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

Percentage Accurate: 99.9% → 99.9%

Time: 9.7s

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: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[Log[y], $MachinePrecision] + N[((-y) - z), $MachinePrecision]), $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. sub-neg 99.9%

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

   2. associate--l+ 99.9%

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

   3. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(t_1 - y\right) - z\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+14} \lor \neg \left(t_2 \leq 0.5\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\log t + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- t_1 y) z)))
   (if (or (<= t_2 -5e+14) (not (<= t_2 0.5))) t_2 (+ (log t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = (t_1 - y) - z;
	double tmp;
	if ((t_2 <= -5e+14) || !(t_2 <= 0.5)) {
		tmp = t_2;
	} else {
		tmp = log(t) + 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 = (t_1 - y) - z
    if ((t_2 <= (-5d+14)) .or. (.not. (t_2 <= 0.5d0))) then
        tmp = t_2
    else
        tmp = log(t) + 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 = (t_1 - y) - z;
	double tmp;
	if ((t_2 <= -5e+14) || !(t_2 <= 0.5)) {
		tmp = t_2;
	} else {
		tmp = Math.log(t) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = (t_1 - y) - z
	tmp = 0
	if (t_2 <= -5e+14) or not (t_2 <= 0.5):
		tmp = t_2
	else:
		tmp = math.log(t) + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(t_1 - y) - z)
	tmp = 0.0
	if ((t_2 <= -5e+14) || !(t_2 <= 0.5))
		tmp = t_2;
	else
		tmp = Float64(log(t) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = (t_1 - y) - z;
	tmp = 0.0;
	if ((t_2 <= -5e+14) || ~((t_2 <= 0.5)))
		tmp = t_2;
	else
		tmp = log(t) + 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[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+14], N[Not[LessEqual[t$95$2, 0.5]], $MachinePrecision]], t$95$2, N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -5e14 or 0.5 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) 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. Taylor expanded in z around inf 99.7%

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

   if -5e14 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 0.5

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 97.7%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \log y - y\right) - z \leq -5 \cdot 10^{+14} \lor \neg \left(\left(x \cdot \log y - y\right) - z \leq 0.5\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t + x \cdot \log y\\ \end{array} \]

Alternative 3: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y - y\right) - z\\ \mathbf{if}\;t_1 \leq -500000000000 \lor \neg \left(t_1 \leq 0.5\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\log \left(t \cdot {y}^{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (* x (log y)) y) z)))
   (if (or (<= t_1 -500000000000.0) (not (<= t_1 0.5)))
     t_1
     (log (* t (pow y x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * log(y)) - y) - z;
	double tmp;
	if ((t_1 <= -500000000000.0) || !(t_1 <= 0.5)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = ((x * log(y)) - y) - z
    if ((t_1 <= (-500000000000.0d0)) .or. (.not. (t_1 <= 0.5d0))) then
        tmp = t_1
    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 t_1 = ((x * Math.log(y)) - y) - z;
	double tmp;
	if ((t_1 <= -500000000000.0) || !(t_1 <= 0.5)) {
		tmp = t_1;
	} else {
		tmp = Math.log((t * Math.pow(y, x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * math.log(y)) - y) - z
	tmp = 0
	if (t_1 <= -500000000000.0) or not (t_1 <= 0.5):
		tmp = t_1
	else:
		tmp = math.log((t * math.pow(y, x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * log(y)) - y) - z)
	tmp = 0.0
	if ((t_1 <= -500000000000.0) || !(t_1 <= 0.5))
		tmp = t_1;
	else
		tmp = log(Float64(t * (y ^ x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * log(y)) - y) - z;
	tmp = 0.0;
	if ((t_1 <= -500000000000.0) || ~((t_1 <= 0.5)))
		tmp = t_1;
	else
		tmp = log((t * (y ^ x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -500000000000.0], N[Not[LessEqual[t$95$1, 0.5]], $MachinePrecision]], t$95$1, N[Log[N[(t * N[Power[y, x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -5e11 or 0.5 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) 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. Taylor expanded in z around inf 99.6%

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

   if -5e11 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 0.5

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 97.6%

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

   5. Taylor expanded in x around 0 97.6%

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

      1. log-pow 97.6%

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

      2. log-prod 97.6%

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

   7. Simplified 97.6%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \log y - y\right) - z \leq -500000000000 \lor \neg \left(\left(x \cdot \log y - y\right) - z \leq 0.5\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log \left(t \cdot {y}^{x}\right)\\ \end{array} \]

Alternative 4: 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. Final simplification 99.9%

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

Alternative 5: 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. Final simplification 99.9%

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

Alternative 6: 98.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+22} \lor \neg \left(x \leq 1.85 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.55e+22) (not (<= x 1.85e-6)))
   (- (- (* x (log y)) y) z)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.55e+22) || !(x <= 1.85e-6)) {
		tmp = ((x * log(y)) - y) - 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) :: tmp
    if ((x <= (-1.55d+22)) .or. (.not. (x <= 1.85d-6))) then
        tmp = ((x * log(y)) - y) - 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 tmp;
	if ((x <= -1.55e+22) || !(x <= 1.85e-6)) {
		tmp = ((x * Math.log(y)) - y) - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.55e+22) or not (x <= 1.85e-6):
		tmp = ((x * math.log(y)) - y) - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.55e+22) || !(x <= 1.85e-6))
		tmp = Float64(Float64(Float64(x * log(y)) - y) - z);
	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 <= -1.55e+22) || ~((x <= 1.85e-6)))
		tmp = ((x * log(y)) - y) - z;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.55e+22], N[Not[LessEqual[x, 1.85e-6]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5500000000000001e22 or 1.8500000000000001e-6 < 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. Taylor expanded in z around inf 99.5%

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

   if -1.5500000000000001e22 < x < 1.8500000000000001e-6

   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. Taylor expanded in x around 0 99.2%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+22} \lor \neg \left(x \leq 1.85 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 7: 59.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+87} \lor \neg \left(z \leq 6 \cdot 10^{+20}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+87) (not (<= z 6e+20))) (- z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+87) || !(z <= 6e+20)) {
		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 <= (-2.2d+87)) .or. (.not. (z <= 6d+20))) 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 <= -2.2e+87) || !(z <= 6e+20)) {
		tmp = -z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+87) or not (z <= 6e+20):
		tmp = -z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+87) || !(z <= 6e+20))
		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 <= -2.2e+87) || ~((z <= 6e+20)))
		tmp = -z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+87], N[Not[LessEqual[z, 6e+20]], $MachinePrecision]], (-z), N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e87 or 6e20 < 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%

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

      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. Taylor expanded in x around 0 78.1%

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

   5. Taylor expanded in z around inf 65.0%

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

      1. neg-mul-1 65.0%

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

   7. Simplified 65.0%

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

   if -2.2000000000000001e87 < z < 6e20

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. associate--l+ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 64.3%

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

      1. mul-1-neg 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in y around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. sub-neg 64.3%

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

   9. Simplified 64.3%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+87} \lor \neg \left(z \leq 6 \cdot 10^{+20}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]

Alternative 8: 69.7% 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. 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. Taylor expanded in x around 0 71.1%

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

5. Final simplification 71.1%

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

Alternative 9: 47.5% accurate, 34.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+98} \lor \neg \left(z \leq 8.5 \cdot 10^{+20}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.8e+98) (not (<= z 8.5e+20))) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.8e+98) || !(z <= 8.5e+20)) {
		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 ((z <= (-9.8d+98)) .or. (.not. (z <= 8.5d+20))) 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 ((z <= -9.8e+98) || !(z <= 8.5e+20)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.8e+98) or not (z <= 8.5e+20):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.8e+98) || !(z <= 8.5e+20))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.8e+98) || ~((z <= 8.5e+20)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.8e+98], N[Not[LessEqual[z, 8.5e+20]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999958e98 or 8.5e20 < 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%

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

      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. Taylor expanded in x around 0 78.1%

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

   5. Taylor expanded in z around inf 65.0%

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

      1. neg-mul-1 65.0%

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

   7. Simplified 65.0%

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

   if -9.79999999999999958e98 < z < 8.5e20

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. associate--l+ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 64.3%

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

      1. mul-1-neg 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in y around inf 42.6%

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

      1. mul-1-neg 42.6%

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

   9. Simplified 42.6%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+98} \lor \neg \left(z \leq 8.5 \cdot 10^{+20}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 10: 30.0% 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. sub-neg 99.9%

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

   2. associate--l+ 99.9%

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

   3. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around inf 42.3%

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

   1. mul-1-neg 42.3%

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

6. Simplified 42.3%

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

7. Taylor expanded in y around inf 30.0%

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

   1. mul-1-neg 30.0%

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

9. Simplified 30.0%

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

10. Final simplification 30.0%

    \[\leadsto -y \]

Reproduce

herbie shell --seed 2023322 
(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)))