadsto 1 \cdot \color{blue}{\log \left(t \cdot e^{x \cdot \log y}\right)} \]

      5. *-commutative 25.8%

         \[\leadsto 1 \cdot \log \left(t \cdot e^{\color{blue}{\log y \cdot x}}\right) \]

      6. exp-to-pow 25.8%

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

   5. Applied egg-rr 25.8%

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

      1. *-lft-identity 25.8%

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

   7. Simplified 25.8%

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

Alternative 6: 59.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+110} \lor \neg \left(z \leq 8 \cdot 10^{+87}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+110) (not (<= z 8e+87))) (- z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+110) || !(z <= 8e+87)) {
		tmp = -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 <= (-8d+110)) .or. (.not. (z <= 8d+87))) then
        tmp = -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 <= -8e+110) || !(z <= 8e+87)) {
		tmp = -z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+110) or not (z <= 8e+87):
		tmp = -z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+110) || !(z <= 8e+87))
		tmp = Float64(-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 <= -8e+110) || ~((z <= 8e+87)))
		tmp = -z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+110], N[Not[LessEqual[z, 8e+87]], $MachinePrecision]], (-z), N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000002e110 or 7.9999999999999997e87 < z

   1. Initial program 99.9%

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

      1. add-cbrt-cube 99.8%

         \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

      2. pow3 99.8%

         \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   5. Taylor expanded in z around inf 66.0%

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

      1. neg-mul-1 66.0%

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

   7. Simplified 66.0%

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

   if -8.0000000000000002e110 < z < 7.9999999999999997e87

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. neg-mul-1 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in y around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. sub-neg 59.0%

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

   8. Simplified 59.0%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+110} \lor \neg \left(z \leq 8 \cdot 10^{+87}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.22 \cdot 10^{+36}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.22e+36) (- (log t) z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.22e+36) {
		tmp = log(t) - 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 (y <= 1.22d+36) then
        tmp = log(t) - 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 (y <= 1.22e+36) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.22e+36:
		tmp = math.log(t) - z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.22e+36)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.22e+36)
		tmp = log(t) - z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.22e+36], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.21999999999999995e36

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 62.9%

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

      1. neg-mul-1 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in z around 0 62.9%

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

      1. neg-mul-1 62.9%

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

      2. sub-neg 62.9%

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

   8. Simplified 62.9%

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

   if 1.21999999999999995e36 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 63.8%

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

      1. neg-mul-1 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. sub-neg 63.8%

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

   8. Simplified 63.8%

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

Alternative 8: 70.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[t], $MachinePrecision] - N[(y + 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. Step-by-step derivation

   1. add-cbrt-cube 99.7%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

   2. pow3 99.8%

      \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

4. Applied egg-rr 99.8%

   \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - y\right) - z\right) + \log t \]

5. Taylor expanded in x around 0 72.4%

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

Alternative 9: 48.3% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+34}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 5.2e+34) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.2e+34) {
		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 <= 5.2d+34) 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 <= 5.2e+34) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 5.2e+34:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 5.2e+34)
		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 <= 5.2e+34)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 5.2e+34], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 5.19999999999999995e34

   1. Initial program 99.8%

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

      1. add-cbrt-cube 99.7%

         \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

      2. pow3 99.7%

         \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   5. Taylor expanded in z around inf 41.3%

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

      1. neg-mul-1 41.3%

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

   7. Simplified 41.3%

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

   if 5.19999999999999995e34 < y

   1. Initial program 99.9%

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

      1. add-cbrt-cube 99.8%

         \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

      2. pow3 99.9%

         \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

   4. Applied egg-rr 99.9%

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

      1. pow1/3 99.6%

         \[\leadsto \left(\left(x \cdot \color{blue}{{\left({\log y}^{3}\right)}^{0.3333333333333333}} - y\right) - z\right) + \log t \]

      2. cube-mult 99.6%

         \[\leadsto \left(\left(x \cdot {\color{blue}{\left(\log y \cdot \left(\log y \cdot \log y\right)\right)}}^{0.3333333333333333} - y\right) - z\right) + \log t \]

      3. unpow-prod-down 99.6%

         \[\leadsto \left(\left(x \cdot \color{blue}{\left({\log y}^{0.3333333333333333} \cdot {\left(\log y \cdot \log y\right)}^{0.3333333333333333}\right)} - y\right) - z\right) + \log t \]

      4. pow1/3 99.8%

         \[\leadsto \left(\left(x \cdot \left(\color{blue}{\sqrt[3]{\log y}} \cdot {\left(\log y \cdot \log y\right)}^{0.3333333333333333}\right) - y\right) - z\right) + \log t \]

      5. pow2 99.8%

         \[\leadsto \left(\left(x \cdot \left(\sqrt[3]{\log y} \cdot {\color{blue}{\left({\log y}^{2}\right)}}^{0.3333333333333333}\right) - y\right) - z\right) + \log t \]

   6. Applied egg-rr 99.8%

      \[\leadsto \left(\left(x \cdot \color{blue}{\left(\sqrt[3]{\log y} \cdot {\left({\log y}^{2}\right)}^{0.3333333333333333}\right)} - y\right) - z\right) + \log t \]
   7. Step-by-step derivation

      1. unpow1/3 99.8%

         \[\leadsto \left(\left(x \cdot \left(\sqrt[3]{\log y} \cdot \color{blue}{\sqrt[3]{{\log y}^{2}}}\right) - y\right) - z\right) + \log t \]

   8. Simplified 99.8%

      \[\leadsto \left(\left(x \cdot \color{blue}{\left(\sqrt[3]{\log y} \cdot \sqrt[3]{{\log y}^{2}}\right)} - y\right) - z\right) + \log t \]

   9. Taylor expanded in y around inf 63.8%

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

       1. mul-1-neg 63.8%

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

   11. Simplified 63.8%

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

Alternative 10: 29.3% 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. Add Preprocessing
3. Step-by-step derivation

   1. add-cbrt-cube 99.7%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

   2. pow3 99.8%

      \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

4. Applied egg-rr 99.8%

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

   1. pow1/3 52.9%

      \[\leadsto \left(\left(x \cdot \color{blue}{{\left({\log y}^{3}\right)}^{0.3333333333333333}} - y\right) - z\right) + \log t \]

   2. cube-mult 52.9%

      \[\leadsto \left(\left(x \cdot {\color{blue}{\left(\log y \cdot \left(\log y \cdot \log y\right)\right)}}^{0.3333333333333333} - y\right) - z\right) + \log t \]

   3. unpow-prod-down 52.9%

      \[\leadsto \left(\left(x \cdot \color{blue}{\left({\log y}^{0.3333333333333333} \cdot {\left(\log y \cdot \log y\right)}^{0.3333333333333333}\right)} - y\right) - z\right) + \log t \]

   4. pow1/3 99.6%

      \[\leadsto \left(\left(x \cdot \left(\color{blue}{\sqrt[3]{\log y}} \cdot {\left(\log y \cdot \log y\right)}^{0.3333333333333333}\right) - y\right) - z\right) + \log t \]

   5. pow2 99.6%

      \[\leadsto \left(\left(x \cdot \left(\sqrt[3]{\log y} \cdot {\color{blue}{\left({\log y}^{2}\right)}}^{0.3333333333333333}\right) - y\right) - z\right) + \log t \]

6. Applied egg-rr 99.6%

   \[\leadsto \left(\left(x \cdot \color{blue}{\left(\sqrt[3]{\log y} \cdot {\left({\log y}^{2}\right)}^{0.3333333333333333}\right)} - y\right) - z\right) + \log t \]
7. Step-by-step derivation

   1. unpow1/3 99.7%

      \[\leadsto \left(\left(x \cdot \left(\sqrt[3]{\log y} \cdot \color{blue}{\sqrt[3]{{\log y}^{2}}}\right) - y\right) - z\right) + \log t \]

8. Simplified 99.7%

   \[\leadsto \left(\left(x \cdot \color{blue}{\left(\sqrt[3]{\log y} \cdot \sqrt[3]{{\log y}^{2}}\right)} - y\right) - z\right) + \log t \]

9. Taylor expanded in y around inf 32.8%

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

    1. mul-1-neg 32.8%

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

11. Simplified 32.8%

    \[\leadsto \color{blue}{-y} \]
12. Add Preprocessing

Alternative 11: 2.3% accurate, 209.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := z

Derivation

1. Initial program 99.9%

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

   1. add-cbrt-cube 99.7%

      \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{\left(\log y \cdot \log y\right) \cdot \log y}} - y\right) - z\right) + \log t \]

   2. pow3 99.8%

      \[\leadsto \left(\left(x \cdot \sqrt[3]{\color{blue}{{\log y}^{3}}} - y\right) - z\right) + \log t \]

4. Applied egg-rr 99.8%

   \[\leadsto \left(\left(x \cdot \color{blue}{\sqrt[3]{{\log y}^{3}}} - y\right) - z\right) + \log t \]

5. Taylor expanded in z around inf 30.5%

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

   1. neg-mul-1 30.5%

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

7. Simplified 30.5%

   \[\leadsto \color{blue}{-z} \]
8. Step-by-step derivation

   1. neg-sub0 30.5%

      \[\leadsto \color{blue}{0 - z} \]

   2. sub-neg 30.5%

      \[\leadsto \color{blue}{0 + \left(-z\right)} \]

   3. add-sqr-sqrt 15.8%

      \[\leadsto 0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   4. sqrt-unprod 7.3%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \]

   5. sqr-neg 7.3%

      \[\leadsto 0 + \sqrt{\color{blue}{z \cdot z}} \]

   6. sqrt-unprod 0.9%

      \[\leadsto 0 + \color{blue}{\sqrt{z} \cdot \sqrt{z}} \]

   7. add-sqr-sqrt 2.3%

      \[\leadsto 0 + \color{blue}{z} \]

9. Applied egg-rr 2.3%

   \[\leadsto \color{blue}{0 + z} \]
10. Step-by-step derivation

    1. +-lft-identity 2.3%

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

11. Simplified 2.3%

    \[\leadsto \color{blue}{z} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(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)))